Preface vii

1. Introduction 1

1.1 Introduction 2

1.2 A History of Control Systems 4

1.3 System Configurations 6

1.4 Analysis and Design Objectives 9

Case Study 11

1.5 The Design Process 14

1.6 Computer-Aided Design 19

1.7 The Control Systems Engineer 20

Summary 21

Review Questions 22

Cyber Exploration Laboratory 22

Bibliography 23

2. Modeling In The Frequency Domain 25

2.1 Introduction 26

2.2 Laplace Transform Review 27

2.3 The Transfer Function 36

2.4 Electrical Network Transfer Functions 39

2.5 Translational Mechanical System Transfer Functions 53

2.6 Rotational Mechanical System Transfer Functions 61

2.7 Transfer Functions for Systems with Gears 65

2.8 Electromechanical System Transfer Functions 69

2.9 Electric Circuit Analogs 75

2.10 Nonlinearities 78

2.11 Linearization 79

Case Studies 84

Summary 87

Review Questions 87

Cyber Exploration Laboratory 88

Hardware Interface Laboratory 91

Bibliography 93

3. Modeling In The Time Domain 95

3.1 Introduction 96

3.2 Some Observations 96

3.3 The General State-Space Representation 100

3.4 Applying the State-Space Representation 102

3.5 Converting a Transfer Function to State Space 110

3.6 Converting from State Space to a Transfer Function 116

3.7 Linearization 118

Case Studies 121

Summary 125

Review Questions 126

Cyber Exploration Laboratory 126

Bibliography 128

4. Time Response 130

4.1 Introduction 131

4.2 Poles, Zeros, and System Response 131

4.3 First-Order Systems 135

4.4 Second-Order Systems: Introduction 137

4.5 The General Second-Order System 142

4.6 Underdamped Second-Order Systems 146

4.7 System Response with Additional Poles 155

4.8 System Response with Zeros 159

4.9 Effects of Nonlinearities upon Time Response 165

4.10 Laplace Transform Solution of State Equations 167

4.11 Time Domain Solution of State Equations 171

Case Studies 175

Summary 181

Review Questions 182

Cyber Exploration Laboratory 183

Hardware Interface Laboratory 186

Bibliography 192

5. Reduction of Multiple Subsystems 194

5.1 Introduction 195

5.2 Block Diagrams 195

5.3 Analysis and Design of Feedback Systems 204

5.4 Signal-Flow Graphs 207

5.5 Mason’s Rule 210

5.6 Signal-Flow Graphs of State Equations 213

5.7 Alternative Representations in State Space 215

5.8 Similarity Transformations 224

Case Studies 231

Summary 237

Review Questions 237

Cyber Exploration Laboratory 238

Bibliography 240

6. Stability 242

6.1 Introduction 243

6.2 Routh-Hurwitz Criterion 246

6.3 Routh-Hurwitz Criterion: Special Cases 248

6.4 Routh-Hurwitz Criterion: Additional Examples 254

6.5 Stability in State Space 261

Case Studies 264

Summary 266

Review Questions 266

Cyber Exploration Laboratory 267

Bibliography 268

7. Steady-State Errors 270

7.1 Introduction 271

7.2 Steady-State Error for Unity Feedback Systems 274

7.3 Static Error Constants and System Type 280

7.4 Steady-State Error Specifications 283

7.5 Steady-State Error for Disturbances 286

7.6 Steady-State Error for Nonunity-Feedback Systems 288

7.7 Sensitivity 291

7.8 Steady-State Error for Systems in 0State Space 294

Case Studies 297

Summary 300

Review Questions 301

Cyber Exploration Laboratory 302

Bibliography 303

8. Root Locus Techniques 305

8.1 Introduction 306

8.2 Defining the Root Locus 310

8.3 Properties of the Root Locus 312

8.4 Sketching the Root Locus 314

8.5 Refining the Sketch 319

8.6 An Example 328

8.7 Transient Response Design via Gain Adjustment 331

8.8 Generalized Root Locus 335

8.9 Root Locus for Positive-Feedback Systems 337

8.10 Pole Sensitivity 339

Case Studies 341

Summary 346

Review Questions 347

Cyber Exploration Laboratory 347

Hardware Interface Laboratory 349

Bibliography 356

9. Design Via Root Locus 358

9.1 Introduction 359

9.2 Improving Steady-State Error via Cascade Compensation 362

9.3 Improving Transient Response via Cascade Compensation 371

9.4 Improving Steady-State Error and Transient Response 383

9.5 Feedback Compensation 396

9.6 Physical Realization of Compensation 404

Case Studies 409

Summary 413

Review Questions 414

Cyber Exploration Laboratory 415

Hardware Interface Laboratory 417

Bibliography 419

10. Frequency Response Techniques 421

10.1 Introduction 422

10.2 Asymptotic Approximations: Bode Plots 427

10.3 Introduction to the Nyquist Criterion 446

10.4 Sketching the Nyquist Diagram 451

10.5 Stability via the Nyquist Diagram 456

10.6 Gain Margin and Phase Margin via the Nyquist Diagram 460

10.7 Stability, Gain Margin, and Phase Margin via Bode Plots 462

10.8 Relation Between Closed-Loop Transient and Closed-Loop Frequency Responses 466

10.9 Relation Between Closed- and Open-Loop Frequency Responses 469

10.10 Relation Between Closed-Loop Transient and Open-Loop Frequency Responses 474

10.11 Steady-State Error Characteristics from Frequency Response 478

10.12 Systems with Time Delay 482

10.13 Obtaining Transfer Functions Experimentally 487

Case Study 491

Summary 492

Review Questions 493

Cyber Exploration Laboratory 494

Bibliography 496

11. Design Via Frequency Response 498

11.1 Introduction 499

11.2 Transient Response via Gain Adjustment 500

11.3 Lag Compensation 503

11.4 Lead Compensation 508

11.5 Lag-Lead Compensation 514

Case Studies 523

Summary 525

Review Questions 525

Cyber Exploration Laboratory 526

Bibliography 527

12. Design Via State Space 528

12.1 Introduction 529

12.2 Controller Design 530

12.3 Controllability 537

12.4 Alternative Approaches to Controller Design 540

12.5 Observer Design 546

12.6 Observability 553

12.7 Alternative Approaches to Observer Design 556

12.8 Steady-State Error Design via Integral Control 563

Case Study 567

Summary 572

Review Questions 573

Cyber Exploration Laboratory 574

Bibliography 575

13. Digital Control Systems 577

13.1 Introduction 578

13.2 Modeling the Digital Computer 581

13.3 The z-Transform 584

13.4 Transfer Functions 589

13.5 Block Diagram Reduction 593

13.6 Stability 596

13.7 Steady-State Errors 603

13.8 Transient Response on the z-Plane 607

13.9 Gain Design on the z-Plane 609

13.10 Cascade Compensation via the s-Plane 612

13.11 Implementing the Digital Compensator 616

Case Studies 619

Summary 623

Review Questions 624

Cyber Exploration Laboratory 625

Bibliography 627

Problems P-1

Appendix A1 List of Symbols A-1

Appendix A2 Antenna Azimuth Position Control System A-5

Appendix A3 Unmanned Free-Swimming Submersible Vehicle A-7

Appendix A4 Key Equations A-8

Glossary G-1

Answers To Selected Problems ANS-1

Index I-1

Appendix B Matlab Tutorial (Available in e-text for students)

Appendix C Simulink Tutorial (Available in e-text for students)

Appendix D LabVIEW Tutorial (Available in e-text for students)

Appendix E MATLAB’s GUI Tools Tutorial (Available in e-text for students)

Appendix F MATLAB’s Symbolic Math Toolbox Tutorial (Available in e-text for students)

Appendix G Matrices, Determinants, and Systems of Equations (Available in e-text for students)

Appendix H Control System Computational Aids (Available in e-text for students)

Appendix I Derivation of a Schematic for a DC Motor (Available in e-text for students)

Appendix J Derivation of the Time Domain Solution of State Equations (Available in e-text for students)

Appendix K Solution of State Equations for t0 ≠ ۰ (Available in e-text for students)

Appendix L Derivation of Similarity Transformations (Available in e-text for students)

Appendix M Root Locus Rules: Derivations (Available in e-text for students)