Preface v

1. Introduction 1

1.1 Introduction 1

1.2 System Configurations 4

1.3 Servomechanism 6

1.4 A History of Control Systems 7

1.5 Analysis and Design Objectives 11

1.6 The Design Process 16

1.7 Multivariable Systems 21

1.8 Computer-Aided Design 22

1.9 The Control Systems Engineer 24

Summary 25

Review Questions 26

Problems 26

Cyber Exploration Laboratory 34

Bibliography 34

2. Modeling in the Frequency Domain 37

2.1 Introduction 37

2.2 Laplace Transform Review 38

2.3 The Transfer Function 48

2.4 Electrical Network Transfer Functions 51

2.5 Translational Mechanical System Transfer Functions 65

2.6 Rotational Mechanical System Transfer Functions 73

2.7 Transfer Functions for Systems with Gears 77

2.8 Electromechanical System Transfer Functions 81

2.9 Electric Circuit Analogs 87

2.10 Nonlinearities 90

2.11 Linearization 91

Summary 99

Review Questions 99

Problems 100

Cyber Exploration Laboratory 114

Hardware Interface Laboratory 117

Bibliography 120

3. Modeling in the Time Domain 123

3.1 Introduction 123

3.2 Some Observations 124

3.3 The General State-Space Representation 129

3.4 Applying the State-Space Representation 131

3.5 Converting a Transfer Function to State Space 139

3.6 Converting from State Space to a Transfer Function 146

3.7 Linearization 148

Summary 156

Review Questions 157

Problems 157

Cyber Exploration Laboratory 169

Bibliography 171

4. Time Response Analysis 173

4.1 Introduction 174

4.2 Poles Zeros and System Response 174

4.3 First-Order Systems 177

4.4 Second-Order Systems: Introduction 180

4.5 The General Second-Order System 185

4.6 Underdamped Second-Order Systems 189

4.7 System Response with Additional Poles 198

4.8 System Response with Zeros 202

4.9 Effects of Nonlinearities upon Time Response 208

4.10 Laplace Transform Solution of State Equations 210

4.11 Time Domain Solution of State Equations 214

Summary 224

Review Questions 225

Problems 226

Cyber Exploration Laboratory 243

Hardware Interface Laboratory 246

Bibliography 252

5. Reduction of Multiple Subsystems 255

5.1 Introduction 255

5.2 Block Diagrams 256

5.3 Analysis and Design of Feedback Systems 265

5.4 Signal-Flow Graphs 268

5.5 Mason’s Rule 271

5.6 Signal-Flow Graphs of State Equations 274

5.7 Alternative Representations in State Space 276

5.8 Similarity Transformations 285

Summary 298

Review Questions 298

Problems 299

Cyber Exploration Laboratory 319

Bibliography 321

6. Stability 323

6.1 Introduction 323

6.2 Routh-Hurwitz Criterion 327

6.3 Routh-Hurwitz Criterion: Special Cases 329

6.4 Routh-Hurwitz Criterion: Additional Examples 335

6.5 Stability in State Space 342

Summary 347

Review Questions 347

Problems 348

Cyber Exploration Laboratory 361

Bibliography 362

7. Steady-state Errors 365

7.1 Introduction 365

7.2 Steady-State Error for Unity-Feedback Systems 369

7.3 Static Error Constants and System Type 375

7.4 Steady-State Error Specifications 378

7.5 Steady-State Error for Disturbances 381

7.6 Steady-State Error for Nonunity-Feedback Systems 383

7.7 Sensitivity 386

7.8 Steady-State Error for Systems in State Space 389

Summary 395

Review Questions 396

Problems 397

Cyber Exploration Laboratory 411

Bibliography 412

8. Root Locus Techniques 415

8.1 Introduction 415

8.2 Defining the Root Locus 420

8.3 Properties of the Root Locus 422

8.4 Sketching the Root Locus 424

8.5 Refining the Sketch 429

8.6 An Example 438

8.7 Transient Response Design via Gain Adjustment 441

8.8 Generalized Root Locus 445

8.9 Root Locus for Positive-Feedback Systems 447

8.10 Pole Sensitivity 449

Summary 456

Review Questions 457

Problems 457

Cyber Exploration Laboratory 479

Hardware Interface Laboratory 481

Bibliography 487

9. Design Via Root Locus 489

9.1 Introduction 489

9.2 Improving Steady-State Error via Cascade Compensation 493

9.3 Improving Transient Response via Cascade Compensation 502

9.4 Improving Steady-State Error and Transient Response 515

9.5 Feedback Compensation 528

9.6 Physical Realization of Compensation 536

9.7 Tuning of PID Controllers 541

Summary 560

Review Questions 561

Problems 561

Cyber Exploration Laboratory 578

Hardware Interface Laboratory 580

Bibliography 582

10. Frequency Response Techniques 585

10.1 Introduction 585

10.2 Asymptotic Approximations: Bode Plots 591

10.3 All-Pass and Nonminimum-Phase

Systems 610

10.4 Introduction to the Nyquist Criterion 615

10.5 Sketching the Nyquist Diagram 619

10.6 Stability via the Nyquist Diagram 625

10.7 Gain Margin and Phase Margin via the Nyquist Diagram 629

10.8 Stability Gain Margin and Phase Margin via Bode Plots 632

10.9 Relation Between Closed-Loop Transient and Closed-Loop Frequency Responses 635

10.10 Relation Between Closed- and Open-Loop Frequency Responses 638

10.11 Relation Between Closed-Loop Transient and Open-Loop Frequency Responses 644

10.12 Steady-State Error Characteristics from Frequency Response 648

10.13 Systems with Time Delay 652

10.14 Obtaining Transfer Functions Experimentally 657

Summary 662

Review Questions 664

Problems 665

Cyber Exploration Laboratory 676

Bibliography 678

11. Design Via Frequency Response 681

11.1 Introduction 681

11.2 Transient Response via Gain Adjustment 683

11.3 Lag Compensation 686

11.4 Lead Compensation 691

11.5 Lag-Lead Compensation 697

Summary 708

Review Questions 708

Problems 709

Cyber Exploration Laboratory 718

Bibliography 719

12. Design Via State Space 721

12.1 Introduction 721

12.2 Controller Design 723

12.3 Controllability 730

12.4 Alternative Approaches to Controller Design 733

12.5 Observer Design 739

12.6 Observability 746

12.7 Alternative Approaches to Observer Design 749

12.8 Steady-State Error Design via Integral Control 756

Summary 765

Review Questions 766

Problems 767

Cyber Exploration Laboratory 776

Bibliography 778

13. Digital Control Systems 779

13.1 Introduction 779

13.2 Modeling the Digital Computer 783

13.3 The z-Transform 786

13.4 Transfer Functions 791

13.5 Block Diagram Reduction 795

13.6 Stability 798

13.7 Steady-State Errors 805

13.8 Transient Response on the z-Plane 809

13.9 Gain Design on the z-Plane 811

13.10 Cascade Compensation via the s-Plane 815

13.11 Implementing the Digital Compensator 818

Summary 825

Review Questions 826

Problems 827

Cyber Exploration Laboratory 836

Bibliography 838

14. Optimal Control Systems 839
(Available Online)

14.1 Introduction 839

14.2 Performance Indices 841

14.3 Optimal Control Problem 846

14.4 Regulator Problem 849

14.5 State Regulator 851

14.6 Output Regulator 859

14.7 Tracking Problem 861

Summary 869

Review Questions 870

Problems 870

Cyber Exploration Laboratory 873

Bibliography 875

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

Online Appendices

Appendix B MATLAB Tutorial

Appendix C Simulink Tutorial

Appendix D LabVIEW Tutorial

Appendix E MATLAB’s GUI Tools Tutorial

Appendix F MATLAB’s Symbolic Math Toolbox Tutorial

Appendix G Matrices Determinants and Systems of Equations

Appendix H Control System Computational Aids

Appendix I Derivation of a Schematic for a DC Motor

Appendix J Derivation of the Time Domain Solution of State Equations

Appendix K Solution of State Equations for t 0 ≠ 0

Appendix L Derivation of Similarity Transformations

Appendix M Root Locus Rules: Derivations