Date post: | 06-Mar-2018 |
Category: |
Documents |
Upload: | doankhuong |
View: | 222 times |
Download: | 5 times |
7182005 Summerschool Bertinoro17-23 July 2005
copy PC Breedveld1
Control Engineering Laboratory
PORT-BASED MODELING OF DYNAMIC SYSTEMS
fundamental concepts and bond graphs
PORT-BASED MODELING OF DYNAMIC SYSTEMS
fundamental concepts and bond graphs
Peter BreedveldPeter Breedveld
Control Engineering Laboratory Faculty of Electrical Engineering Mathematics and Computer ScienceUniversity of Twente Netherlands
pcbreedveldutwentenl
Some remarksSome remarks
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (2)
bullbull Role of concepts (lsquointellectrsquo multiple views)Role of concepts (lsquointellectrsquo multiple views)bullbull Ports from a historical energy point of viewPorts from a historical energy point of view
(energy states)(energy states)bullbull Focus on linear motion and fixed axis rotation Focus on linear motion and fixed axis rotation
simple configuration constraints no need for simple configuration constraints no need for abstract geometrical concepts (like in the rest of abstract geometrical concepts (like in the rest of the course)the course)
bullbull Separation between configuration state and energy Separation between configuration state and energy statestatestructures influence of kinematic constraintsstructures influence of kinematic constraints
General OutlineGeneral Outline
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (3)
bullbull Background and historyBackground and historybullbull Introduction to ports bonds and Introduction to ports bonds and
physical domainsphysical domainsbullbull Introduction to bond graph modelingIntroduction to bond graph modeling
causality domaincausality domain--independence etcindependence etc
Assumed prerequisitesAssumed prerequisites
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (4)
bullbull Some experience inSome experience inndashndash Block diagram modelsBlock diagram modelsndashndash Numerical simulation (methods)Numerical simulation (methods)ndashndash Linear and nonlinear analysisLinear and nonlinear analysisndashndash Basic physics (electrical circuits simple Basic physics (electrical circuits simple
rigid body mechanisms principles of rigid body mechanisms principles of thermodynamics etcthermodynamics etc
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (5)
ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)
bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements
ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
Some remarksSome remarks
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (2)
bullbull Role of concepts (lsquointellectrsquo multiple views)Role of concepts (lsquointellectrsquo multiple views)bullbull Ports from a historical energy point of viewPorts from a historical energy point of view
(energy states)(energy states)bullbull Focus on linear motion and fixed axis rotation Focus on linear motion and fixed axis rotation
simple configuration constraints no need for simple configuration constraints no need for abstract geometrical concepts (like in the rest of abstract geometrical concepts (like in the rest of the course)the course)
bullbull Separation between configuration state and energy Separation between configuration state and energy statestatestructures influence of kinematic constraintsstructures influence of kinematic constraints
General OutlineGeneral Outline
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (3)
bullbull Background and historyBackground and historybullbull Introduction to ports bonds and Introduction to ports bonds and
physical domainsphysical domainsbullbull Introduction to bond graph modelingIntroduction to bond graph modeling
causality domaincausality domain--independence etcindependence etc
Assumed prerequisitesAssumed prerequisites
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (4)
bullbull Some experience inSome experience inndashndash Block diagram modelsBlock diagram modelsndashndash Numerical simulation (methods)Numerical simulation (methods)ndashndash Linear and nonlinear analysisLinear and nonlinear analysisndashndash Basic physics (electrical circuits simple Basic physics (electrical circuits simple
rigid body mechanisms principles of rigid body mechanisms principles of thermodynamics etcthermodynamics etc
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (5)
ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)
bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements
ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
General OutlineGeneral Outline
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (3)
bullbull Background and historyBackground and historybullbull Introduction to ports bonds and Introduction to ports bonds and
physical domainsphysical domainsbullbull Introduction to bond graph modelingIntroduction to bond graph modeling
causality domaincausality domain--independence etcindependence etc
Assumed prerequisitesAssumed prerequisites
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (4)
bullbull Some experience inSome experience inndashndash Block diagram modelsBlock diagram modelsndashndash Numerical simulation (methods)Numerical simulation (methods)ndashndash Linear and nonlinear analysisLinear and nonlinear analysisndashndash Basic physics (electrical circuits simple Basic physics (electrical circuits simple
rigid body mechanisms principles of rigid body mechanisms principles of thermodynamics etcthermodynamics etc
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (5)
ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)
bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements
ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
Assumed prerequisitesAssumed prerequisites
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (4)
bullbull Some experience inSome experience inndashndash Block diagram modelsBlock diagram modelsndashndash Numerical simulation (methods)Numerical simulation (methods)ndashndash Linear and nonlinear analysisLinear and nonlinear analysisndashndash Basic physics (electrical circuits simple Basic physics (electrical circuits simple
rigid body mechanisms principles of rigid body mechanisms principles of thermodynamics etcthermodynamics etc
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (5)
ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)
bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements
ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (5)
ndashndash Modular modeling (prevailing trend in Modular modeling (prevailing trend in modeling and simulation of complex modeling and simulation of complex physical systems)physical systems)
bullbull represented as a network interconnection of represented as a network interconnection of ideal elementsideal elements
ndashndash AdvantagesAdvantagesbullbull flexibilityflexibilitybullbull rere--usability of model partsusability of model partsbullbull physical insightphysical insightbullbull support for automated modelingsupport for automated modelingbullbull fundamental to systems and control theoryfundamental to systems and control theory
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
IntroductionIntroduction
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (6)
ndashndash DisadvantagesDisadvantagesbullbull equations of motion obtained directly from equations of motion obtained directly from
network modeling are oftennetwork modeling are oftenndashndash complicatedcomplicatedndashndash without apparent structurewithout apparent structurendashndash will easily contain will easily contain algebraic constraintsalgebraic constraints arising arising
from the interconnection of the subfrom the interconnection of the sub--systemssystemsbullbull no problem for digital simulation butno problem for digital simulation butbullbull may not be very wellmay not be very well--suited to analysis and suited to analysis and
control purposes (nonlinear systems)control purposes (nonlinear systems)
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (7)
ndashndash particular type of network modeling viz particular type of network modeling viz portport--based modelingbased modeling
bullbull subsub--systems are interacting through power systems are interacting through power exchange represented by pairs of exchange represented by pairs of conjugated variablesconjugated variables
bullbull unified way to deal with systems from unified way to deal with systems from different physical domains (eg mechanical different physical domains (eg mechanical and electrical) and electrical)
bullbull resulting systems of equations possess an resulting systems of equations possess an underlying generalized Hamiltonian underlying generalized Hamiltonian structure leading to the geometric notion of structure leading to the geometric notion of a porta port--Hamiltonian systemHamiltonian system
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
Course objectivesCourse objectives
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (8)
bullbull exploiting the underlying Hamiltonian exploiting the underlying Hamiltonian structure offers many possibilities forstructure offers many possibilities for
ndashndash analysisanalysisndashndash simulationsimulationndashndash controlcontrol
of complex physical systemsof complex physical systemsbullbull illustrated in variety of application areasillustrated in variety of application areasbullbull possible extension to classes of possible extension to classes of
distributeddistributed--parameter systemsparameter systems
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (9)
AppetizerNewton cradle example
AppetizerNewton cradle example
bullbull ExperimentExperiment
bullbull 2020--sim sim demdemoobullbull AnimationAnimation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (10)
Dual role exampleFalling and bouncing object
Dual role exampleFalling and bouncing object
bullbull generally considered as conceptually generally considered as conceptually complexcomplexndashndash switching models switching models reinitializationreinitialization timing timingndashndash energy bookkeepingenergy bookkeepingndashndash prone to sign errorsprone to sign errors
bullbull portport--based approach with explicit based approach with explicit structure allows conceptually simple structure allows conceptually simple solutionsolution
AimAim
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (11)
bullbull System theoretic approach to physical system dynamics System theoretic approach to physical system dynamics based onbased onndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull shown how as a resultshown how as a resultndashndash variables and relations describing physical systems may be variables and relations describing physical systems may be
classifiedclassifiedndashndash models may be organized as (lsquoportmodels may be organized as (lsquoport--based approachrsquo)based approachrsquo)
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a a
generalized networkgeneralized networkndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy gy
and entropyand entropybullbull special attentionspecial attention
ndashndash role of analogiesrole of analogiesndashndash analogue behavioranalogue behavior
Fundamental issuesFundamental issues
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (12)
bull introduction amp some philosophybull Why physical systems modelingbull What is physical systems modelingbull Context of explanation (focus of engineering
physics) versus justification (focus of math)bull elements and components theory buildingbull synthesis between classical approaches
bull choice of variablesndashndash mechanical versus thermodynamic mechanical versus thermodynamic
frameworkframework
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (13)
lsquoWhyrsquoThree-world meta-model
lsquoWhyrsquoThree-world meta-model
bullbull Real worldReal world (assuming existence of (assuming existence of lsquolsquoobjectiveobjectiversquorsquoenvironmentenvironmentrsquorsquo))
bullbull Conceptual worldConceptual world (in our brain)(in our brain)bullbull lsquolsquoPaperPaperrsquorsquo worldworld including electronically stored including electronically stored
datadata
ndashndash Only invia the paper worldOnly invia the paper worldbullbull CommunicationCommunicationbullbull SupportSupportbullbull SystematizationSystematization
ndashndash exchangeable abstractionsconcepts gtgtgtexchangeable abstractionsconcepts gtgtgtndashndash importance of importance of symbolssymbols amp amp notation notation (representation)(representation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (14)
lsquoWhyrsquoAre physical concepts lsquorealrsquo
lsquoWhyrsquoAre physical concepts lsquorealrsquo
bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip
bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation
YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
AimAim
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (11)
bullbull System theoretic approach to physical system dynamics System theoretic approach to physical system dynamics based onbased onndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull shown how as a resultshown how as a resultndashndash variables and relations describing physical systems may be variables and relations describing physical systems may be
classifiedclassifiedndashndash models may be organized as (lsquoportmodels may be organized as (lsquoport--based approachrsquo)based approachrsquo)
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a a
generalized networkgeneralized networkndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy gy
and entropyand entropybullbull special attentionspecial attention
ndashndash role of analogiesrole of analogiesndashndash analogue behavioranalogue behavior
Fundamental issuesFundamental issues
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (12)
bull introduction amp some philosophybull Why physical systems modelingbull What is physical systems modelingbull Context of explanation (focus of engineering
physics) versus justification (focus of math)bull elements and components theory buildingbull synthesis between classical approaches
bull choice of variablesndashndash mechanical versus thermodynamic mechanical versus thermodynamic
frameworkframework
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (13)
lsquoWhyrsquoThree-world meta-model
lsquoWhyrsquoThree-world meta-model
bullbull Real worldReal world (assuming existence of (assuming existence of lsquolsquoobjectiveobjectiversquorsquoenvironmentenvironmentrsquorsquo))
bullbull Conceptual worldConceptual world (in our brain)(in our brain)bullbull lsquolsquoPaperPaperrsquorsquo worldworld including electronically stored including electronically stored
datadata
ndashndash Only invia the paper worldOnly invia the paper worldbullbull CommunicationCommunicationbullbull SupportSupportbullbull SystematizationSystematization
ndashndash exchangeable abstractionsconcepts gtgtgtexchangeable abstractionsconcepts gtgtgtndashndash importance of importance of symbolssymbols amp amp notation notation (representation)(representation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (14)
lsquoWhyrsquoAre physical concepts lsquorealrsquo
lsquoWhyrsquoAre physical concepts lsquorealrsquo
bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip
bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation
YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Fundamental issuesFundamental issues
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (12)
bull introduction amp some philosophybull Why physical systems modelingbull What is physical systems modelingbull Context of explanation (focus of engineering
physics) versus justification (focus of math)bull elements and components theory buildingbull synthesis between classical approaches
bull choice of variablesndashndash mechanical versus thermodynamic mechanical versus thermodynamic
frameworkframework
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (13)
lsquoWhyrsquoThree-world meta-model
lsquoWhyrsquoThree-world meta-model
bullbull Real worldReal world (assuming existence of (assuming existence of lsquolsquoobjectiveobjectiversquorsquoenvironmentenvironmentrsquorsquo))
bullbull Conceptual worldConceptual world (in our brain)(in our brain)bullbull lsquolsquoPaperPaperrsquorsquo worldworld including electronically stored including electronically stored
datadata
ndashndash Only invia the paper worldOnly invia the paper worldbullbull CommunicationCommunicationbullbull SupportSupportbullbull SystematizationSystematization
ndashndash exchangeable abstractionsconcepts gtgtgtexchangeable abstractionsconcepts gtgtgtndashndash importance of importance of symbolssymbols amp amp notation notation (representation)(representation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (14)
lsquoWhyrsquoAre physical concepts lsquorealrsquo
lsquoWhyrsquoAre physical concepts lsquorealrsquo
bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip
bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation
YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (13)
lsquoWhyrsquoThree-world meta-model
lsquoWhyrsquoThree-world meta-model
bullbull Real worldReal world (assuming existence of (assuming existence of lsquolsquoobjectiveobjectiversquorsquoenvironmentenvironmentrsquorsquo))
bullbull Conceptual worldConceptual world (in our brain)(in our brain)bullbull lsquolsquoPaperPaperrsquorsquo worldworld including electronically stored including electronically stored
datadata
ndashndash Only invia the paper worldOnly invia the paper worldbullbull CommunicationCommunicationbullbull SupportSupportbullbull SystematizationSystematization
ndashndash exchangeable abstractionsconcepts gtgtgtexchangeable abstractionsconcepts gtgtgtndashndash importance of importance of symbolssymbols amp amp notation notation (representation)(representation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (14)
lsquoWhyrsquoAre physical concepts lsquorealrsquo
lsquoWhyrsquoAre physical concepts lsquorealrsquo
bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip
bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation
YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (14)
lsquoWhyrsquoAre physical concepts lsquorealrsquo
lsquoWhyrsquoAre physical concepts lsquorealrsquo
bullbull For exampleFor examplendashndash energy time momentum causalityhellipenergy time momentum causalityhellip
bullbull In a context of In a context of justificationjustification NONObullbull In a context of In a context of discoverydiscoveryexplanationexplanation
YES YES but rather lsquoreally usefulrsquo than but rather lsquoreally usefulrsquo than just lsquorealrsquojust lsquorealrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (15)
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
lsquoWhyrsquoThe useless lsquoquest for truthrsquo
bullbull A model is necessarily A model is necessarily incompleteincompletelsquolsquoall models are wrongall models are wrongrsquorsquo but but lsquolsquotruthtruthrsquorsquo is is notnot
what countswhat countsbullbull The issue is whether a model is The issue is whether a model is
competentcompetent (to solve a problem in a (to solve a problem in a given given problem contextproblem context in the most in the most generic sense of the word)generic sense of the word)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
What is a modelWhat is a model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (16)
Some sort of abstraction Some sort of abstraction (in the (in the lsquolsquopaperpaperrsquorsquo world)world) that enablesthat enablesbullbull insight insight in in the real world counterpartthe real world counterpartbullbull communicationcommunication about about the real world counterpartthe real world counterpartbullbull observationobservation of of the real world counterpartthe real world counterpartbullbull troubleshootingtroubleshooting of of the real world counterpartthe real world counterpartbullbull designdesign of new aspects related to the real world counterpartof new aspects related to the real world counterpartbullbull modificationsmodifications of of the real world counterpartthe real world counterpartbullbull lsquolsquoexplanationexplanationrsquorsquo of of functionalityfunctionality of the real world counterpartof the real world counterpartbullbull measurementmeasurement of of the real world counterpartthe real world counterpart
but most importantly that is but most importantly that is bullbull competentcompetent to solve a given problem and make decisions to solve a given problem and make decisions
related to the real worldrelated to the real world
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
ModelingModeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (17)
bull Given a specific problem context the decision process to obtain a competent model to solve this problem
bull Approaches between two extremesndashndash a priori knowledgea priori knowledgendashndash lsquolsquoblack boxblack boxrsquorsquo (also an axiomatic concept with a priori (also an axiomatic concept with a priori
assumptions)assumptions)bullbull concept concept lsquolsquoinputinputrsquorsquo implicitly contains model of imposing some implicitly contains model of imposing some
action with negligible back effect (action with negligible back effect (lsquolsquohigh input impedancehigh input impedancersquorsquo))bullbull concept concept lsquolsquooutputoutputrsquorsquo implicitly contains model of measurement implicitly contains model of measurement
with negligible effect on the system being observed (with negligible effect on the system being observed (lsquolsquolow low output impedanceoutput impedancersquorsquo))
bullbull after a competent inputafter a competent input--output relation is found it is not output relation is found it is not open for modifications or physical interpretationopen for modifications or physical interpretation
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
lsquoSpecialrsquo stateslsquoSpecialrsquo states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (18)
PositiondisplacementPositiondisplacementbullbull has a has a dualdual naturenature
ndashndash energyenergy state (related to a conservation or symmetry principle state (related to a conservation or symmetry principle like all other states)like all other states)
ndashndash configurationconfiguration statestatebullbull does does notnot transform as a transform as a tensortensorMatterMatterbullbull convectsconvects all matterall matter--bound properties (not volume)bound properties (not volume)bullbull conjugate intensity depends on other intensitiesconjugate intensity depends on other intensitiesbullbull boundary criterionboundary criterionVolumeVolumebullbull boundary criterionboundary criterionEntropyEntropybullbull can be lsquolocallyrsquo can be lsquolocallyrsquo producedproduced (only lsquolocallyrsquo conserved) (only lsquolocallyrsquo conserved)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Model representationModel representation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (19)
bullbull model model representationrepresentationndashndash symbols used to representsymbols used to represent
bullbull the the conceptsconcepts being usedbeing usedbullbull (the structure of) their (the structure of) their relationsrelations (interconnection)(interconnection)
bullbull model model manipulationmanipulation (as opposed to modeling) (as opposed to modeling) ndashndash transformation to transformation to differentdifferent representations (including representations (including
the the lsquolsquosolutionsolutionrsquorsquo) to) tobullbull increase insightincrease insightbullbull draw conclusions etcdraw conclusions etc
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Role of representationsRole of representations
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (20)
Process timeProcess timeversusversus
processprocessinging timetime
A
A
A
A
A
T
T
T
T
T
a
b
c
d
e
x1
x2
x3
x4
x5
SequentialSequential
A
T
T
A
x
t
x1 x5x4
x3x2
SimultaneousSimultaneous
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
What are we trying to describeWhat are we trying to describe
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (21)
bullbull (dynamic) behavior(dynamic) behaviorbullbull engineering systemsengineering systemsbullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic models of systems that obey models of systems that obey basic basic principlesprinciples of of macroscopicmacroscopic physicsphysics
bullbull energyenergy conservationconservation ((lsquolsquofirst lawfirst lawrsquorsquo))bullbull positive positive entropyentropy productionproduction ((lsquolsquosecond lawsecond lawrsquorsquo))
bullbull that describe the temporal trajectory of the that describe the temporal trajectory of the common physical propertiescommon physical propertiesndashndash mechanical (incl hydraulic and pneumatic) mechanical (incl hydraulic and pneumatic)
electrical magnetic electrical magnetic chemical material thermalchemical material thermal etc gtgtgt multidomainetc gtgtgt multidomain
ndashndash configurationconfiguration
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Physical systems modelingPhysical systems modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (22)
bullbull all concepts used in the model are or have a direct relation all concepts used in the model are or have a direct relation to to physically relevant conceptsphysically relevant concepts (use of a priori knowledge)(use of a priori knowledge)
bullbull physicalphysical relationsrelations are maintained as much as possibleare maintained as much as possiblebullbull herein constrained to (for sake of herein constrained to (for sake of lsquolsquosimplicitysimplicityrsquorsquo))
ndashndash deterministicdeterministic mathematical models of mathematical models of macroscopicmacroscopic systems systems thatthat
bullbull obey obey basic principlesbasic principles of macroscopic physicsof macroscopic physicsndashndash energyenergy conservationconservationndashndash positive positive entropyentropy productionproduction
bullbull describe the describe the behaviorbehavior in time of the common physical propertiesin time of the common physical propertiesndashndash mechanical (incl hydraulic and pneumatic)mechanical (incl hydraulic and pneumatic)ndashndash electricalelectricalndashndash magneticmagneticndashndash chemicalchemicalndashndash materialmaterial
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
time amp uncertaintytime amp uncertainty
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (23)
bullbull timetimendashndash derivedderived measure for lsquomeasure for lsquoregularityregularityrsquo based on rsquo based on
counting lsquoticksrsquo of a lsquotimecounting lsquoticksrsquo of a lsquotime--basersquo based on basersquo based on repetitive behaviorrepetitive behavior requiringrequiring statestate and and change change (in (in order to be able to count)order to be able to count)
ndashndash within the smallest unit used necessarily within the smallest unit used necessarily uncertainty uncertainty
bullbull cf Heisenberg ur for displacement (= elastic state cf Heisenberg ur for displacement (= elastic state kinetic state of change) and momentum (= elastic state kinetic state of change) and momentum (= elastic state of change kinetic state)of change kinetic state)
ndashndash dialectic conceptsdialectic concepts
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (24)
concepts oflsquostatersquo amp lsquochangersquo
concepts oflsquostatersquo amp lsquochangersquo
bullbull dialecticdialectic fundamental conceptsfundamental conceptsbullbull basis for any basis for any dynamicdynamic model (more model (more
than time)than time)bullbull within a within a context of discoverycontext of discovery a shift to a shift to
spacespace--time is understandable and time is understandable and useful like the shift from positionuseful like the shift from position--momentum in Hamiltonian mechanics to momentum in Hamiltonian mechanics to positionposition--velocity in Lagrangian velocity in Lagrangian mechanicsmechanics
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Contents of the sequelContents of the sequel
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (25)
bullbull Modeling pitfallsModeling pitfallsbullbull PortPort--based modeling based modeling bullbull Basic Concepts (ports bonds)Basic Concepts (ports bonds)bullbull Dynamic conjugation (effort flow)Dynamic conjugation (effort flow)bullbull Multidomain modeling and the role of Multidomain modeling and the role of
energyenergybullbull (Computational) Causality(Computational) Causality
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Modeling pitfallsModeling pitfalls
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (26)
bullbull lsquolsquoEvery model is wrongrsquoEvery model is wrongrsquo
bullbull Model depends on problem contextModel depends on problem context
bullbull Competent modelsCompetent models
bullbull Analogies are not identitiesAnalogies are not identities
bullbull Avoid implicit assumptionsAvoid implicit assumptions
bullbull Avoid model extrapolationAvoid model extrapolation
bullbull Confusion of components with elementsConfusion of components with elements
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
Port-based modelingPort-based modeling
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (27)
bullbull multidomainmultidomain approachapproachndashndash lsquomechatronicsrsquo (and beyond)lsquomechatronicsrsquo (and beyond)
bullbull multiple viewmultiple view approach other graphical approach other graphical representations iconic diagrams (linear representations iconic diagrams (linear graphs) block diagrams graphs) block diagrams bond graphsbond graphs etc and etc and equationsequations
bullbull domain independentdomain independent notation using portsnotation using portsndashndash bond graphs (amp some other benefitshellip)bond graphs (amp some other benefitshellip)
bullbull portport--basedbased approachapproachndashndash underlying structure of underlying structure of 2020--simsim ideal tool for ideal tool for
demonstrationdemonstrationbullbull what are what are portsports and what are and what are bond graphsbond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (28)
Physical components versus ideal elements
Physical components versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (29)
Physical component versus ideal elements
Physical component versus ideal elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (30)
Physical component versus ideal elements
Physical component versus ideal elements
Component mounterComponent mounter
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (31)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (32)
Physical components versus conceptual elements
Physical components versus conceptual elements
physical componentphysical componentpiece of rubber hosepiece of rubber hose
dominant behaviordominant behaviorbullbullwhen falling when falling ideal massideal massbullbullwhen pulling load when pulling load ideal springideal springbullbullfor vibration isolation for vibration isolation ideal resistorideal resistorbullbulletcetc
lsquoParasiticrsquo elementslsquoParasiticrsquo elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (33)
bullbull Next to dominant behaviorNext to dominant behavior
In engineering modelsIn engineering models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (34)
bullbull Avoid implicit assumptions eg aboutAvoid implicit assumptions eg aboutndashndash problem contextproblem context
ndashndash referencereference
ndashndash orientationorientation
ndashndash coordinatescoordinates
ndashndash metricmetric
ndashndash lsquonegligiblersquo phenomena etclsquonegligiblersquo phenomena etc
bullbull Avoid model extrapolationAvoid model extrapolationndashndash danger of ignoring earlier assumptionsdanger of ignoring earlier assumptions
bullbull Focus at competence not lsquotruthrsquoFocus at competence not lsquotruthrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (35)
Intuitive introduction of the lsquoportrsquo concept
Intuitive introduction of the lsquoportrsquo concept
ideal ideal motormotor
J
ideal ideal inertiainertiaideal ideal
transmissiontransmission
ideal current ideal current sourcesource
P
potentiometerpotentiometer
Dominant behaviorDominant behavior
(not necessarily competent in each context)(not necessarily competent in each context)
Simple modelSimple model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (36)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
lsquoParasiticrsquo elementslsquoParasiticrsquo elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (33)
bullbull Next to dominant behaviorNext to dominant behavior
In engineering modelsIn engineering models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (34)
bullbull Avoid implicit assumptions eg aboutAvoid implicit assumptions eg aboutndashndash problem contextproblem context
ndashndash referencereference
ndashndash orientationorientation
ndashndash coordinatescoordinates
ndashndash metricmetric
ndashndash lsquonegligiblersquo phenomena etclsquonegligiblersquo phenomena etc
bullbull Avoid model extrapolationAvoid model extrapolationndashndash danger of ignoring earlier assumptionsdanger of ignoring earlier assumptions
bullbull Focus at competence not lsquotruthrsquoFocus at competence not lsquotruthrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (35)
Intuitive introduction of the lsquoportrsquo concept
Intuitive introduction of the lsquoportrsquo concept
ideal ideal motormotor
J
ideal ideal inertiainertiaideal ideal
transmissiontransmission
ideal current ideal current sourcesource
P
potentiometerpotentiometer
Dominant behaviorDominant behavior
(not necessarily competent in each context)(not necessarily competent in each context)
Simple modelSimple model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (36)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
In engineering modelsIn engineering models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (34)
bullbull Avoid implicit assumptions eg aboutAvoid implicit assumptions eg aboutndashndash problem contextproblem context
ndashndash referencereference
ndashndash orientationorientation
ndashndash coordinatescoordinates
ndashndash metricmetric
ndashndash lsquonegligiblersquo phenomena etclsquonegligiblersquo phenomena etc
bullbull Avoid model extrapolationAvoid model extrapolationndashndash danger of ignoring earlier assumptionsdanger of ignoring earlier assumptions
bullbull Focus at competence not lsquotruthrsquoFocus at competence not lsquotruthrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (35)
Intuitive introduction of the lsquoportrsquo concept
Intuitive introduction of the lsquoportrsquo concept
ideal ideal motormotor
J
ideal ideal inertiainertiaideal ideal
transmissiontransmission
ideal current ideal current sourcesource
P
potentiometerpotentiometer
Dominant behaviorDominant behavior
(not necessarily competent in each context)(not necessarily competent in each context)
Simple modelSimple model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (36)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (35)
Intuitive introduction of the lsquoportrsquo concept
Intuitive introduction of the lsquoportrsquo concept
ideal ideal motormotor
J
ideal ideal inertiainertiaideal ideal
transmissiontransmission
ideal current ideal current sourcesource
P
potentiometerpotentiometer
Dominant behaviorDominant behavior
(not necessarily competent in each context)(not necessarily competent in each context)
Simple modelSimple model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (36)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Simple modelSimple model
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (36)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (37)
Addition of relevant parasitic behavior
Addition of relevant parasitic behavior
Depending on Depending on problem problem contextcontext
Polymorphic Polymorphic modelingmodeling
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
What are portsWhat are ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (38)
MECH
J
ii∆∆uu11
ii ii
∆∆uu22 ∆∆uu33∆∆TT22 ∆∆TT33
ωω ωω
PP ==∆∆uusdotsdot ii(power)(power)
PP ==∆∆TTsdotsdotωω(power)(power)
ii∆∆uu44
∆∆TT11
ωω
electrical portselectrical ports
mechanical portsmechanical ports
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (39)
Comparison with familiar model views
Comparison with familiar model views
Iconic diagramsIconic diagrams(lsquoideal physical modelsrsquo)(lsquoideal physical modelsrsquo)
R L
C
R
K=1CFext
Usource
i v
F m
electricalelectrical mechanicalmechanical
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (40)
Port-based but domain dependentPortPort--based but based but domain dependentdomain dependent
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Iconic diagram symbolsIconic diagram symbols
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (41)
C-type storage
I -type storage
(M)R (dissipation
irreversible transduction)
Se (effort source)
Sf (flow source)
TF (transformer)
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Iconic diagramsIconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (42)
bullbull Icons do not (always) represent Icons do not (always) represent physical structurephysical structure
1
i
2020--simsim
iconicon
TF (transformer)TF (transformer)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (43)
Common block diagram models
Common block diagram models
R L
C
R
K=1CFext
Usource
i v
F m
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (44)
Common block diagram models
Common block diagram models
Note not all signals Note not all signals are physically are physically
meaningful variablesmeaningful variables
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (45)
R L
C
R
K=1CFext
Usource
i v
F m
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Ports in iconic diagramsPorts in iconic diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (46)
R L
C
R
K=1C
Fext
Usource
i
v
F
m
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Ports in block diagramsPorts in block diagrams
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (47)
Note each signal is a physically Note each signal is a physically meaningful variablemeaningful variable
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Structure as multiportStructure as multiport
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (48)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (49)
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Different formsDifferent forms
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (50)
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (51)
Source
Coil
Capacitor
Resistor
Source
Mass
Spring
Damper
Domain dependent
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Compact amp domain independentCompact amp domain independent
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (52)
I
C
R
Se
I
C
R
1Se
Domain independent
1
Structure explicitlyStructure explicitly
representedrepresented
as multiportas multiport
JUNCTIONJUNCTION
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Ports in bond graph viewPorts in bond graph view
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (53)
C
R
Se
I
1
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Bond graphsBond graphs
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (54)
Inventor (MIT 1959) Prof Henry M Paynter (1923-2002)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (55)
Analog simulation withOP-AMPS
Analog simulation withOP-AMPS
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (56)
BondsBonds
Energy exchange = powerEnergy exchange = power
Storage of kinetic energyStorage of kinetic energyStorage of elastic energyStorage of elastic energy
C ICompact notationCompact notation
bullbullTerminology and notation induced by chemical bondsTerminology and notation induced by chemical bonds
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Ports and power bondsPorts and power bonds
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (57)
bullbull (power) bond connecting two elements (power) bond connecting two elements via (power) ports (Harold Wheeler via (power) ports (Harold Wheeler 1949)1949)
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
mass-spring systemmass-spring system
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (58)
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Dynamic conjugationDynamic conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (59)
bullbull Between signals of bilateral signal Between signals of bilateral signal flow of relationflow of relationndashndash rate of change lsquoflowrsquo (zero in rate of change lsquoflowrsquo (zero in
equilibrium)equilibrium)bullbull eg molar rate during diffusioneg molar rate during diffusion
ndashndash equilibrium determining variable lsquoeffortrsquoequilibrium determining variable lsquoeffortrsquobullbull eg concentrationeg concentration
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Power conjugationPower conjugation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (60)
= special case of dynamic conjugation = special case of dynamic conjugation ndashndash lsquoeffortrsquo and lsquoflowrsquo relate to lsquoeffortrsquo and lsquoflowrsquo relate to powerpowerndashndash functional relation is commonly a functional relation is commonly a productproduct
ndashndash sumsum in case of scattering variablesin case of scattering variables
part part= = + = +
part part
part= =
partpart
= =part
sum sum sum sumddd
d d d
d effort
d
d flow
d
jii i j j
i ji j i j
ji j
i
ii j
j
pqE E EP e f e f
t q t p t
pEe e
q t
q Ef f
t p
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (61)
Conjugate variables amp corresponding statesConjugate variables amp corresponding states
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (62)
Basic dynamic behaviorsamp mnemonic codes
Basic dynamic behaviorsamp mnemonic codes
bullbull StorageStorage (reversible)(reversible)ndashndash CC I (qI (q--type and ptype and p--type storage) type storage)
bullbull Irreversible transformationIrreversible transformation (lsquodissipationrsquo)(lsquodissipationrsquo)ndashndash (M)(M)RR(S)(S)
bullbull DistributionDistributionndashndash 00--junction junction 11--junctionjunction
bullbull Supply and demandSupply and demandndashndash (M)(M)SeSe ( (M)M)SfSf
bullbull Reversible transformationReversible transformationndashndash (M)(M)TFTF (M) (M)GYGY
bullbull gtgt gtgt 9 basic elements9 basic elements
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Orientation conventionsOrientation conventions
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (63)
bullbull 11--ports into most elements (R C I) except ports into most elements (R C I) except sources (Se sources (Se SfSf))
bullbull 22--port transducers 1 in 1 outport transducers 1 in 1 outbullbull junction structure elements arbitraryjunction structure elements arbitrarybullbull multiport generalizations same as simple formmultiport generalizations same as simple formbullbull MOST IMPORTANT obeying grammar rules MOST IMPORTANT obeying grammar rules
minimizes sign errorsminimizes sign errors
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (64)
Convention on effort and flow positions
Convention on effort and flow positions
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Basic one-port elementsBasic one-port elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (65)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (66)
Basic two- and multiport elements
Basic two- and multiport elements
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (67)
Constitutive relations not necessarily linear
Constitutive relations not necessarily linear
eg zener diodeeg zener diodedominant behaviordominant behavior
irreversible irreversible transduction transduction (resistor)(resistor)
with nonlinear with nonlinear constitutive relationconstitutive relation
R
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (68)
Other form of non-linearityModulation
Other form of non-linearityModulation
eg modulation of a transducereg modulation of a transducer iconic diagram (IPM)iconic diagram (IPM)
MR
capstancapstan
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (69)
Bilateral signal flow (computational causality)
Bilateral signal flow (computational causality)
2 possibilities2 possibilities
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
NotationNotation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (70)
Causal strokeCausal stroke
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (71)
C
R
Se
I
1
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Back to the exampleBack to the example
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (72)
C
R
Se
I
1
2020--sim demosim demo
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Causal port propertiesCausal port properties
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (73)
bullbull FixedFixed causalitycausality
bullbull PreferredPreferred (integral) causality(integral) causality
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Causal constraintsCausal constraints
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (74)
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Arbitrary causalityArbitrary causality
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (75)
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Causality assignmentCausality assignment
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (76)
Algorithmic (SCAP)Algorithmic (SCAP)ndashndash 1) fixed causal ports with propagation via 1) fixed causal ports with propagation via
constraintsconstraintscausal lsquoconflictrsquo causal lsquoconflictrsquo lsquoilllsquoill--posednessposednessrsquorsquo
ndashndash 2) preferred causal ports with 2) preferred causal ports with propagation via constraintspropagation via constraintscausal lsquoconflictrsquo causal lsquoconflictrsquo dependent state(s)dependent state(s)
ndashndash 3) choice of arbitrary causal port with 3) choice of arbitrary causal port with propagation via constraintspropagation via constraintsmeans existence of means existence of algebraic algebraic loop(sloop(s))
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
ExampleExample
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (77)
Se GY
II
R
1
R
1
2nd order loop2nd order loop
1st order loop1st order loop1st order loop1st order loop
bullbullImportant modeling feedbackImportant modeling feedback
bullbullAutomatic in 20Automatic in 20--simsim
bullbullVisible in bond graph causalityVisible in bond graph causality
bullbulllsquoHiddenrsquo in case of iconic diagramslsquoHiddenrsquo in case of iconic diagrams
J
u
i u
i
u
i
u
i
u
i
T
ω
T
ω
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Positive orientationPositive orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (78)
orientationorientation NOT THE SAME AS NOT THE SAME AS directiondirection
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Causality does NOT affect orientationCausality does NOT affect orientation
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (79)
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Basic form of physical modelsBasic form of physical models
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (80)
second lsquolawrsquoirreversible
transformation
boundaryaddition
structureconstraint relationsdistribution reversible
transformationtransport
first lsquolawrsquoconservation lsquolawsrsquo
storage
interfaces and structurehave to satisfy basic laws in degenerate way
storage = 0 production = 0 Basic lsquolawsrsquo
constitutive relationsdetermine particular occurrence (instantiation)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (81)
Thermodynamic approachThermodynamic approach
Energy balanceEnergy balance
for the totalfor the total
systemsystem
Gibbsrsquo relation Gibbsrsquo relation (Energy (Energy
lsquobalancersquo of the lsquobalancersquo of the reversible part)reversible part)
bullbull Difference is used to find the entropy productionDifference is used to find the entropy production
bullbull Power continuous structure not made explicitPower continuous structure not made explicitexcept for instantaneous except for instantaneous CarnotCarnot engines (1engines (1--junction for entropy flow)junction for entropy flow)
System boundarySystem boundary
Irreversible Irreversible thermodynamics of thermodynamics of lsquoforcesrsquo and lsquofluxesrsquo lsquoforcesrsquo and lsquofluxesrsquo (irreversible part)(irreversible part)
GJSGJSGJS
Power continuous Power continuous junction structurejunction structure
Structure is Structure is conceptualconceptual
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (82)
Mechanical versus Thermodynamic framework
Mechanical versus Thermodynamic framework
Split domains (Split domains (thermtherm) and couple by SGY ) and couple by SGY (mech)(mech)
CC--SGYSGY--CC
Only relaxation Only relaxation behavior Cbehavior C--RR
Oscillatory behavior Oscillatory behavior (damped) C(damped) C--I(I(--R)R)
OneOne type of storagetype of storageTwoTwo types of storagetypes of storageThermodynamicsThermodynamicsMechanicsMechanics
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Symplectic gyratorSymplectic gyrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (83)
bullbull Unit gyratorUnit gyrator
bullbull SGYSGY
bullbull Multiport
r = 1GY0 0C C
SGY0 0C C
0 -1+1 0
C11 C12C12 C22 SGYC 0Multiport
2020--sim demosim demo
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Symplectic GYratorSymplectic GYrator
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (84)
bullbull Mechanical (Mechanical (xxpp))
ndashndash Only in Only in inertialinertial frames (Newtons 2nd law)frames (Newtons 2nd law)
bullbull Electrical network (Electrical network (qqλλ))
ndashndash Only Only quasiquasi--stationarystationary (non(non--radiating)radiating)
SGY0 0C C
SGY0 0C C
part=
partpotEex
dd
=potxft
part=
partkinEep
dd
=kinpft
dd
= minuspFt
=potf v
=pote F=kine v
dd
= minuspFt
λpart
=partmagEe
ddλ
=magft
ddλ
minus = ut
=mage i
dd
=elecqft
=elecf i
part=
partelecEeq=elece u
ddλ
minus = ut
=mage i
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Unit gyrator (SGY) as lsquodualizerrsquoUnit gyrator (SGY) as lsquodualizerrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (85)
Port equivalentPort equivalent Port equivalentPort equivalentOriginalOriginal OriginalOriginal
C1 SGY 1 I
R1 SGY 1 R
1 SGY TF SGY 0 1 TF 0
SGY GY SGY 1 1 GY 1
SGY1
1 TF 0SGY1
1 GY 1
0GY
TF 1
1 0SGY SGY1
0
SGY
1
1
0
1 0
0
SGY SGY0
1
SGY
1 0
1
1
0
0
Se SGY 1
0Sf SGY
Sf 1
Se 0
I 0 C0 SGY
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (86)
Basic model structure(generalized bond graph)
Basic model structure(generalized bond graph)
AntiAnti--reciprocal reciprocal part (generalized part (generalized
gyrator)gyrator)
Weighted Junction Weighted Junction Structure Structure
(reciprocal)(reciprocal)
Simple Junction Simple Junction Structure (generalized Structure (generalized
KirchhoffKirchhoff laws)laws)
Weighted part (generalized Weighted part (generalized transformer)transformer)
Generalized Junction Generalized Junction Structure (power Structure (power
continuous)continuous)Boundary conditionsBoundary conditions
(sources)(sources)
Energy storageEnergy storageIrreversible Irreversible transformationtransformation
(entropy production)(entropy production)
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (87)
Mechanical framework of variables
Mechanical framework of variables
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (88)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
q f t= int d
q i t= int d
λ = intu td
int= tSS f d
int= tNN f d
f flow
eeffort generalized state
electric icurrent
uvoltage charge
magnetic uvoltage
icurrent magnetic flux linkage
thermal Ttemperature
fSentropy flow
entropy
chemical microchemical potential
fNmolar flow
number of moles
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (89)
Generalized thermodynamic framework of variables
Generalized thermodynamic framework of variables
f flow
eeffort generalized state
elasticpotential translation
vvelocity
Fforce displacement
kinetic translation
Fforce
vvelocity momentum
elasticpotential rotation
ωangular velocity
Ttorque angular displacement
kinetic rotation Ttorque
ωangularvelocity
angularmomentum
elastic hydraulic ϕvolume flow
ppressure
volume
kinetic hydraulic ppressure
ϕvolume flow
momentum of a flow tube
θ = int ωdt
b T t= int d
V t= int ϕd
dp tΓ = int
p F t= int d
x v t= int d
q f t= int d
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Energy as starting pointEnergy as starting point
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (90)
bullbull EnergyEnergyndashndashndashndash Homogeneous function of set of state variablesHomogeneous function of set of state variables
bullbull In (lsquogeneralizedrsquo) In (lsquogeneralizedrsquo) mechanics mechanics Hamiltonian Hamiltonianndashndash
bullbull In In thermodynamicsthermodynamics of lsquosimplersquo systems of lsquosimplersquo systems internal energyinternal energyndashndashndashndash more speciesmore species
( ) ( )1 i nE E q E q q q= =
( ) ( )1 1 i k i kE H q p H q q q p p p= =
( ) ( ) E U q U V S N= =
( ) ( )( )( )
1
1 1
i m
i m
E U q U V S N
U V S N N N
U V S N N N Nminus
= = =
= =
=
( ) ( )( )
2
2
i n
i n
U U q U S q q q
S S U q q q
= =
=
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (91)
Configuration influence on energetic structure
Configuration influence on energetic structure
bullbull can become an additional energy state geometric can become an additional energy state geometric parameter in storage relation results in a forceparameter in storage relation results in a force
ndashndash examples LVDT electret microphone relay examples LVDT electret microphone relay (ideal) gas(ideal) gasetc (MP C)etc (MP C)
ndashndash cycles allow transductioncycles allow transductionndashndash changes of causality correspond to Legendre transforms changes of causality correspond to Legendre transforms
(relation to dissipation)(relation to dissipation)bullbull can modulate an energy relationcan modulate an energy relation
ndashndash examples crankexamples crank--slider slider mechanismmechanism etc (MTF) etc (MTF)bullbull can switch a contact (behavior) can switch a contact (behavior)
( ) ( )
E q xF q x
xpart
=part
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Modulated capacitorModulated capacitor
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (92)
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
System (boundary) definitionSystem (boundary) definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (93)
bullbull Open (thermodynamic) systemsOpen (thermodynamic) systemsbullbull ddNN = 0= 0 lsquo lsquoLagrangianLagrangian coordinatesrsquocoordinatesrsquo
N not a stateN not a statebullbull ddVV = 0= 0 lsquo lsquoEulerianEulerian coordinatesrsquocoordinatesrsquo
V not a stateV not a statebullbull Almost always Almost always mixed boundariesmixed boundaries
NN and and VV remain statesremain statesbullbull NetworkNetwork globally globally EulerianEulerian locally locally
LagrangianLagrangian (eg network of tubes)(eg network of tubes)
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
lsquoClassical network casersquolsquoClassical network casersquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (94)
bullbull Both Both NN and and V V ndashndash constantconstantndashndash NOT CONSIDERED STATES but NOT CONSIDERED STATES but parametersparameters
bullbull As a resultAs a resultndashndash energy function not necessarily first order energy function not necessarily first order
homogenoushomogenousndashndash no dependency between storage port efforts no dependency between storage port efforts
(no generalized Gibbs(no generalized Gibbs--DuhemDuhem equation)equation)ndashndash no clear distinction between intensive and no clear distinction between intensive and
extensive descriptionextensive description
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
If not a networkIf not a network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (95)
bullbull Globally Globally LagrangianLagrangian and locally and locally EulerianEulerian possiblepossible
bullbull Example balloonExample balloon
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
Part of a tube networkPart of a tube network
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (96)
daxialV=0(V not a convected property)daxial Nne0
dradialN=0dradial Vne0(flexible tube local changes)
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
System boundary definitionSystem boundary definition
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (97)
bullbull Mechanical system of masses Mechanical system of masses springs dampers etc (network)springs dampers etc (network)ndashndash globally globally EulerianEulerian coordinatescoordinates
bullbull because the network (topology) of spatial because the network (topology) of spatial elements lsquocellsrsquo is constantelements lsquocellsrsquo is constant
ndashndash locally locally LagrangianLagrangian coordinatescoordinatesbullbull eg the constant mass with its motion eg the constant mass with its motion
restricted to the element cellrestricted to the element celllsquoone element passing a neighboring element lsquoone element passing a neighboring element
destroys the topologyrsquodestroys the topologyrsquo
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher
copy Peter BreedveldSummerschool Bertinoro 17-23 July 2005 (98)
SummarySummarybullbull System theoretic approach to physical system dynamicsSystem theoretic approach to physical system dynamics based onbased on
ndashndash classification of phenomena in terms of energyclassification of phenomena in terms of energyndashndash fundamental principles of thermodynamicsfundamental principles of thermodynamics
bullbull as a resultas a resultndashndash variables and relations describing physical systems may be classvariables and relations describing physical systems may be classifiedifiedndashndash models may be organized asmodels may be organized as
bullbull multiport elementsmultiport elementsbullbull interconnected in an interconnection structure corresponding to interconnected in an interconnection structure corresponding to a generalized a generalized
networknetwork
ndashndash multiport elements describe basic behaviors with respect to enermultiport elements describe basic behaviors with respect to energy and gy and entropyentropy
bullbull Explicit conceptual separation between two roles of displacementExplicit conceptual separation between two roles of displacementvariablevariable
ndashndash energy state (stored potential or elastic energy)energy state (stored potential or elastic energy)ndashndash configuration state (lsquoposition in spacersquo)configuration state (lsquoposition in spacersquo)
bullbull strongly reduces conceptual complexity even though numerical strongly reduces conceptual complexity even though numerical complexity may become temporarily highercomplexity may become temporarily higher