Modeling and Analysis of Dynamic Systems, Third Edition

619 Pages·2018·10.09 MB·English

by  Esfandiari

Modeling and Analysis
of Dynamic Systems
Third Edition

Modeling and Analysis
of Dynamic Systems
Third Edition
By
Ramin S. Esfandiari
Bei Lu
MATLAB® is a trademark of The MathWorks, Inc. and is used with permission. The MathWorks does not warrant the accuracy
of the text or exercises in this book. This book’s use or discussion of MATLAB® s oftware or related products does not constitute
endorsement or sponsorship by The MathWorks of a particular pedagogical approach or particular use of the MATLAB® software.
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Library of Congress Cataloging-in-Publication:
Names: Esfandiari, Ramin S., author. | Lu, Bei, 1974- author.
Title: Modeling and analysis of dynamic systems / Ramin S. Esfandiari & Bei Lu.
Description: Third edition. | Boca Raton : Taylor & Francis, CRC Press, 2018.
| Includes bibliographical references and index.
Identifiers: LCCN 2017040056| ISBN 9781138726420 (hardback) | ISBN
9781315191294 (ebook)
Subjects: LCSH: Mathematical models. | Dynamics. | System theory.
Classification: LCC TA342 .E88 2018 | DDC 621.01/5118--dc23
LC record available at https://lccn.loc.gov/2017040056
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K32292_Discl.indd 1 12/23/17 7:39:15 AM
To my wife Haleh,
my sisters Mandana and Roxana,
and my parents to whom I owe it all.
Ramin S. Esfandiari
To my husband Qifu,
my daughters Meixin and Meiling,
and my parents.
Bei Lu

Contents
Preface .............................................................................................................................................xv
Acknowledgment ........................................................................................................................xix
Authors .........................................................................................................................................xxi
1. Introduction to MATLAB, Simulink, and Simscape ......................................................1
1.1 MATLAB Command Window and Command Prompt ..........................................1
1.2 Vectors and Matrices ....................................................................................................2
1.2.1 Linspace.............................................................................................................3
1.2.2 Matrices .............................................................................................................4
1.2.3 Determinant, Transpose, and Inverse ...........................................................5
1.2.4 Slash Operators ................................................................................................5
1.2.5 Element-by-Element Operations ....................................................................6
1.3 Symbolic Math Toolbox ................................................................................................7
1.3.1 Anonymous Functions ....................................................................................7
1.3.2 MATLAB Function ..........................................................................................8
1.3.3 Differentiation ..................................................................................................8
1.3.4 Integration .........................................................................................................9
1.3.5 Differential Equations ...................................................................................10
1.4 Plotting .........................................................................................................................11
1.4.1 Subplot .............................................................................................................11
1.4.2 Plotting Analytical Expressions ..................................................................12
1.4.3 Multiple Plots ..................................................................................................12
1.5 User-Defined Functions and Script Files .................................................................13
1.5.1 Creating a Script File .....................................................................................14
1.6 Simulink .......................................................................................................................14
1.6.1 Block Library ..................................................................................................15
1.6.2 Building a New Model ..................................................................................16
1.6.3 Simulation .......................................................................................................19
1.7 Simscape .......................................................................................................................20
1.7.1 Block Library ..................................................................................................21
1.7.2 Building a New Model ..................................................................................22
1.7.3 Simulation .......................................................................................................24
Review Problems ...................................................................................................................26
2. Complex Analysis, Differential Equations, and Laplace Transformation ...............31
2.1 Complex Analysis .......................................................................................................31
2.1.1 Complex Numbers in Rectangular Form ...................................................31
2.1.1.1 Magnitude .......................................................................................32
2.1.1.2 Complex Conjugate ........................................................................33
vii
viii Contents
2.1.2 Complex Numbers in Polar Form................................................................34
2.1.2.1 Complex Algebra Using the Polar Form .....................................36
2.1.2.2 Integer Powers of Complex Numbers .........................................38
2.1.2.3 Roots of Complex Numbers ..........................................................38
2.1.3 Complex Variables and Complex Functions ..............................................39
2.2 Differential Equations ................................................................................................40
2.2.1 Linear, First-Order Differential Equations .................................................40
2.2.2 Second-Order Differential Equations with Constant Coefficients .........41
2.2.2.1 Homogeneous Solution .................................................................42
2.2.2.2 Particular Solution .........................................................................42
2.3 Laplace Transformation .............................................................................................45
2.3.1 Linearity of Laplace and Inverse Laplace Transforms .............................48
2.3.2 Differentiation and Integration of Laplace Transforms ...........................48
2.3.2.1 Differentiation of Laplace Transforms ........................................48
2.3.2.2 Integration of Laplace Transforms ...............................................49
2.3.3 Special Functions ...........................................................................................50
2.3.3.1 Unit-Step Function .........................................................................50
2.3.3.2 Unit-Ramp Function ......................................................................52
2.3.3.3 Unit-Pulse Function .......................................................................53
2.3.3.4 Unit-Impulse (Dirac Delta) Function ...........................................53
2.3.3.5 The Relation between Unit-Impulse and Unit-Step
Functions .....................................................................................54
2.3.3.6 Periodic Functions ..........................................................................54
2.3.4 Laplace Transforms of Derivatives and Integrals .....................................55
2.3.4.1 Laplace Transforms of Derivatives ..............................................56
2.3.4.2 Laplace Transforms of Integrals ...................................................56
2.3.5 Inverse Laplace Transformation ..................................................................57
2.3.5.1 Partial-Fraction Expansion Method.............................................57
2.3.5.2 Performing Partial-Fraction Expansion in MATLAB ...............60
2.3.5.3 Convolution Method ......................................................................61
2.3.6 Final-Value Theorem and Initial-Value Theorem ......................................64
2.3.6.1 Final-Value Theorem ......................................................................64
2.3.6.2 Initial-Value Theorem ....................................................................65
2.4 Summary ......................................................................................................................70
Review Problems ...................................................................................................................71
3. Matrix Analysis .....................................................................................................................75
3.1 Vectors and Matrices ..................................................................................................75
3.1.1 Special Matrices .............................................................................................77
3.1.2 Elementary Row Operations ........................................................................77
3.1.3 Rank of a Matrix ............................................................................................78
3.1.4 Determinant of a Matrix ...............................................................................79
3.1.4.1 Properties of Determinant ............................................................80
3.1.4.2 Rank in Terms of Determinant ....................................................80
3.1.4.3 Block Diagonal and Block Triangular Matrices .........................81
3.1.5 Inverse of a Matrix .........................................................................................82
3.1.5.1 Adjoint Matrix ................................................................................82
Contents ix
3.2 Solution of Linear Systems of Equations .................................................................86
3.2.1 Gauss Elimination Method ..........................................................................87
3.2.2 Using the Inverse of the Coefficient Matrix ...............................................87
3.2.2.1 MATLAB Built-in Function "\" .....................................................87
3.2.3 Cramer’s Rule .................................................................................................88
3.2.4 Homogeneous Systems .................................................................................89
3.3 Matrix Eigenvalue Problem .......................................................................................92
3.3.1 Solving the Eigenvalue Problem ..................................................................92
3.3.1.1 Eigenvalue Properties of Matrices ...............................................92
3.3.2 Algebraic Multiplicity and Geometric Multiplicity ..................................94
3.3.2.1 Generalized Eigenvectors .............................................................96
3.3.2.2 Generalized Eigenvectors in MATLAB .......................................96
3.3.2.3 Similarity Transformations ...........................................................97
3.3.2.4 Matrix Diagonalization .................................................................97
3.3.2.5 Defective Matrices ..........................................................................98
3.4 Summary ....................................................................................................................100
Review Problems .................................................................................................................101
4. System Model Representation .........................................................................................105
4.1 Configuration Form ..................................................................................................105
4.1.1 Second-Order Matrix Form ........................................................................106
4.2 State-Space Form .......................................................................................................108
4.2.1 State Variables, State-Variable Equations, and State Equation ..............108
4.2.1.1 State-Variable Equations ..............................................................109
4.2.1.2 State Equation ...............................................................................110
4.2.2 Output Equation and State-Space Form ...................................................111
4.2.2.1 Output Equation ...........................................................................112
4.2.2.2 State-Space Form ..........................................................................113
4.2.2.3 State-Space Form in MATLAB® ...........................................114
4.2.3 Decoupling the State Equation...................................................................115
4.3 Input–Output Equation and Transfer Function ...................................................119
4.3.1 Input–Output Equations from the System Model ..................................119
4.3.2 Transfer Functions from the System Model .............................................120
4.4 Relations between State-Space Form, Input–Output Equation, and
Transfer Matrix ..........................................................................................................125
4.4.1 Input–Output Equation to State-Space Form ...........................................125
4.4.1.1 Controller Canonical Form ..................................................127
4.4.2 State-Space Form to Transfer Matrix .........................................................129
4.4.2.1 MATLAB Command "ss2tf" ............................................130
4.5 Block Diagram Representation ...............................................................................134
4.5.1 Block Diagram Operations .........................................................................134
4.5.1.1 Summing Junction .......................................................................134
4.5.1.2 Series Combinations of Blocks ...................................................135
4.5.1.3 Parallel Combinations of Blocks ................................................136
4.5.1.4 Integrator .......................................................................................137
4.5.1.5 Closed-Loop Systems ...................................................................138