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1Introduction to Control Systems 1

1.1 Introduction 2

1.2 History of automatic control 4

1.3 Two examples of engineering creativity 7

1.4 Control engineering practice 8

1.5 Examples of modern control systems 10

1.6 Control engineering design 20

1.7 Design example 20

Exercises 22

Problems 23

Design problems 29

Terms and concepts 31

References 31

2Mathematical Models of Systems 35

2.1 Introduction 36

2.2 Differential equations of physical systems 36

2.3 Linear approximations of physical systems 42

2.4 The Laplace transform 45

2.5 The transfer function of linear systems 52

2.6 Block diagram models 64

2.7 Signal-flow graph models 69

2.8 Computer analysis of control systems 75

2.9 Design examples 79

2.10 Summary 84

Exercises 85

Problems 92

Design problems 110

Terms and concepts 112

References 112

3Feedback Control System Characteristics 115

3.1 Open- and closed-loop control systems 116

3.2 Sensitivity of control systems to parameter variations 117

3.3 Control of the transient response of control systems 121

3.4 Disturbance signals in a feedback control system 124

3.5 Steady-state error 129

3.6 The cost of feedback 132

3.7 Design example 134

3.8 Summary 137

Exercises 139

Problems 141

Design problems 152

Terms and concepts 154

References 155

4The Performance of Feedback Control Systems 157

4.1 Introduction 158

4.2 Time-domain performance specifications 159

4.3 The s-plane root location and the transient response 170

4.4 The steady-state error of feedback control systems 171

4.5 Performance indices 176

4.6 The simplilication of linear systems 185

4.7 Design example 188

4.8 Summary 191

Exercises 192

Problems 196

Design problems 204

Terms and concepts 205

References 205

5The Stability of Linear Feedback Systems 207

5.1 The concept of stability 208

5.2 The Routh-Hurwitz stability criterion 211

5.3 The relative stability of feedback control systems 218

5.4 The determination of root locations in the s-plane 220

5.5 Design example 223

5.6 Summary 225

Exercises 225

Problems 227

Design problems 231

Terms and concepts 233

References 233

6The Root Locus Method 235

6.1 Introduction 236

6.2 The root locus concept 236

6.3 The root locus procedure 241

6.4 An example of a control system analysis and design utilizing the root locus method 256

6.5 Parameter design by the root locus method 260

6.6 Sensitivity and the root locus 265

6.7 Design example 274

6.8 Summary 277

Exercises 277

Problems 282

Design problems 296

Terms and concepts 299

References 300

7Frequency Response Methods 301

7.1 Introduction 302

7.2 Frequency response plots 304

7.3 An example of drawing the Bode diagram 321

7.4 Frequency response measurements 325

7.5 Performance specifications in the frequency domain 327

7.6 Log magnitude and phase diagrams 330

7.7 Design example 332

7.8 Summary 335

Exercises 335

Problems 339

Design problems 349

Terms and concepts 351

References 352

8Stability in the Frequency Domain 353

8.1 Introduction 354

8.2 Mapping contours in the s-plane 355

8.3 The Nyquist criterion 360

8.4 Relative stability and the Nyquist criterion 371

8.5 The closed-loop frequency response 378

8.6 The stability of control systems with time delays 386

8.7 System bandwidth 388

8.8 Design example 392

8.9 Summary 403

Exercises 404

Problems 409

Design problems 424

Terms and concepts 427

References 428

9Time-Domain Analysis of Control Systems 429

9.1 Introduction 430

9.2 The state variables of a dynamic system 431

9.3 The state vector differential equation 434

9.4 Signal-flow graph state models 436

9.5 The stability of systems in the time domain 444

9.6 The time response and the transition matrix 450

9.7 A discrete-time evaluation of the time response 454

9.8 Design example 462

9.9 Summary 466

Exercises 466

Problems 470

Design problems 483

Terms and concepts 485

References 485

10The Design and Compensation of Feedback ControlSystems 487

10.1 Introduction 488

10.2 Approaches to compensation 490

10.3 Cascade compensation networks 492

10.4 System compensation on the Bode diagram using thephase-lead network 497

10.5 Compensation on the s-plane using the phase-leadnetwork 504

10.6 System compensation using integration networks 512

10.7 Compensation on the s-plane using a phase-lag network 515

10.8 Compensation on the Bode diagram using a phase-lagnetwork 520

10.9 Compensation on the Bode diagram using analytical andcomputer methods 526

10.10 The design of control systems in the time domain 527

10.11 State-variable feedback 539

10.12 Design example 542

10.13 Summary 546

Exercises 548

Problems 552

Design problems 567

Terms and concepts 570

References 571

11Robust Control Systems 573

11.1 Introduction 574

11.2 Digital computer control system applications 574

11.3 Automatic assembly and robots 576

11.4 Robust control systems 578

11.5 The design of robust control systems 583

11.6 Three-term controllers 590

11.7 The design of robust PID controlled systems 594

11.8 The future evolution of robotics and control systems 600

11.9 Summary 601

Exercises 603

Problems 604

Design problems 609

Terms and concepts 615

References 615

12Design Case Studies 617

12.1 Engineering design 618

12.2 Control system design 619

12.3 The design of an X-Y plotter 621

12.4 The design of a space telescope control system 624

12.5 The design of a robot control system 628

12.6 The design of a mobile robot control system 631

12.7 The design of an ROV control system 633

12.8 The design of a solar-powered racing car motor control system 637

12.9 Summary 640

Design problems 641

Terms and concepts 655

References 655

Appendix A 659

Laplace transform pairs 659

Appendix B 663

Symbols, units, and conversion factors 663

Appendix C 665

An introduction to matrix algebra 665

Appendix D 675

Decibel conversion 675

Appendix E 677

Complex numbers 677

Appendix F 683

The Control System Design Program 683

Answers to Selected Problems 703

Index and Glossary 709