Process Modelling and Simulation
with Application to the MATLAB/Simulink Environment
November, 2016 Università di Cagliari, Sardinia (IT)
František Gazdoš ([email protected])
CZECH REPUBLIC
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš
COUNTRIES & REGIONS…
Italy / Sardinia / Cagliari (60M / 1.6M / 154k )
Czech Republic / Zlín Region / Zlín
(10.5M / 600k / 75k)
UNIVERSITIES…
Università di Cagliari (more than 30.000 students)
Faculty of Biology and Pharmacy
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Law and Political Sciences
Tomas Bata University in Zlín
(more than 10.000 students)
Faculty of Technology
Faculty of Management and Economics
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Faculty of Logistics and Crisis
Management
Faculty of Humanities
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš
Faculty of Applied Informatics
Studies: Bachelor’s Degree studies
Follow-on Master’s Degree studies
Ph.D. Degree studies
A number of courses in English
for International students!
R&D in:
Applied Informatics
Security Technologies
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Measurement and Instrumentation
You are Welcome!
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš
Process modelling and simulation… / contents
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 2
CONTENTS
1 Motivation – Why?
2 Approaches – How?
3 Illustrative examples
room heating process
mass-spring-damper system
tubular heat exchanger
4 Introduction to MATLAB & Simulink
5 Further - What else?
…
basics of MATLAB programming (displaying process static characteristics)
building Simulink blocks, masking…
basics of Simulink (solving differential equations – process dynamics responses)
Process modelling and simulation… / …why…?
1. MOTIVATION – WHY?
it saves health & lives!
(hazardous real-time experiments, dangerous conditions…)
it saves time!
(slow real-time experiments…)
it saves costs!
(expensive real-time experiments, repairs…)
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 3
Process modelling and simulation… / …how..?
2. APPROACHES – HOW?
structure & behaviour model
(model variables & parameters correspond
to real process variables & parameters)
knowledge of the process +
mathemathics, physics, chemistry, bilogy…
ANALYTICAL approach:
analytical (internal, state-space)
model
mathematical description of physical,
chemical, bilogical sub-processes…
material & energy balances
design stage of a new technology
(real plant still does not exists…)
valid in wide range of input variables and modes
(often not allowable under real conditions…)
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 4
Process modelling and simulation… / …how..?
2. APPROACHES – HOW?
only behaviour model
(model variables & parameters DO NOT correspond
to real process variables & parameters)
EMPIRICAL approach:
experimental (external, input-output)
model
measured data processing & evaluation
(model structure choice, identification,…)
real-time measurements (input output)
usually simpler model
process must already exist
(real-time measurements)
often more accurate model
(for the measured range of input signals!)
usually time-demanding…
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 5
Process modelling and simulation… / …how..?
2. APPROACHES – HOW?
mathematical model = SIMPLIFIED reality
(some sub-processes unknown, some neglected…)
COMBINATION
analytical + empirical
(basic model structure by an analysis + parameters via experiments…)
TRADE-OFF
(model accuracy x model complexity)
…what to model…? …what to neglect…?
…how complex the model
can be…?
…how accurate model
is needed…?
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Process modelling and simulation… / …how..?
2. APPROACHES – HOW?
definition of variables (input, output, state)
simplifying assumptions
energy / material balances
steady-states analysis
choice / estimate / determination of model parameters
choice of initial / boundary conditions & operating point(s) for simulation
implementation of the model
simulation experiments
experiments evaluation
model verification / corrections…
process variables limits, model validity
schematic picture
…
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 7
Process modelling and simulation… / …examples…
3. ILLUSTRATIVE EXAMPLES
ROOM heating process: schematic picture:
definition of variables:
inputs: - heat power P(t) in [W]
- outdoor temperature TC(t) in [K]
states: - room temperature T(t) in [K]
outputs: - room temperature T(t) in [K]
simplifying assumptions:
- ideal air mixing
- constant process parameters
(air volume V, density , heat capacity cP,
overall heat transfer coefficient a,
heat transfer surface area A , …)
- heat accumulation in the walls
neglected
- …
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 8
Process modelling and simulation… / …examples…
3. ILLUSTRATIVE EXAMPLES
ROOM heating process:
energy / material balances:
heat input = heat output + heat accumulation
steady-states analysis:
(steady variables)
(heat loss due to exchange
of air and heat conduction
through the walls)
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 9
Process modelling and simulation… / …examples…
3. ILLUSTRATIVE EXAMPLES
ROOM heating process:
choice / estimate / determination of model parameters:
process variables limits, model validity
choice of initial / boundary conditions & operating point(s) for simulation
- no singular states…
- model valid in common (reasonable chosen) conditions…
T(0) = 25 [°C] = 298.15 [K]
P = 2000 [W]
Tc = 5 [°C] = 278.15 [K]
A = 55 [m2], V = 70 [m3] …measured
a = 1.82 [W/(m2K)] … estimated (steady-state model for Ps = 2000 [W] and Ts = 20 [K])
= 1.205 [kg/m3], cp = 1005 [J/(kgK)] …taken from the literature (for T = 20 [°C])
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 10
Process modelling and simulation… / …examples…
3. ILLUSTRATIVE EXAMPLES
ROOM heating process:
implementation of the model (steady-state model, dynamic model…)
simulation experiments
experiments evaluation
model verification / corrections…
- linear 1st order system,
- with lumped parameters,
- continuous-time,
- deterministic,
- multivariable (MIMO),
- time-invariant…
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 11
Process modelling and simulation… / …MATLAB…
4. INTRODUCTION TO MATLAB & SIMULINK
basics of MATLAB programming (displaying process static characteristics)
basics of Simulink (solving differential equations – process dynamics responses)
building Simulink blocks, masking…
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 12
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
(simplified car shock absorber) schematic picture:
definition of variables:
inputs: - forcing function F(t) in [N]
states: - position y(t) in [m]
- velocity v(t) = dy(t)/dt in [m/s]
outputs: - position y(t) in [m]
simplifying assumptions:
- ideal spring
- well lubricated, sliding surface
(wall friction modelled as viscous damper)
- constant process parameters
(spring constant k, friction constant b,
mass of load m, …)
- …
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 13
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
…performing a force balance:
(& utilizing Newton’s 2nd law of motion…)
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 14
steady-states analysis:
spring force friction force (viscous damper)
(steady variables)
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
choice / estimate / determination of model parameters:
process variables limits, model validity
choice of initial / boundary conditions & operating point(s) for simulation
- no singular states…
- model valid in common (reasonable chosen) conditions…
y(0) = dy(0)/dt = 0 [m]
F = 50 [N]
m = 500 [kg] … load of mass (measured)
k = 2000 [N/m] … spring constant (taken form the literature)
b = 400 [N/(m/s)] … friction constant / viscous damping coefficient (taken from the literature)
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 15
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
implementation of the model (steady-state model, dynamic model…)
simulation experiments
experiments evaluation
- linear 2nd order system,
- with lumped parameters,
- continuous-time,
- deterministic,
- single-input single-output (SISO),
- time-invariant…
model verification / corrections…
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 16
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
transfer function description (using the Laplace transform):
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 17
Gain “K”
time-constant “T”
damping coefficient
“ ”
steady-state gain:
damping coefficient:
time-constant
(natural period / inverse natural frequency): natural frequency:
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
state-space description:
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 18
define states as: …and input as: …then output will be:
then it holds: …and the 2nd order model can be rewritten into two 1st order DE:
in the matrix form: A B
C D
in the compact form: …with matrices as:
Process modelling and simulation… / …examples…
ILLUSTRATIVE EXAMPLES
Mass-spring-damper system:
state-space description:
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 19
and initial conditions:
…easy simulation in the MATLAB/Simulink using the “Transfer Fcn” or “State-Space” blocks...
Process modelling and simulation… / …what else..?
5. FURTHER…for control engineers…
linearization in a chosen operating point (for nonlinear models…)
deviation variables & proper scaling…
system analysis… - linear / nonlinear…?
- with lumped / distributed parameters...?
- continuous / discrete-time...?
- deterministic / stochastic...?
- single-variable / multi-variable...?
- time-invariant / variant...?
- state-space / transfer function description...?
- controllabilty & observability...?
- system degree & type (P/I/D)...?
- system gain & time-constants...?
- (un)stable...?
- (a)periodic response...?
- (non-)minimum-phase behaviour...?
- with(out) time-delay…?
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš 20
Process modelling and simulation… / …what else..?
5. FURTHER…for self-study…
WELLSTEAD, P. Introduction to Physical Modelling. Academic Press, 1980.
SEVERANCE, F.L. System Modeling and Simulation: An Introduction. Wiley, 2001.
INGHAM et al. Chemical Engineering Dynamics: Modelling with PC Simulation. Wiley, 1994.
LUYBEN, W.L. Process Modeling, Simulation and Control for Chemical Engineers. McGraw-Hill,
1990.
HANSELMAN, D.C. & LITTLEFIELD, B.L. Mastering MATLAB. Prentice Hall, 2011.
DABNEY, J.B. & HARMAN, T.L. Mastering Simulink. Prentice Hall, 2003.
SKOGESTAD, S & I. POSTLETHWAITE, I. Multivariable Feedback Control: Analysis and Design.
Chichester: Wiley, 2005.
Thank you
for your attention!
Erasmus lectures at Università di Cagliari in November 2016 / František Gazdoš