1 INTRODUCTION TO SYSTEM DYNAMICS 1
1-1 Introduction 1
1-2 Mathematical Modeling of Dynamic Systems 3
1-3 Analysis and Design of Dynamic Systems 5
1-4 Summary 6
2 THE LAPLACE TRANSFORM 8
2-1 Introduction 8
2-2 Complex Numbers，Complex Variables，and Complex Functions 8
2-3 Laplace Transformation 14
2-4 Inverse Laplace Transformation 29
2-5 Solving Linear，Time-Invariant Differential Equations 34
Example Problems and Solutions 36
Problems 49
3 MECHANICAL SYSTEMS 53
3-1 Introduction 53
3-2 Mechanical Elements 57
3-3 Mathematical Modeling of Simple Mechanical Systems 61
3-4 Work，Energy，and Power 73
Example Problems and Solutions 81
Problems 100
4 TRANSFER-FUNCTION APPROACH TO MODELING DYNAMIC SYSTEMS 106
4-1 Introduction 106
4-2 Block Diagrams 109
4-3 Partial-Fraction Expansion with MATLAB 112
4-4 Transient-Response Analysis with MATLAB 119
Example Problems and Solutions 135
Problems 162
5 STATE-SPACE APPROACH TO MODELING DYNAMIC SYSTEMS 169
5-1 Introduction 169
5-2 Transient-Response Analysis of Systems in State-Space Form with MATLAB 174
5-3 State-Space Modeling of Systems with No Input Derivatives 181
5-4 State-Space Modeling of Systems with Input Derivatives 187
5-5 Transformation of Mathematical Models with MATLAB 202
Example Problems and Solutions 209
Problems 239
6 ELECTRICAL SYSTEMS AND ELECTROMECHANICAL SYSTEMS 251
6-1 Introduction 251
6-2 Fundamentals of Electrical Circuits 254
6-3 Mathematical Modeling of Electrical Systems 261
6-4 Analogous Systems 270
6-5 Mathematical Modeling of Electromechanical Systems 274
6-6 Mathematical Modeling of Operational-Amplifier Systems 281
Example Problems and Solutions 288
Problems 312
7 FLUID SYSTEMS AND THERMAL SYSTEMS 323
7-1 Introduction 323
7-2 Mathematical Modeling of Liquid-Level Systems 324
7-3 Mathematical Modeling of Pneumatic Systems 332
7-4 Linearization of Nonlinear Systems 337
7-5 Mathematical Modeling of Hydraulic Systems 340
7-6 Mathematical Modeling of Thermal Systems 348
Example Problems and Solutions 352
Problems 375
8 TIME-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS 383
8-1 Introduction 383
8-2 Transient-Response Analysis of First-Order Systems 384
8-3 Transient-Response Analysis of Second-Order Systems 388
8-4 Transient-Response Analysis of Higher Order Systems 399
8-5 Solution of the State Equation 400
Example Problems and Solutions 409
Problems 424
9 FREQUENCY-DOMAIN ANALYSIS OF DYNAMIC SYSTEMS 431
9-1 Introduction 431
9-2 Sinusoidal Transfer Function 432
9-3 Vibrations in Rotating Mechanical Systems 438
9-4 Vibration Isolation 441
9-5 Dynamic Vibration Absorbers 447
9-6 Free Vibrations in Multi-Degrees-of-Freedom Systems 453
Example Problems and Solutions 458
Problems 484
10 TIME-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS 491
10-1 Introduction 491
10-2 Block Diagrams and Their Simplification 494
10-3 Automatic Controllers 501
10-4 Transient-Response Analysis 506
10-5 Transient-Response Specifications 513
10-6 Improving Transient-Response and Steady-State Characteristics 522
10-7 Stability Analysis 538
10-8 Root-Locus Analysis 545
10-9 Root-Locus Plots with MATLAB 562
10-10 Tuning Rules for PID Controllers 566
Example Problems and Solutions 576
Problems 600
11 FREQUENCY-DOMAIN ANALYSIS AND DESIGN OF CONTROL SYSTEMS 608
11-1 Introduction 608
11-2 Bode Diagram Representation of the Frequency Response 609
11-3 Plotting Bode Diagrams with MATLAB 629
11-4 Nyquist Plots and the Nyquist Stability Criterion 630
11-5 Drawing Nyquist Plots with MATLAB 640
11-6 Design of Control Systems in the Frequency Domain 643
Example Problems and Solutions 668
Problems 690
APPENDIX A SYSTEMS OF UNITS 695
APPENDIX B CONVERSION TABLES 700
APPENDIX C VECTOR-MATRIX ALGEBRA 705
APPENDIX D INTRODUCTION TO MATLAB 720
REFERENCES 757
INDEX 759