Dynamic Systems

Student solution available in interactive e-text

Preface viii

1 Introduction to Dynamic Systems and Control 1

1.1 Introduction 1

1.2 Classification of Dynamic Systems 2

1.3 Modeling Dynamic Systems 3

1.4 Objectives and Textbook Outline 4

References 5

2 Modeling Mechanical Systems 6

2.1 Introduction 6

2.2 Mechanical Element Laws 6

2.3 Translational Mechanical Systems 11

2.4 Rotational Mechanical Systems 21

Summary 26

References 27

3 Modeling Electrical and Electromechanical Systems 28

3.1 Introduction 28

3.2 Electrical Element Laws 28

3.3 Electrical Systems 31

3.4 Operational-Amplifier Circuits 38

3.5 Electromechanical Systems 41

Summary 51

References 52

4 Modeling Fluid and Thermal Systems 53

4.1 Introduction 53

4.2 Hydraulic Systems 53

4.3 Pneumatic Systems 65

4.4 Thermal Systems 70

Summary 75

References 75

5 Standard Models for Dynamic Systems 76

5.1 Introduction 76

5.2 State-Variable Equations 76

5.3 State-Space Representation 79

5.4 Linearization 88

5.5 Input¢"Output Equations 93

5.6 Transfer Functions 95

5.7 Block Diagrams 98

5.8 Standard Input Functions 102

Summary 104

Reference 104

6 Numerical Simulation of Dynamic Systems 105

6.1 Introduction 105

6.2 System Response Using MATLAB Commands 105

6.3 Building Simulations Using Simulink 111

6.4 Simulating Linear Systems Using Simulink 113

6.5 Simulating Nonlinear Systems 117

6.6 Building Integrated Systems 124

Summary 129

References 129

7 Analytical Solution of Linear Dynamic Systems 131

7.1 Introduction 131

7.2 Analytical Solutions to Linear Differential Equations 131

7.3 First-Order System Response 138

7.4 Second-Order System Response 145

7.5 Higher-Order Systems 161

7.6 State-Space Representation and Eigenvalues 162

7.7 Approximate Models 165

Summary 167

Reference 168

8 System Analysis Using Laplace Transforms 169

8.1 Introduction 169

8.2 Laplace Transformation 169

8.3 Inverse Laplace Transformation 176

8.4 Analysis of Dynamic Systems Using Laplace Transforms 180

Summary 191

References 191

9 Frequency-Response Analysis 192

9.1 Introduction 192

9.2 Frequency Response 192

9.3 Bode Diagrams 203

9.4 Vibrations 218

Summary 223

References 224

10 Introduction to Control Systems 225

10.1 Introduction 225

10.2 Feedback Control Systems 225

10.3 Feedback Controllers 231

10.4 Steady-State Accuracy 245

10.5 Closed-Loop Stability 250

10.6 Root-Locus Method 252

10.7 Stability Margins 271

10.8 Implementing Control Systems 278

Summary 281

References 282

11 Case Studies in Dynamic Systems and Control 283

11.1 Introduction 283

11.2 Vibration Isolation System for a Commercial Vehicle 283

11.3 Solenoid Actuator¢"Valve System 294

11.4 Pneumatic Air-Brake System 301

11.5 Hydraulic Servomechanism Control 311

11.6 Feedback Control of a Magnetic Levitation System 326

Summary 335

References 336

Problems P-1

Appendix A Units A-1

Appendix B MATLAB Primer for Analyzing Dynamic Systems A-2

B.1 Introduction A-2

B.2 Basic MATLAB Computations A-2

B.3 Plotting with MATLAB A-5

B.4 Constructing Basic M-files A-6

B.5 Commands for Linear System Analysis A-7

B.6 Commands for Laplace Transform Analysis A-8

B.7 Commands for Control System Analysis A-9

Appendix C Simulink Primer A-11

C.1 Introduction A-11

C.2 Building Simulink Models of Linear Systems A-11

C.3 Building Simulink Models of Nonlinear Systems A-19

C.4 Summary of Useful Simulink Blocks A-22

Index I-1