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INTRODUCTION TO THE COURSE
MODELLING OF MECHATRONICS SYSTEMS
MEX3273
2014Prepared by: D C Wijewardene
OUTLINE Course Information
Overview of modelling
Types of Systems
Introduction to models
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COURSE INFORMATION Academic Coordinator
B G D Achintha MadhusankaContact : 011 2881265/0716166779Email :
[email protected]/[email protected]
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D T GanegodaContact : 011 2881085
Course Coordinator
COURSE INFORMATION Web Resource MyOUSL
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COURSE INFORMATIONObjectives Primary objective is to understand
the
methodologies of formulating system models
To be able to use various methodologies of system
representation
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COURSE INFORMATIONObjectives To gain a hands on practice of
using
software tools to build and simulate system models
To explore the modeling of mixed systems (Multi-domain systems)
Only a brief introduction
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COURSE INFORMATIONContent Introduction to modelling
Introduction to signals & systems
Fundamentals of dynamic system modelling
Formulation of system models
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COURSE INFORMATIONContent System representation
State Space representation
Block Diagram representation Linear graph representation
Introduction to modelling of multi-
domain systems
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COURSE INFORMATIONResources Course note sets ( 02 Books)
Course reading (Selected text from : de Silva, C.W..MECHATRONICS
An Integrated approach, Taylor & Francis/CRC Press, Boca Raton.
FL.2005
Referencing
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SYSTEMS
An entity separable from rest of the surroundings by means of a
boundary ( physical or conceptual) and having interacting elements
or subsystems disturbances)
What is a system?
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SYSTEMSWhat is a system?
SystemInputsOutputs
Boundary
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SYSTEMSA system will react to changes in the surroundings and
also exchange information and energy
SystemInputsOutputs
Boundary
Disturbances
Energy & Information
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SYSTEMS - EXAMPLES
Eco-systems
Transport systems
Biological systems
Technical systems
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SYSTEMS - EXAMPLESCan you think of any other systems?
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MODELSWhat is a model? A models is an abstract representation of
reality (system, object or a phenomenon)
Real system ModelsModelling
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MODELS Models embody system characteristics
that are important to the models users
Also, models simplify reality by eliminating other
characteristics that are not important for their purpose
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TYPES OF MODELS Conceptual models
A conceptual model is the mental model people have of a
system.
These are qualitative in nature and helps highlight important
connections in real world systems and processes.
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TYPES OF MODELS Physical models
A physical model is a physical copy of a object or a system
It can be smaller/larger or equal in size to the real
object/system
Physical models allow visualization of the real
object/system
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TYPES OF MODELS Physical models
A physical models may also be modeled virtually
2D/3D models, Prototypes, architectural models are some
examples
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TYPES OF MODELS Physical models
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TYPES OF MODELS Mathematical models
Mathematical models comprises equations that determine how a
system changes from one state to the next (differential equations)
and/or how one variable depends on the value or state of other
variables (state equations)
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TYPES OF MODELS Mathematical models
Or simply, A mathematical model is an abstract model that uses
mathematical language to describe the behavior of a system.
Can be divided in to numerical models and analytical models
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TYPES OF MODELS Numerical models
Numerical models uses some sort of numerical time-stepping
procedure to obtain the models behavior over time.
The mathematical solution is represented by a generated table
and/or graph
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TYPES OF MODELS Numerical models
Examples are, FEA, CFD weather prediction models.
FAE ModelCFD Model
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TYPES OF MODELS Analytical models
Analytical models have a closed form solution, i.e. the solution
to the equations used to describe changes in a system can be
expressed as a mathematical analytic function.
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TYPES OF MODELS Analytical models Further explanation
Assume you have a mathematical model and you want to understand
its behavior. That is, you want to find a solution to the set of
equations.
One of the ways of doing this is by using mathematical
techniques such as trigonometry, calculus etc., to write down the
solutions. (solve the equations)
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TYPES OF MODELS Analytical models Further explanation
Assume you have a mathematical model and you want to understand
its behavior. That is, you want to find a solution to the set of
equations.
One of the ways of doing this is by using mathematical
techniques such as trigonometry, calculus etc., to write down the
solutions. (solve the equations)
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TYPES OF MODELS Analytical models
This is called the analytic solution, because youve used
analysis to figure it out.
It is also referred to as a closed form solution.
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TYPES OF MODELS Important!
Closed form solutions are only applicable to simple models. For
more complex models, the math becomes much too complicated. Then
you have to use numerical methods of solving the equations
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TYPES OF MODELS Statistical models
Includes statistical characterization of numerical data,
estimating the probabilistic future behavior of a system based on
past behavior, extrapolation or interpolation of data based on some
best-fit, error estimates of observations, or spectral analysis of
data or model generated output.
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TYPES OF MODELSIn this course we will be mainly looking at
analytical models!
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BUILDING BLOCKS OF MODELS Typically, an analytical model
will
comprise of variables
There can be many types of variables in a analytical model.
Therefore the variables are generally represented by vectors
variables
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BUILDING BLOCKS OF MODELS
Decision Variables (Independent variables)
Input Variables
Exogenous Variables (Constants or parameters)
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BUILDING BLOCKS OF MODELS
State Variables (Variables that describes the state of a
system)
Output Variables (Variables that are dependent on the state of
the system)
Random Variables (Noise or disturbances)
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CLASSIFICATION OF ANALYTICAL MODELS/SYSTEMS Dynamic vs.
static
Distributive parameter vs. lumped parameter
Linear vs. non-linear Deterministic vs. Probabilistic
(Stochastic)
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MODELLING OF SYSTEMS
Model
Input
Output
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SOLUTION TECHNIQUES
Analytical models are formed by obtaining mathematical
relationships of the variables discussed previously, and several
forms of solution techniques are used for analyzing these
models
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SOLUTION TECHNIQUES State-space method
Linear graphs
Bond graphs
Transfer function models
Frequency domain models
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IMPORTANCE OF MODELLING
Modelling of systems help us to develop a tool to conduct
simulation and predict and investigate the behavior of the system
to various inputs and disturbances
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IMPORTANCE OF MODELLING
The result of the simulation can be used for; taking necessary
control or corrective
actions predicting the behavior of a complex
system such as the weather
enhancing the design of a product
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ADVANTAGES OF MODELLING Some systems states cannot be
brought
about in the real system, or at least not in a non-destructive
manner
In comparison to real experiments, virtual experiments are less
costly
In some cases real experiment is ruled out for moral reasons
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ADVANTAGES OF MODELLING Simulated models are usually
completely
controllable. Therefore all input variables and parameters of
the system can be pre-determined
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ADVANTAGES OF MODELLING Simulated models are generally fully
monitorable. All output variables and system states are
available, whereas in real systems this would require sophisticated
measuring devices to monitor such variables and parameters
determined
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LIMITATIONS OF MODELLING Every simulated modelling
experiment
requires a complete, validated and verified modelling of the
system
The accuracy to which details are reproduced and the simulation
speed of the model is limited by the power of the computer used for
the simulation
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MODEL DEVELOPMENT
Real System
Conceptual Model
Executable Model
Analysis
Implementation
Simulation
Verification
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MODEL DEVELOPMENT
AnalysisThe Process of obtaining a conceptual model by applying
suitable relationships of nature, equations, or verbal descriptions
to the real system
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MODEL DEVELOPMENT
Implementation Transformation from the conceptual model to a
executable (simulatable) model. This mainly involves the setting up
of instructions that describes the systems response to an external
stimuli
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MODEL DEVELOPMENT
Simulation Processing of the instructions in the executable
model usually by using a computer
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MODEL DEVELOPMENTQualification Determining a correct field of
application to the conceptual model. A conceptual model is
adequately qualified for a pre-determined field of application if
it produces the required degree of correspondence with the real
system
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MODEL DEVELOPMENT
Verification Investigates whether the executable model reflects
the conceptual model within the specified limits of accuracy.
Verification basically transforms the conceptual models field of
application to the executable model
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MODEL DEVELOPMENT
Validation Gives us information whether the executable model is
suitable for fulfilling the envisaged task within its field of
application
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MODEL DEVELOPMENT
Verification ensures that the system model is right, whereas,
Validation is about modelling the right system
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SUMMARY Course Information
Introduction to systems
Overview of models and types of models
Introduction to model development
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