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1Introduction to Control Systems1

1.1 Introduction2

1.2 History of automatic control4

1.3 Two examples of engineering creativity7

1.4 Control engineering practice8

1.5 Examples of modern control systems10

1.6 Control engineering design20

1.7 Design example20

Exercises22

Problems23

Design problems29

Terms and concepts31

References31

2Mathematical Models of Systems35

2.1 Introduction36

2.2 Differential equations of physical systems36

2.3 Linear approximations of physical systems42

2.4 The Laplace transform45

2.5 The transfer function of linear systems52

2.6 Block diagram models64

2.7 Signal-flow graph models69

2.8 Computer analysis of control systems75

2.9 Design examples79

2.10 Summary84

Exercises85

Problems92

Design problems110

Terms and concepts112

References112

3Feedback Control System Characteristics115

3.1 Open- and closed-loop control systems116

3.2 Sensitivity of control systems to parameter variations117

3.3 Control of the transient response of control systems121

3.4 Disturbance signals in a feedback control system124

3.5 Steady-state error129

3.6 The cost of feedback132

3.7 Design example134

3.8 Summary137

Exercises139

Problems141

Design problems152

Terms and concepts154

References155

4The Performance of Feedback Control Systems157

4.1 Introduction158

4.2 Time-domain performance specifications159

4.3 The s-plane root location and the transient response170

4.4 The steady-state error of feedback control systems171

4.5 Performance indices176

4.6 The simplilication of linear systems185

4.7 Design example188

4.8 Summary191

Exercises192

Problems196

Design problems204

Terms and concepts205

References205

5The Stability of Linear Feedback Systems207

5.1 The concept of stability208

5.2 The Routh-Hurwitz stability criterion211

5.3 The relative stability of feedback control systems218

5.4 The determination of root locations in the s-plane220

5.5 Design example223

5.6 Summary225

Exercises225

Problems227

Design problems231

Terms and concepts233

References233

6The Root Locus Method235

6.1 Introduction236

6.2 The root locus concept236

6.3 The root locus procedure241

6.4 An example of a control system analysis and design utilizing the root locus method256

6.5 Parameter design by the root locus method260

6.6 Sensitivity and the root locus265

6.7 Design example274

6.8 Summary277

Exercises277

Problems282

Design problems296

Terms and concepts299

References300

7Frequency Response Methods301

7.1 Introduction302

7.2 Frequency response plots304

7.3 An example of drawing the Bode diagram321

7.4 Frequency response measurements325

7.5 Performance specifications in the frequency domain327

7.6 Log magnitude and phase diagrams330

7.7 Design example332

7.8 Summary335

Exercises335

Problems339

Design problems349

Terms and concepts351

References352

8Stability in the Frequency Domain353

8.1 Introduction354

8.2 Mapping contours in the s-plane355

8.3 The Nyquist criterion360

8.4 Relative stability and the Nyquist criterion371

8.5 The closed-loop frequency response378

8.6 The stability of control systems with time delays386

8.7 System bandwidth388

8.8 Design example392

8.9 Summary403

Exercises404

Problems409

Design problems424

Terms and concepts427

References428

9Time-Domain Analysis of Control Systems429

9.1 Introduction430

9.2 The state variables of a dynamic system431

9.3 The state vector differential equation434

9.4 Signal-flow graph state models436

9.5 The stability of systems in the time domain444

9.6 The time response and the transition matrix450

9.7 A discrete-time evaluation of the time response454

9.8 Design example462

9.9 Summary466

Exercises466

Problems470

Design problems483

Terms and concepts485

References485

10The Design and Compensation of Feedback ControlSystems487

10.1 Introduction488

10.2 Approaches to compensation490

10.3 Cascade compensation networks492

10.4 System compensation on the Bode diagram using thephase-lead network497

10.5 Compensation on the s-plane using the phase-leadnetwork504

10.6 System compensation using integration networks512

10.7 Compensation on the s-plane using a phase-lag network515

10.8 Compensation on the Bode diagram using a phase-lagnetwork520

10.9 Compensation on the Bode diagram using analytical andcomputer methods526

10.10 The design of control systems in the time domain527

10.11 State-variable feedback539

10.12 Design example542

10.13 Summary546

Exercises548

Problems552

Design problems567

Terms and concepts570

References571

11Robust Control Systems573

11.1 Introduction574

11.2 Digital computer control system applications574

11.3 Automatic assembly and robots576

11.4 Robust control systems578

11.5 The design of robust control systems583

11.6 Three-term controllers590

11.7 The design of robust PID controlled systems594

11.8 The future evolution of robotics and control systems600

11.9 Summary601

Exercises603

Problems604

Design problems609

Terms and concepts615

References615

12Design Case Studies617

12.1 Engineering design618

12.2 Control system design619

12.3 The design of an X-Y plotter621

12.4 The design of a space telescope control system624

12.5 The design of a robot control system628

12.6 The design of a mobile robot control system631

12.7 The design of an ROV control system633

12.8 The design of a solar-powered racing car motor control system637

12.9 Summary640

Design problems641

Terms and concepts655

References655

Appendix A659

Laplace transform pairs659

Appendix B663

Symbols, units, and conversion factors663

Appendix C665

An introduction to matrix algebra665

Appendix D675

Decibel conversion675

Appendix E677

Complex numbers677

Appendix F683

The Control System Design Program683

Answers to Selected Problems703

Index and Glossary709