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
6.1Introduction, 243
6.2Routh-Hurwitz Criterion, 246
6.3Routh-Hurwitz Criterion: Special Cases, 248
6.4Routh-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 State 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
8.7Transient 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 (Available in e-text for students) P-1

APPENDIX A1 List of Symbols A-1.1
APPENDIX A2 Antenna Azimuth Position Control System A-2.1
APPENDIX A3 Unmanned Free-Swimming Submersible Vehicle A-3.1
APPENDIX A4 Key Equations A-4.1

GLOSSARY 628
ANSWERS TO SELECTED PROBLEMS (Available in ext for students) 636 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)

Table of Contents