Dynamic Systems: Modeling, Simulation, and Control

Preface vi

1 Introduction to Dynamic Systems and Control 1

1.1 Introduction 1

1.2 Classification of Dynamic Systems 2

1.3 Modeling Dynamic Systems 4

1.4 Objectives and Textbook Outline 5

References 6

2 Modeling Mechanical Systems 7

2.1 Introduction 7

2.2 Mechanical Element Laws 7

2.3 Translational Mechanical Systems 13

2.4 Rotational Mechanical Systems 24

Summary 30

References 30

Problems 30

3 Modeling Electrical and Electromechanical Systems 43

3.1 Introduction 43

3.2 Electrical Element Laws 43

3.3 Electrical Systems 46

3.4 Operational-Amplifier Circuits 54

3.5 Electromechanical Systems 57

Summary 68

References 69

Problems 69

4 Modeling Fluid and Thermal Systems 80

4.1 Introduction 80

4.2 Hydraulic Systems 80

4.3 Pneumatic Systems 93

4.4 Thermal Systems 99

Summary 104

References 105

Problems 105

5 Standard Models for Dynamic Systems 115

5.1 Introduction 115

5.2 State-Variable Equations 115

5.3 State-Space Representation 119

5.4 Linearization 128

5.5 Input-Output Equations 133

5.6 Transfer Functions 136

5.7 Block Diagrams 139

5.8 Standard Input Functions 143

Summary 145

Problems 146

6 Numerical Simulation of Dynamic Systems 156

6.1 Introduction 156

6.2 System Response Using MATLAB Commands 157

6.3 Building Simulations Using Simulink 162

6.4 Simulating Linear Systems Using Simulink 165

6.5 Simulating Nonlinear Systems 170

6.6 Building Integrated Systems 178

Summary 183

References 184

Problems 184

7 Analytical Solution of Linear Dynamic Systems 197

7.1 Introduction 197

7.2 Analytical Solutions to Linear Differential Equations 197

7.3 First-Order System Response 205

7.4 Second-Order System Response 213

7.5 Higher-Order Systems 230

7.6 State-Space Representation and Eigenvalues 232

7.7 Approximate Models 235

Summary 237

Reference 238

Problems 238

8 System Analysis Using Laplace Transforms 247

8.1 Introduction 247

8.2 Laplace Transformation 247

8.3 Inverse Laplace Transformation 254

8.4 Analysis of Dynamic Systems Using Laplace Transforms 259

Summary 271

References 271

Problems 271

9 Frequency-Response Analysis 277

9.1 Introduction 277

9.2 Frequency Response 277

9.3 Bode Diagrams 290

9.4 Vibrations 306

Summary 313

References 313

Problems 313

10 Introduction to Control Systems 322

10.1 Introduction 322

10.2 Feedback Control Systems 322

10.3 Feedback Controllers 329

10.4 Steady-State Accuracy 344

10.5 Closed-Loop Stability 350

10.6 Root-Locus Method 352

10.7 Stability Margins 373

10.8 Implementing Control Systems 381

Summary 385

References 385

Problems 386

11 Case Studies in Dynamic Systems and Control 397

11.1 Introduction 397

11.2 Vibration Isolation System for a Commercial Vehicle 397

11.3 Solenoid Actuator–Valve System 409

11.4 Pneumatic Air-Brake System 417

11.5 Hydraulic Servomechanism Control 427

11.6 Feedback Control of a Magnetic Levitation System 444

Summary 455

References 455

Appendix A Units 457

Appendix B MATLAB Primer for Analyzing Dynamic Systems 459

B.1 Introduction 459

B.2 Basic MATLAB Computations 459

B.3 Plotting with MATLAB 462

B.4 Constructing Basic M-files 463

B.5 Commands for Linear System Analysis 464

B.6 Commands for Laplace Transform Analysis 465

B.7 Commands for Control System Analysis 467

Appendix C Simulink Primer 469

C.1 Introduction 469

C.2 Building Simulink Models of Linear Systems 469

C.3 Building Simulink Models of Nonlinear Systems 478

C.4 Summary of Useful Simulink Blocks 482

Index 485