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Contents

PREFACE, vii 1 INTRODUCTION, 1 1.1 Introduction, 2 1.2 A History of Control Systems, 4 1.3 System Con?gurations, 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 Speci?cations, 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 De?ning the Root Locus, 310 8.3 Properties of the Root Locus, 312 8.4 Sketching the Root Locus, 314 8.5 Re?ning 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)

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