System Dynamics
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Preface xi
1 Introduction 1
1.1 Models of Systems 4
1.2 Systems, Subsystems, and Components 7
1.3 State-Determined Systems 9
1.4 Uses of Dynamic Models 10
1.5 Linear and Nonlinear Systems 11
1.6 Automated Simulation 12
References 13
Problems 14
2 Multiport Systems and Bond Graphs 17
2.1 Engineering Multiports 17
2.2 Ports, Bonds, and Power 24
2.3 Bond Graphs 27
2.4 Inputs, Outputs, and Signals 30
Problems 33
3 Basic Bond Graph Elements 37
3.1 Basic 1-Port Elements 37
3.2 Basic 2-Port Elements 50
3.3 The 3-Port Junction Elements 57
3.4 Causality Considerations for the Basic Elements 63
3.4.1 Causality for Basic 1-Ports 64
3.4.2 Causality for Basic 2-Ports 65
3.4.3 Causality for Basic 3-Ports 66
3.5 Causality and Block Diagrams 67
Reference 71
Problems 71
4 System Models 77
4.1 Electrical Systems 78
4.1.1 Electrical Circuits 78
4.1.2 Electrical Networks 84
4.2 Mechanical Systems 91
4.2.1 Mechanics of Translation 91
4.2.2 Fixed-Axis Rotation 100
4.2.3 Plane Motion 106
4.3 Hydraulic and Acoustic Circuits 121
4.3.1 Fluid Resistance 122
4.3.2 Fluid Capacitance 125
4.3.3 Fluid Inertia 130
4.3.4 Fluid Circuit Construction 132
4.3.5 An Acoustic Circuit Example 135
4.4 Transducers and Multi-Energy-Domain Models 136
4.4.1 Transformer Transducers 137
4.4.2 Gyrator Transducers 139
4.4.3 Multi-Energy-Domain Models 142
References 144
Problems 144
5 State-Space Equations and Automated Simulation 162
5.1 Standard Form for System Equations 165
5.2 Augmenting the Bond Graph 168
5.3 Basic Formulation and Reduction 175
5.4 Extended Formulation Methods-Algebraic Loops 183
5.4.1 Extended Formulation Methods-Derivative Causality 188
5.5 Output Variable Formulation 196
5.6 Nonlinear and Automated Simulation 198
5.6.1 Nonlinear Simulation 198
5.6.2 Automated Simulation 202
Reference 207
Problems 207
6 Analysis and Control of Linear Systems 218
6.1 Introduction 218
6.2 Solution Techniques for Ordinary Differential Equations 219
6.3 Free Response and Eigenvalues 222
6.3.1 A First-Order Example 223
6.3.2 Second-Order Systems 225
6.3.3 Example: The Undamped Oscillator 230
6.3.4 Example: The Damped Oscillator 232
6.3.5 The General Case 236
6.4 Transfer Functions 239
6.4.1 The General Case for Transfer Functions 241
6.5 Frequency Response 244
6.5.1 Example Transfer Functions and Frequency Responses 249
6.5.2 Block Diagrams 255
6.6 Introduction to Automatic Control 258
6.6.1 Basic Control Actions 259
6.6.2 Root Locus Concept 273
6.6.3 General Control Considerations 285
6.7 Summary 310
References 311
Problems 311
7 Multiport Fields and Junction Structures 326
7.1 Energy-Storing Fields 327
7.1.1 C-Fields 327
7.1.2 Causal Considerations for C-Fields 333
7.1.3 I -Fields 340
7.1.4 Mixed Energy-Storing Fields 348
7.2 Resistive Fields 350
7.3 Modulated 2-Port Elements 354
7.4 Junction Structures 357
7.5 Multiport Transformers 359
References 364
Problems 365
8 Transducers, Amplifiers, and Instruments 371
8.1 Power Transducers 372
8.2 Energy-Storing Transducers 380
8.3 Amplifiers and Instruments 385
8.4 Bond Graphs and Block Diagrams for Controlled Systems 392
References 397
Problems 397
9 Mechanical Systems with Nonlinear Geometry 411
9.1 Multidimensional Dynamics 412
9.1.1 Coordinate Transformations 416
9.2 Kinematic Nonlinearities in Mechanical Dynamics 420
9.2.1 The Basic Modeling Procedure 422
9.2.2 Multibody Systems 433
9.2.3 Lagrangian or Hamiltonian IC -Field Representations 440
9.3 Application to Vehicle Dynamics 445
9.4 Summary 452
References 452
Problems 453
10 Distributed-Parameter Systems 470
10.1 Simple Lumping Techniques for Distributed Systems 471
10.1.1 Longitudinal Motions of a Bar 471
10.1.2 Transverse Beam Motion 476
10.2 Lumped Models of Continua through Separation of Variables 482
10.2.1 The Bar Revisited 483
10.2.2 Bernoulli-Euler Beam Revisited 491
10.3 General Considerations of Finite-Mode Bond Graphs 499
10.3.1 How Many Modes Should Be Retained? 499
10.3.2 How to Include Damping 503
10.3.3 Causality Consideration for Modal Bond Graphs 503
10.4 Assembling Overall System Models 508
10.5 Summary 512
References 512
Problems 512
11 Magnetic Circuits and Devices 519
11.1 Magnetic Effort and Flow Variables 519
11.2 Magnetic Energy Storage and Loss 524
11.3 Magnetic Circuit Elements 528
11.4 Magnetomechanical Elements 532
11.5 Device Models 534
References 543
Problems 544
12 Thermofluid Systems 548
12.1 Pseudo-Bond Graphs for Heat Transfer 548
12.2 Basic Thermodynamics in True Bond Graph Form 551
12.3 True Bond Graphs for Heat Transfer 558
12.3.1 A Simple Example of a True Bond Graph Model 561
12.3.2 An Electrothermal Resistor 563
12.4 Fluid Dynamic Systems Revisited 565
12.4.1 One-Dimensional Incompressible Flow 569
12.4.2 Representation of Compressibility Effects in True Bond Graphs 573
12.4.3 Inertial and Compressibility Effects in One-Dimensional Flow 576
12.5 Pseudo-Bond Graphs for Compressible Gas Dynamics 578
12.5.1 The Thermodynamic Accumulator-A Pseudo-Bond Graph Element 579
12.5.2 The Thermodynamic Restrictor-A Pseudo-Bond Graph Element 584
12.5.3 Constructing Models with Accumulators and Restrictors 587
12.5.4 Summary 590
References 592
Problems 592
13 Nonlinear System Simulation 600
13.1 Explicit First-Order Differential Equations 601
13.2 Differential Algebraic Equations Caused by Algebraic Loops 604
13.3 Implicit Equations Caused by Derivative Causality 608
13.4 Automated Simulation of Dynamic Systems 612
13.4.1 Sorting of Equations 613
13.4.2 Implicit and Differential Algebraic Equation Solvers 614
13.4.3 Icon-Based Automated Simulation 614
13.5 Example Nonlinear Simulation 616
13.5.1 Some Simulation Results 620
13.6 Summary 623
References 624
Problems 624
Appendix: Typical Material Property Values Useful in Modeling
Mechanical, Acoustic, and Hydraulic Elements 630
Index 633
