Table of Contents

PREFACE, vii

1. INTRODUCTION, 1

1.1 Introduction, 2

1.2 A History of Control Systems, 4

1.3 System Configurations, 7

1.4 Analysis and Design Objectives, 10

Case Study, 12

1.5 The Design Process, 15

1.6 Computer–Aided Design, 20

1.7 The Control Systems Engineer, 21

Summary, 23

Review Questions, 23

Problems, 24

Cyber Exploration Laboratory, 30

Bibliography, 31

2. MODELING IN THE FREQUENCY DOMAIN, 33

2.1 Introduction, 34

2.2 Laplace Transform Review, 35

2.3 The Transfer Function, 44

2.4 Electrical Network Transfer Functions, 47

2.5 Translational Mechanical System Transfer Functions, 61

2.6 Rotational Mechanical System Transfer Functions, 69

2.7 Transfer Functions for Systems with Gears, 74

2.8 Electromechanical System Transfer Functions, 79

2.9 Electric Circuit Analogs, 84

2.10 Nonlinearities, 88

2.11 Linearization, 89

Case Studies, 94

Summary, 97

Review Questions, 97

Problems, 98

Cyber Exploration Laboratory, 112

Bibliography, 115

3. MODELING IN THE TIME DOMAIN, 117

3.1 Introduction, 118

3.2 Some Observations, 119

3.3 The General State–Space Representation, 123

3.4 Applying the State–Space Representation, 124

3.5 Converting a Transfer Function to State Space, 132

3.6 Converting from State Space to a Transfer Function, 139

3.7 Linearization, 141

Case Studies, 144

Summary, 148

Review Questions, 149

Problems, 149

Cyber Exploration Laboratory, 157

Bibliography, 159

4. TIME RESPONSE, 161

4.1 Introduction, 162

4.2 Poles, Zeros, and System Response, 162

4.3 First–Order Systems, 166

4.4 Second–Order Systems: Introduction, 168

4.5 The General Second–Order System, 173

4.6 Underdamped Second–Order Systems, 177

4.7 System Response with Additional Poles, 186

4.8 System Response With Zeros, 191

4.9 Effects of Nonlinearities Upon Time Response, 196

4.10 Laplace Transform Solution of State Equations, 199

4.11 Time Domain Solution of State Equations, 203

Case Studies, 207

Summary, 213

Review Questions, 214

Problems, 215

Cyber Exploration Laboratory, 228

Bibliography, 232

5. REDUCTION OF MULTIPLE SUBSYSTEMS, 235

5.1 Introduction, 236

5.2 Block Diagrams, 236

5.3 Analysis and Design of Feedback Systems, 245

5.4 Signal–Flow Graphs, 248

5.5 Mason s Rule, 251

5.6 Signal–Flow Graphs of State Equations, 254

5.7 Alternative Representations in State Space, 256

5.8 Similarity Transformations, 266

Case Studies, 272

Summary, 278

Review Questions, 279

Problems, 280

Cyber Exploration Laboratory, 297

Bibliography, 299

6. STABILITY, 301

6.1 Introduction, 302

6.2 Routh–Hurwitz Criterion, 305

6.3 Routh–Hurwitz Criterion: Special Cases, 308

6.4 Routh–Hurwitz Criterion: Additional Examples, 314

6.5 Stability in State Space, 320

Case Studies, 323

Summary, 325

Review Questions, 325

Problems, 326

Cyber Exploration Laboratory, 335

Bibliography, 336

7. STEADY–STATE ERRORS, 339

7.1 Introduction, 340

7.2 Steady–State Error for Unity Feedback Systems, 343

7.3 Static Error Constants and System Type, 349

7.4 Steady–State Error Specifications, 353

7.5 Steady–State Error for Disturbances, 356

7.6 Steady–State Error for Nonunity Feedback Systems, 358

7.7 Sensitivity, 362

7.8 Steady–State Error for Systems in State Space, 364

Case Studies, 368

Summary, 371

Review Questions, 372

Problems, 373

Cyber Exploration Laboratory, 384

Bibliography, 386

8. ROOT LOCUS TECHNIQUES, 387

8.1 Introduction, 388

8.2 Defining the Root Locus, 392

8.3 Properties of the Root Locus, 394

8.4 Sketching the Root Locus, 397

8.5 Refining the Sketch, 402

8.6 An Example, 411

8.7 Transient Response Design via Gain Adjustment, 415

8.8 Generalized Root Locus, 419

8.9 Root Locus for Positive–Feedback Systems, 421

8.10 Pole Sensitivity, 424

Case Studies, 426

Summary, 431

Review Questions, 432

Problems, 432

Cyber Exploration Laboratory, 450

Bibliography, 452

9. DESIGN VIA ROOT LOCUS, 455

9.1 Introduction, 456

9.2 Improving Steady–State Error via Cascade Compensation, 459

9.3 Improving Transient Response via Cascade Compensation, 469

9.4 Improving Steady–State Error and Transient Response, 482

9.5 Feedback Compensation, 495

9.6 Physical Realization of Compensation, 503

Case Studies, 508

Summary, 513

Review Questions, 514

Problems, 515

Cyber Exploration Laboratory, 530

Bibliography, 531

10. FREQUENCY RESPONSE TECHNIQUES, 533

10.1 Introduction, 534

10.2 Asymptotic Approximations: Bode Plots, 540

10.3 Introduction to the Nyquist Criterion, 559

10.4 Sketching the Nyquist Diagram, 564

10.5 Stability via the Nyquist Diagram, 569

10.6 Gain Margin and Phase Margin via the Nyquist Diagram, 574

10.7 Stability, Gain Margin, and Phase Margin via Bode Plots, 576

10.8 Relation Between Closed–Loop Transient and Closed–Loop Frequency Responses, 580

10.9 Relation Between Closed– and Open–Loop Frequency Responses, 583

10.10 Relation Between Closed–Loop Transient and Open–Loop Frequency Responses, 589

10.11 Steady–State Error Characteristics from Frequency Response, 593

10.12 Systems with Time Delay, 597

10.13 Obtaining Transfer Functions Experimentally, 602

Case Study, 606

Summary, 607

Review Questions, 609

Problems, 610

Cyber Exploration Laboratory, 621

Bibliography, 623

11. DESIGN VIA FREQUENCY RESPONSE, 625

11.1 Introduction, 626

11.2 Transient Response via Gain Adjustment, 627

11.3 Lag Compensation, 630

11.4 Lead Compensation, 635

11.5 Lag–Lead Compensation, 641

Case Studies, 650

Summary, 652

Review Questions, 653

Problems, 653

Cyber Exploration Laboratory, 660

Bibliography, 661

12. DESIGN VIA STATE SPACE, 663

12.1 Introduction, 664

12.2 Controller Design, 665

12.3 Controllability, 672

12.4 Alternative Approaches to Controller Design, 676

12.5 Observer Design, 682

12.6 Observability, 689

12.7 Alternative Approaches to Observer Design, 693

12.8 Steady–State Error Design Via Integral Control, 700

Case Study, 704

Summary, 709

Review Questions, 710

Problems, 711

Cyber Exploration Laboratory, 719

Bibliography, 721

13. DIGITAL CONTROL SYSTEMS, 723

13.1 Introduction , 724

13.2 Modeling the Digital Computer, 727

13.3 The z–Transform, 730

13.4 Transfer Functions, 735

13.5 Block Diagram Reduction, 739

13.6 Stability, 742

13.7 Steady–State Errors, 749

13.8 Transient Response on the z–Plane, 753

13.9 Gain Design on the z–Plane, 755

13.10 Cascade Compensation via the s–Plane, 758

13.11 Implementing the Digital Compensator, 762

Case Studies, 765

Summary, 769

Review Questions, 770

Problems, 771

Cyber Exploration Laboratory, 778

Bibliography, 780

Appendix A List of Symbols, 783

Appendix B MATLAB Tutorial, 787

B.1 Introduction, 787

B.2 MATLAB Examples, 788

B.3 Command Summary, 833

Bibliography, 835

Appendix C MATLAB s Simulink Tutorial, 836

C.1 Introduction, 836

C.2 Using Simulink, 836

C.3 Examples, 841

Summary, 855

Bibliography, 856

Appendix D LabVIEW Tutorial, 857

D.1 Introduction, 857

D.2 Control Systems Analysis, Design, and Simulation, 858

D.3 Using LabVIEW, 859

D.4 Analysis and Design Examples, 862

D.5 Simulation Examples, 876

Summary, 885

Bibliography, 886

Glossary, 887

Answers to Selected Problems (Online) Credits, 903

Index, 907

Appendix E MATLAB s GUI Tools Tutorial (Online)

Appendix F MATLAB s Symbolic Math Toolbox Tutorial (Online)

Appendix G Matrices, Determinants, and Systems of Equations (Online)

Appendix H Control System Computational Aids (Online)

Appendix I Derivation of a Schematic for a DC Motor (Online)

Appendix J Derivation of the Time Domain Solution of State Equations (Online)

Appendix K Solution of State Equations for t0 6¼ 0 (Online)

Appendix L Derivation of Similarity Transformations (Online)

Appendix M Root Locus Rules: Derivations (Online)

Control Systems Engineering Toolbox (Online)

Cyber Exploration Laboratory Experiments Covers Sheets (Online)

Lecture Graphics (Online)

Solutions to Skill–Assessment Exercises (Online)

Online location is www.wiley.com/go/global/nise