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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