Modeling and Simulation with Compose and Activate

453 Pages·2018·24.828 MB·English

by  Stephen L. Campbell, Ramine Nikoukhah

Stephen L. Campbell · Ramine Nikoukhah
Modeling
and Simulation
with Compose
and Activate
Modeling and Simulation with Compose
and Activate
Stephen L. Campbell Ramine Nikoukhah
(cid:129)
Modeling and Simulation
with Compose and Activate
123
StephenL. Campbell RamineNikoukhah
Department ofMathematics Altair Engineering France
NorthCarolina State University Antony,France
Raleigh, NC,USA
ISBN978-3-030-04884-6 ISBN978-3-030-04885-3 (eBook)
https://doi.org/10.1007/978-3-030-04885-3
LibraryofCongressControlNumber:2018962375
Mathematics Subject Classification (2010): 34A01, 34A04, 34A38, 34H05, 68U07, 68U20, 37M05,
65Y15
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This book is dedicated to our wives and
children. They make the whole journey
worthwhile; Homa Nikoukhah and daughters
TinaandDana,GailCampbellandsonsMatt
and Eric.
Preface
System modeling and simulation is a fundamental aspect of most areas of science
and engineering. This has led to the development of software packages aimed at
helping speed up the process of modeling, simulation, optimization, analysis, and
assessment of systems.
More advanced system modeling software provide multiple ways of creating
models: Models can be programmed in specialized languages, and they can be
graphically constructed as block diagrams and state machines, or expressed
mathematically inequation-based languages.This book isabout two new software
™ ™
packages, called Altair Compose and Altair Activate , providing all these
modeling facilities.
Compose is a multi-language environment for scientific computation with spe-
cial emphasis on modeling, simulation, optimization, and assessment. This book
will focus on the newly developed open matrix language (OML). OML is part
oftheMATLAB-likefamilyoflanguagessuchasMATLAB®,Scilab,andOctave.OML
is compatible with Octave and provides bridges to Python and Tcl/Tk. An
open-source version of OML has been released in 2018, available from www.
openmatrix.org.
Activate is an open-system graphical modeling and simulation environment
providing signal-based modeling as well as physical system component-based
modeling, where the latter supports Modelica and Spice libraries. OML is the
underlying scripting language in Activate for defining model parameters, pro-
grammatically constructing models and performing pre- and post-processing.
Basic editions of Compose and Activate are available for free from Altair at
https://www.altair.com/mbd2019/. Basic Compose OML includes a number of
toolboxes, such as the Control Toolbox. Basic Activate includes many libraries as
well.Alltheexamplesinthisbookhavebeenmodeledandsimulatedwiththebasic
editions.ComposeandActivaterunundertheWindowsoperatingsystem.Thereis
also a Linux version of Compose with OML. A Linux version of Activate is in
development and should be available in 2019.
The professional versions integrate with numerous 1D and 3D simulation tools
and are available from Altair as well.
vii
viii Preface
This book provides a tutorial in the use of Compose and Activate. Part I
introduces Compose and OML and its use for modeling, simulation, and opti-
mization of dynamical systems. Part II describes graphical system modeling and
optimization with Activate. The support of equation-based modeling language
Modelica in Activate is also presented and illustrated through a number of
examples.
Throughout the book, numerous examples of varying complexity are carefully
developedandworkedout.Theexamplesaredrawnfromseveralapplicationareas
including mechanical systems, biological systems, electrical systems, and control
and signal processing systems.
Anumberofpeoplehavesupportedusinmanyways.Wewouldespeciallylike
to acknowledge Michael Hoffmann and James Dagg for their support and contri-
butions to the development of Compose and Activate, and especially James Scapa
for making it all happen.
Raleigh, NC, USA Stephen L. Campbell
Antony, France Ramine Nikoukhah
October 2018
Contents
Part I Altair Compose and OML
1 General Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 What Is OML? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Compose OML. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 OML in Modeling and Simulation. . . . . . . . . . . . . . . . . . . . . . 8
2 Introduction to OML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 OML Objects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.1.1 Matrix Construction and Manipulation. . . . . . . . . . . . . 11
2.1.2 Strings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
2.1.3 Boolean Matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.1.4 Polynomial Matrices. . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.1.5 Structures and Cells . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.1.6 Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.2 OML Programming. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.2.1 Branching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.2.2 Iterations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.2.3 OML Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.2.4 User Defined C/C++ Functions . . . . . . . . . . . . . . . . . . 40
2.3 Input and Output Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.1 Display of Variables. . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.3.2 User Input During Computation . . . . . . . . . . . . . . . . . 44
2.3.3 Formatted Input and Output . . . . . . . . . . . . . . . . . . . . 44
2.4 OML Graphics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.1 Basic Graphing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
2.4.2 Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
2.4.3 Graphic Tour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.4.4 Subplots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
ix
x Contents
3 Modeling and Simulation in OML . . . . . . . . . . . . . . . . . . . . . . . . . 61
3.1 Types of Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
3.1.1 Ordinary Differential Equations. . . . . . . . . . . . . . . . . . 62
3.1.2 Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . 63
3.1.3 Difference Equations. . . . . . . . . . . . . . . . . . . . . . . . . . 64
3.1.4 Differential Algebraic Equations . . . . . . . . . . . . . . . . . 65
3.1.5 Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.2 OML Simulation Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.2.1 Implicit Differential Equations. . . . . . . . . . . . . . . . . . . 74
3.2.2 Linear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.2.3 Root Finding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
3.2.4 Boundary Value Problems . . . . . . . . . . . . . . . . . . . . . 75
3.2.5 Difference Equations. . . . . . . . . . . . . . . . . . . . . . . . . . 76
3.2.6 Hybrid Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
3.3 Control Toolbox. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
4 Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.1 Comments on Optimization and Solving Nonlinear
Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.1.1 Nonlinear Equation Solving . . . . . . . . . . . . . . . . . . . . 99
4.2 General Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.2.1 Genetic Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3 Solving Nonlinear Equations . . . . . . . . . . . . . . . . . . . . . . . . . . 105
4.4 Parameter Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
4.4.1 Linear Programs. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
5 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.1 Boundary Value Problems by Shooting . . . . . . . . . . . . . . . . . . 111
5.2 Parameter Fitting and Implicit Models . . . . . . . . . . . . . . . . . . . 118
5.2.1 Mathematical Model. . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2.2 OML Implementation . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.3 Open-Loop Control of a Pendulum . . . . . . . . . . . . . . . . . . . . . 126
5.3.1 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3.2 Control Problem Formulation: Tracking. . . . . . . . . . . . 127
5.3.3 Control Problem Formulation: Minimizing Time . . . . . 130
5.3.4 Optimization Problem. . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.5 Implementation in OML . . . . . . . . . . . . . . . . . . . . . . . 134
5.4 PDEs and Time-Delay Systems Using MOL . . . . . . . . . . . . . . 137
5.4.1 Solving PDEs Using MOL . . . . . . . . . . . . . . . . . . . . . 138
5.4.2 Systems with Delays . . . . . . . . . . . . . . . . . . . . . . . . . 144
5.5 Plane Boarding Strategies . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.6 Introduction to Block Diagrams. . . . . . . . . . . . . . . . . . . . . . . . 151
Contents xi
Part II Altair Activate
6 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157
6.1 Modeling and Simulation in Activate. . . . . . . . . . . . . . . . . . . . 159
6.1.1 Running Activate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
6.1.2 Constructing a First Model . . . . . . . . . . . . . . . . . . . . . 159
6.1.3 Support of Vectors and Matrices in Activate . . . . . . . . 164
6.1.4 Time Delay Blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . 170
6.1.5 Activation Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
6.2 Virtual Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 177
6.2.1 Modeling a Traffic Light as a State Machine . . . . . . . . 177
6.3 Synchronism and Special Blocks . . . . . . . . . . . . . . . . . . . . . . . 183
7 Expression Blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
7.2 Activate MathExpression Block. . . . . . . . . . . . . . . . . . . . . . . . . 188
7.2.1 MathExpressions Block . . . . . . . . . . . . . . . . . . . . . . . . 189
7.2.2 Example: Bouc-Wen Model . . . . . . . . . . . . . . . . . . . . 190
7.3 Activate MatrixExpression Block. . . . . . . . . . . . . . . . . . . . . . . . 191
7.3.1 The Matrix Expression Language . . . . . . . . . . . . . . . . 192
7.3.2 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
7.4 Activate OmlExpression Block . . . . . . . . . . . . . . . . . . . . . . . . . 204
8 Beyond Single Run Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.1 End Block . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.1.1 Stop Option . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
8.1.2 Restart Option. . . . . . . . . . . . . . . . . . . . . . . . . . . . 206
8.1.3 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 208
8.2 BobyqaOpt Block. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213
8.2.1 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214
9 Examples. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.1 Predator Prey Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
9.2 Thermostat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223
9.3 Generic Extended Kalman Filter Model . . . . . . . . . . . . . . . . . . 226
9.4 Signal Processing Application . . . . . . . . . . . . . . . . . . . . . . . . . 234
9.5 Neuroscience Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
9.6 Active Cruise Controller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
9.6.1 Model Construction . . . . . . . . . . . . . . . . . . . . . . . . . . 239
9.6.2 Implementation of the Adaptive Cruise Control . . . . . . 241
9.7 Swing-Up Pendulum Problem . . . . . . . . . . . . . . . . . . . . . . . . . 247