Modeling and Simulation of Systems Using MATLAB and Simulink

2010·14.98 MB·English

by  Devendra K. Chaturvedi

Cover Page: 1
Half Title Page: 2
Title Page Page: 3
Copyright Page Page: 4
Dedication Page: 5
Table of Contents Page: 6
Preface Page: 9
Supplementary Resources Disclaimer Page: 10
Acknowledgments Page: 11
Author Page: 12
1. Introduction to Systems Page: 13
1.1 System Page: 13
1.1.1 System Boundary Page: 13
1.1.2 System Components and Their Interactions Page: 14
1.1.3 Environment Page: 14
1.2 Classification of Systems Page: 14
1.2.1 According to the Time Frame Page: 14
1.2.2 According to the Complexity of the System Page: 15
1.2.3 According to the Interactions Page: 15
1.2.4 According to the Nature and Type of Components Page: 15
1.2.5 According to the Uncertainties Involved Page: 15
1.2.5.1 Static vs. Dynamic Systems Page: 15
1.2.5.2 Linear vs. Nonlinear Systems Page: 15
1.3 Linear Systems Page: 16
1.3.1 Superposition Theorem Page: 16
1.3.2 Homogeneity Page: 16
1.3.3 Mathematical Viewpoint of a Linear System Page: 16
1.3.3.1 Linear Differential Equation Page: 16
1.3.3.2 Nonlinear Differential Equations Page: 16
1.4 Time-Varying vs. Time-Invariant Systems Page: 17
1.5 Lumped vs. Distributed Parameter Systems Page: 17
1.6 Continuous-Time and Discrete-Time Systems Page: 17
1.7 Deterministic vs. Stochastic Systems Page: 17
1.7.1 Complexity of Systems Page: 18
1.8 Hard and Soft Systems Page: 18
1.9 Analysis of Systems Page: 18
1.10 Synthesis of Systems Page: 18
1.11 Introduction to System Philosophy Page: 18
1.11.1 Method of Science Page: 19
1.11.1.1 Reductionism Page: 19
1.11.1.2 Repeatability Page: 19
1.11.1.3 Refutation Page: 20
1.11.2 Problems of Science and Emergence of System Page: 20
1.12 System Thinking Page: 20
1.13 Large and Complex Applied System Engineering: A Generic Modeling Page: 21
1.14 Review Questions Page: 24
1.15 Bibliographical Notes Page: 24
2. Systems Modeling Page: 25
2.1 Introduction Page: 25
2.2 Need of System Modeling Page: 26
2.3 Modeling Methods for Complex Systems Page: 26
2.4 Classification of Models Page: 26
2.4.1 Physical vs. Abstract Model Page: 26
2.4.2 Mathematical vs. Descriptive Model Page: 27
2.4.3 Static vs. Dynamic Model Page: 27
2.4.4 Steady State vs. Transient Model Page: 27
2.4.5 Open vs. Feedback Model Page: 27
2.4.6 Deterministic vs. Stochastic Models Page: 27
2.4.7 Continuous vs. Discrete Models Page: 27
2.5 Characteristics of Models Page: 27
2.6 Modeling Page: 27
2.6.1 Fundamental Axiom (Modeling Hypothesis) Page: 28
2.6.2 Component Postulate (First Postulate) Page: 28
2.6.3 Model Evaluation Page: 28
2.6.4 Generic Description of Two-Terminal Components Page: 28
2.6.4.1 Dissipater Type Components Page: 29
2.6.4.2 Delay Type Elements Page: 29
2.6.4.3 Accumulator Type Page: 29
2.6.4.4 Sources or Drivers Page: 29
2.7 Mathematical Modeling of Physical Systems Page: 29
2.7.1 Modeling of Mechanical Systems Page: 30
2.7.1.1 Translational Mechanical Systems Page: 30
2.7.1.2 Rotational Mechanical Systems Page: 33
2.7.2 Modeling of Electrical Systems Page: 36
2.7.3 Modeling of Electromechanical Systems Page: 37
2.7.4 Modeling of Fluid Systems Page: 37
2.7.4.1 Hydraulic Systems Page: 37
2.7.5 Modeling of Thermal Systems Page: 38
2.8 Review Questions Page: 39
2.9 Bibliographical Notes Page: 40
3. Formulation of State Space Model of Systems Page: 41
3.1 Physical Systems Theory Page: 41
3.2 System Components and Interconnections Page: 41
3.3 Computation of Parameters of a Component Page: 42
3.4 Single Port and Multiport Systems Page: 43
3.4.1 Linear Perfect Couplers Page: 43
3.4.2 Summary of Two-Terminal and Multiterminal Components Page: 43
3.4.3 Multiterminal Components Page: 43
3.5 Techniques of System Analysis Page: 43
3.5.1 Lagrangian Technique Page: 43
3.5.2 Free Body Diagram Method Page: 44
3.5.3 Linear Graph Theoretic Approach Page: 44
3.6 Basics of Linear Graph Theoretic Approach Page: 44
3.7 Formulation of System Model for Conceptual System Page: 45
3.7.1 Fundamental Axioms Page: 45
3.7.2 Component Postulate Page: 45
3.7.3 System Postulate Page: 45
3.7.3.1 Cutset Postulate Page: 45
3.7.3.2 Circuit Postulate Page: 46
3.8 Formulation of System Model for Physical Systems Page: 47
3.9 Topological Restrictions Page: 48
3.9.1 Perfect Coupler Page: 48
3.9.2 Gyrator Page: 48
3.9.3 Short Circuit Element (“A” Type) Page: 48
3.9.4 Open Circuit Element (“B” Type) Page: 48
3.9.5 Dissipater Type Elements Page: 48
3.9.6 Delay Type Elements Page: 48
3.9.7 Accumulator Type Elements Page: 48
3.9.8 Across Drivers Page: 48
3.9.9 Through Drivers Page: 48
3.10 Development of State Model of Degenerative System Page: 51
3.10.1 Development of State Model for Degenerate System Page: 51
3.10.2 Symbolic Formulation of State Model for Nondegenerative Systems Page: 52
3.10.3 State Model of System with Multiterminal Components Page: 53
3.10.4 State Model for Systems with Time Varying and Nonlinear Components Page: 54
3.11 Solution of State Equations Page: 55
3.12 Controllability Page: 57
3.13 Observability Page: 57
3.14 Sensitivity Page: 57
3.15 Liapunov Stability Page: 58
3.16 Performance Characteristics of Linear Time Invariant Systems Page: 58
3.17 Formulation of State Space Model Using Computer Program (SYSMO) Page: 59
3.17.1 Preparation of the Input Data Page: 59
3.17.2 Algorithm for the Formulation of State Equations Page: 59
3.18 Review Questions Page: 59
3.19 Bibliographical Notes Page: 61
4. Model Order Reduction Page: 62
4.1 Introduction Page: 62
4.2 Difference between Model Simplification and Model Order Reduction Page: 62
4.3 Need for Model Order Reduction Page: 63
4.4 Principle of Model Order Reduction Page: 63
4.5 Methods of Model Order Reduction Page: 63
4.5.1 Time Domain Simplification Techniques Page: 64
4.5.1.1 Dominant Eigenvalue Approach Page: 64
4.5.1.2 Aggregation Method Page: 65
4.5.1.3 Subspace Projection Method Page: 65
4.5.1.4 Optimal Order Reduction Page: 65
4.5.1.5 Hankel Matrix Approach Page: 66
4.5.1.6 Hankel–Norm Model Order Reduction Page: 66
4.5.2 Model Order Reduction in Frequency Domain Page: 66
4.5.2.1 Pade Approximation Method Page: 66
4.5.2.2 Continued Fraction Expansion Page: 66
4.5.2.3 Moment-Matching Method Page: 66
4.5.2.4 Balanced Realization-Based Reduction Method Page: 66
4.5.2.5 Balanced Truncation Page: 67
4.5.2.6 Frequency-Weighted Balanced Model Reduction Page: 69
4.5.2.7 Time Moment Matching Page: 70
4.5.2.8 Continued Fraction Expansion Page: 71
4.5.2.9 Model Order Reduction Based on the Routh Stability Criterion Page: 73
4.5.2.10 Differentiation Method for Model Order Reduction Page: 73
4.6 Applications of Reduced-Order Models Page: 75
4.7 Review Questions Page: 75
4.8 Bibliographical Notes Page: 75
5. Analogous of Linear Systems Page: 76
5.1 Introduction Page: 76
5.1.1 D’Alembert’s Principle Page: 76
5.2 Force–Voltage (f–v) Analogy Page: 76
5.2.1 Rule for Drawing f–v Analogous Electrical Circuits Page: 76
5.3 Force–Current (f–i) Analogy Page: 76
5.3.1 Rule for Drawing f–i Analogous Electrical Circuits Page: 76
5.4 Review Questions Page: 79
6. Interpretive Structural Modeling Page: 80
6.1 Introduction Page: 80
6.2 Graph Theory Page: 80
6.2.1 Net Page: 81
6.2.2 Loop Page: 81
6.2.3 Cycle Page: 81
6.2.4 Parallel Lines Page: 81
6.2.5 Properties of Relations Page: 81
6.3 Interpretive Structural Modeling Page: 81
6.4 Review Questions Page: 84
6.5 Bibliographical Notes Page: 84
7. System Dynamics Techniques Page: 85
7.1 Introduction Page: 85
7.2 System Dynamics of Managerial and Socioeconomic System Page: 85
7.2.1 Counterintuitive Nature of System Dynamics Page: 85
7.2.2 Nonlinearity Page: 85
7.2.3 Dynamics Page: 85
7.2.4 Causality Page: 85
7.2.5 Endogenous Behavior Page: 85
7.3 Traditional Management Page: 85
7.3.1 Strength of the Human Mind Page: 85
7.3.2 Limitation of the Human Mind Page: 85
7.4 Sources of Information Page: 85
7.4.1 Mental Database Page: 85
7.4.2 Written/Spoken Database Page: 86
7.4.3 Numerical Database Page: 86
7.5 Strength of System Dynamics Page: 86
7.6 Experimental Approach to System Analysis Page: 87
7.7 System Dynamics Technique Page: 87
7.8 Structure of a System Dynamic Model Page: 87
7.9 Basic Structure of System Dynamics Models Page: 87
7.9.1 Level Variables Page: 87
7.9.2 Flow-Rate Variables Page: 87
7.9.3 Decision Function Page: 87
7.10 Different Types of Equations Used in System Dynamics Techniques Page: 89
7.10.1 Level Equation Page: 89
7.10.2 Rate Equation (Decision Functions) Page: 90
7.10.3 Auxiliary Equations Page: 90
7.11 Symbol Used in Flow Diagrams Page: 90
7.11.1 Levels Page: 90
7.11.2 Source and Sinks Page: 90
7.11.3 Information Takeoff Page: 90
7.11.4 Auxiliary Variables Page: 91
7.11.5 Parameters (Constants) Page: 91
7.12 Dynamo Equations Page: 91
7.13 Modeling and Simulation of Parachute Deceleration Device Page: 96
7.13.1 Parachute Inflation Page: 97
7.13.2 Canopy Stress Distribution Page: 97
7.13.3 Modeling and Simulation of Parachute Trajectory Page: 97
7.14 Modeling of Heat Generated in a Parachute during Deployment Page: 98
7.14.1 Dynamo Equations Page: 98
7.15 Modeling of Stanchion System of Aircraft Arrester Barrier System Page: 98
7.15.1 Modeling and Simulation of Forces Acting on Stanchion System Using System Dynamic Technique Page: 99
7.15.2 Dynamic Model Page: 100
7.15.3 Results Page: 100
7.16 Review Questions Page: 100
7.17 Bibliographical Notes Page: 101
8. Simulation Page: 102
8.1 Introduction Page: 102
8.2 Advantages of Simulation Page: 102
8.3 When to Use Simulations Page: 103
8.4 Simulation Provides Page: 103
8.5 How Simulations Improve Analysis and Decision Making? Page: 103
8.6 Application of Simulation Page: 103
8.7 Numerical Methods for Simulation Page: 103
8.7.1 The Rectangle Rule Page: 103
8.7.2 The Trapezoid and Tangent Formulae Page: 103
8.7.3 Simpson’s Rule Page: 104
8.7.4 One-Step Euler’s Method Page: 104
8.7.5 Runge–Kutta Methods of Integration Page: 105
8.7.5.1 Physical Interpretation Page: 105
8.7.6 Runge–Kutta Fourth-Order Method Page: 105
8.7.7 Adams–Bashforth Predictor Method Page: 105
8.7.8 Adams–Moulton Corrector Method Page: 106
8.8 The Characteristics of Numerical Methods Page: 106
8.9 Comparison of Different Numerical Methods Page: 106
8.10 Errors during Simulation with Numerical Methods Page: 106
8.10.1 Truncation Error Page: 106
8.10.2 Round Off Error Page: 106
8.10.3 Step Size vs. Error Page: 107
8.10.4 Discretization Error Page: 107
8.11 Review Questions Page: 110
9. Nonlinear and Chaotic System Page: 111
9.1 Introduction Page: 111
9.2 Linear vs. Nonlinear System Page: 111
9.3 Types of Nonlinearities Page: 111
9.4 Nonlinearities in Flight Control of Aircraft Page: 111
9.4.1 Basic Control Surfaces Used in Aircraft Maneuvers Page: 112
9.4.2 Principle of Flight Controls Page: 112
9.4.3 Components Used in Pitch Control Page: 112
9.4.4 Modeling of Various Components of Pitch Control System Page: 112
9.4.5 Simulink Model of Pitch Control in Flight Page: 113
9.4.5.1 Simulink Model of Pitch Control in Flight Using Nonlinearities Page: 113
9.4.6 Study of Effects of Different Nonlinearities on Behavior of the Pitch Control Model Page: 113
9.4.6.1 Effects of Dead-Zone Nonlinearities Page: 113
9.4.6.2 Effects of Saturation Nonlinearities Page: 113
9.4.6.3 Effects of Backlash Nonlinearities Page: 113
9.4.6.4 Cumulative Effects of Backlash, Saturation, Dead-Zone Nonlinearities Page: 113
9.4.7 Designing a PID Controller for Pitch Control in Flight Page: 113
9.4.7.1 Designing a PID Controller for Pitch Control in Flight with the Help of Root Locus Method (Feedback Compensation) Page: 113
9.4.7.2 Designing a PID Controller (Connected in Cascade with the System) for Pitch Control in Flight Page: 114
9.4.7.3 Design of P, I, D, PD, PI, PID, and Fuzzy Controllers Page: 115
9.4.8 Design of Fuzzy Controller Page: 115
9.4.8.1 Basic Structure of a Fuzzy Controller Page: 115
9.4.8.2 The Components of a Fuzzy System Page: 115
9.4.9 Tuning Fuzzy Controller Page: 116
9.5 Conclusions Page: 117
9.6 Introduction to Chaotic System Page: 117
9.6.1 General Meaning Page: 117
9.6.2 Scientific Meaning Page: 117
9.6.3 Definition Page: 118
9.7 Historical Prospective Page: 118
9.8 First-Order Continuous-Time System Page: 118
9.9 Bifurcations Page: 119
9.9.1 Saddle Node Bifurcation Page: 119
9.9.2 Transcritical Bifurcation Page: 120
9.9.3 Pitchfork Bifurcation Page: 120
9.9.3.1 Supercritical Pitchfork Bifurcation Page: 120
9.9.4 Catastrophes Page: 120
9.9.4.1 Globally Attracting Point for Stability Page: 120
9.10 Second-Order System Page: 121
9.11 Third-Order System Page: 121
9.11.1 Lorenz Equation: A Chaotic Water Wheel Page: 122
9.12 Review Questions Page: 122
9.13 Bibliographical Notes Page: 122
10. Modeling with Artificial Neural Network Page: 123
10.1 Introduction Page: 123
10.1.1 Biological Neuron Page: 123
10.1.2 Artificial Neuron Page: 123
10.2 Artificial Neural Networks Page: 123
10.2.1 Training Phase Page: 123
10.2.1.1 Selection of Neuron Characteristics Page: 123
10.2.1.2 Selection of Topology Page: 124
10.2.1.3 Error Minimization Process Page: 124
10.2.1.4 Selection of Training Pattern and Preprocessing Page: 124
10.2.1.5 Stopping Criteria of Training Page: 124
10.2.2 Testing Phase Page: 124
10.2.2.1 ANN Model Page: 124
10.2.2.2 Building ANN Model Page: 124
10.2.2.3 Backpropagation Page: 125
10.2.2.4 Training Algorithm Page: 125
10.2.2.5 Applications of Neural Network Modeling Page: 125
10.3 Review Questions Page: 127
11. Modeling Using Fuzzy Systems Page: 129
11.1 Introduction Page: 129
11.2 Fuzzy Sets Page: 129
11.3 Features of Fuzzy Sets Page: 130
11.4 Operations on Fuzzy Sets Page: 130
11.4.1 Fuzzy Intersection Page: 130
11.4.2 Fuzzy Union Page: 130
11.4.3 Fuzzy Complement Page: 130
11.4.4 Fuzzy Concentration Page: 130
11.4.5 Fuzzy Dilation Page: 131
11.4.6 Fuzzy Intensification Page: 131
11.4.7 Bounded Sum Page: 131
11.4.8 Strong α-Cut Page: 131
11.4.9 Linguistic Hedges Page: 131
11.5 Characteristics of Fuzzy Sets Page: 132
11.5.1 Normal Fuzzy Set Page: 132
11.5.2 Convex Fuzzy Set Page: 132
11.5.3 Fuzzy Singleton Page: 132
11.5.4 Cardinality Page: 132
11.6 Properties of Fuzzy Sets Page: 132
11.7 Fuzzy Cartesian Product Page: 132
11.8 Fuzzy Relation Page: 132
11.9 Approximate Reasoning Page: 133
11.10 Defuzzification Methods Page: 135
11.11 Introduction to Fuzzy Rule-Based Systems Page: 135
11.12 Applications of Fuzzy Systems to System Modeling Page: 136
11.12.1 Single Input Single Output Systems Page: 137
11.12.2 Multiple Input Single Output Systems Page: 137
11.12.3 Multiple Input Multiple Output Systems Page: 137
11.13 Takagi–Sugeno–Kang Fuzzy Models Page: 138
11.14 Adaptive Neuro-Fuzzy Inferencing Systems Page: 138
11.15 Steady State DC Machine Model Page: 140
11.16 Transient Model of a DC Machine Page: 141
11.17 Fuzzy System Applications for Operations Research Page: 144
11.18 Review Questions Page: 146
11.19 Bibliography and Historical Notes Page: 146
12. Discrete-Event Modeling and Simulation Page: 147
12.1 Introduction Page: 147
12.2 Some Important Definitions Page: 148
12.3 Queuing System Page: 148
12.4 Discrete-Event System Simulation Page: 148
12.5 Components of Discrete-Event System Simulation Page: 148
12.6 Input Data Modeling Page: 149
12.7 Family of Distributions for Input Data Page: 149
12.8 Random Number Generation Page: 149
12.8.1 Uniform Distribution Page: 149
12.8.2 Gaussian Distribution of Random Number Generation Page: 150
12.9 Chi-Square Test Page: 150
12.10 Kolomogrov–Smirnov Test Page: 150
12.11 Review Questions Page: 150
Appendix A Page: 151
A.1 What Is MATLAB®? Page: 151
A.2 Learning MATLAB Page: 151
A.3 The MATLAB System Page: 151
A.3.1 Development Environment Page: 151
A.3.2 The MATLAB Mathematical Function Library Page: 151
A.3.3 The MATLAB Language Page: 151
A.3.4 Handle Graphics Page: 151
A.3.5 The MATLAB Application Program Interface (API) Page: 151
A.4 Starting and Quitting MATLAB Page: 151
A.5 MATLAB Desktop Page: 151
A.6 Desktop Tools Page: 151
A.6.1 Command Window Page: 151
A.6.2 Command History Page: 151
A.6.2.1 Running External Programs Page: 151
A.6.2.2 Launch Pad Page: 152
A.6.2.3 Help Browser Page: 152
A.6.2.4 Current Directory Browser Page: 152
A.6.2.5 Workspace Browser Page: 152
A.6.2.6 Array Editor Page: 152
A.6.2.7 Editor/Debugger Page: 152
A.6.2.8 Other Development Environment Features Page: 152
A.7 Entering Matrices Page: 152
A.8 Subscripts Page: 153
A.9 The Colon Operator Page: 153
A.10 The Magic Function Page: 153
A.11 Expressions Page: 153
A.11.1 Variables Page: 153
A.11.2 Numbers Page: 153
A.11.3 Operators Page: 154
A.11.4 Functions Page: 154
A.11.4.1 Generating Matrices Page: 154
A.12 The Load Command Page: 154
A.13 The Format Command Page: 154
A.14 Suppressing Output Page: 155
A.15 Entering Long Command Lines Page: 155
A.16 Basic Plotting Page: 155
A.16.1 Creating a Plot Page: 155
A.16.2 Multiple Data Sets in One Graph Page: 155
A.16.3 Plotting Lines and Markers Page: 155
A.16.4 Adding Plots to an Existing Graph Page: 155
A.16.5 Multiple Plots in One Figure Page: 155
A.16.6 Setting Grid Lines Page: 155
A.16.7 Axis Labels and Titles Page: 155
A.16.8 Saving a Figure Page: 155
A.16.9 Mesh and Surface Plots Page: 155
A.17 Images Page: 156
A.18 Handle Graphics Page: 156
A.18.1 Setting Properties from Plotting Commands Page: 156
A.18.2 Different Types of Graphs Page: 156
A.18.2.1 Bar and Area Graphs Page: 156
A.19 Animations Page: 157
A.20 Creating Movies Page: 157
A.21 Flow Control Page: 157
A.21.1 If Page: 157
A.21.2 Switch and Case Page: 158
A.21.2.1 For Page: 158
A.21.2.2 While Page: 158
A.21.2.3 Continue Page: 158
A.21.2.4 Break Page: 158
A.22 Other Data Structures Page: 158
A.22.1 Multidimensional Arrays Page: 158
A.22.2 Cell Arrays Page: 159
A.22.3 Characters and Text Page: 159
A.23 Scripts and Functions Page: 160
A.23.1 Scripts Page: 160
A.23.2 Functions Page: 160
A.23.2.1 Global Variables Page: 160
A.23.2.2 Passing String Arguments to Functions Page: 161
A.23.2.3 Constructing String Arguments in Code Page: 161
A.23.2.4 A Cautionary Note Page: 161
A.23.2.5 The Eval Function Page: 161
A.23.2.6 Vectorization Page: 161
A.23.2.7 Preallocation Page: 161
A.23.2.8 Function Handles Page: 161
A.23.2.9 Function Functions Page: 161
Appendix B: Simulink Page: 163
B.1 Introduction Page: 163
B.2 Features of Simulink Page: 163
B.3 Simulation Parameters and Solvers Page: 163
B.4 Construction of Block Diagram Page: 163
B.5 Review Questions Page: 163
Appendix C: Glossary Page: 164
C.1 Modeling and Simulation Page: 164
C.2 Artificial Neural Network Page: 167
C.3 Fuzzy Systems Page: 168
C.4 Genetic Algorithms Page: 169
Bibliography Page: 169
Index Page: 177