Control Systems Engineering

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