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Copyright, ii
Preface, xiii
1. An Overview and Brief History of Feedback Control, 1
A Perspective on Feedback Control, 1
Chapter Overview, 2
1.1. A Simple Feedback System, 3
1.2. A First Analysis of Feedback, 6
1.3. A Brief History, 9
1.4. An Overview of the Book, 14
Summary, 16
Review Questions, 16
Problems, 17
2. Dynamic Models, 20
A Perspective on Dynamic Models, 20
Chapter Overview, 21
2.1. Dynamics of Mechanical Systems, 21
2.1.1. Translational Motion, 21
2.1.2. Rotational Motion, 27
2.1.3. Combined Rotation and Translation, 36
2.1.4. Distributed Parameter Systems, 38
2.1.5. Summary: Developing Equations of Motion for Rigid Bodies, 40
2.2. Models of Electric Circuits, 41
2.3. Models of Electromechanical Systems, 45
2.4. Heat and Fluid-Flow Models, 50
2.4.1. Heat Flow, 50
2.4.2. Incompressible Fluid Flow, 54
2.5. Historical Perspective, 60
Summary, 62
Review Questions, 63
Problems, 64
3. Dynamic Response, 74
A Perspective on System Response, 74
Chapter Overview, 75
3.1. Review of Laplace Transforms, 75
3.1.1. Response by Convolution, 75
3.1.2. Transfer Functions and Frequency Response, 80
3.1.3. The L- Laplace Transform, 87
3.1.4. Properties of Laplace Transforms, 89
3.1.5. Inverse Laplace Transform by Partial-Fraction Expansion, 91
3.1.6. The Final Value Theorem, 93
3.1.7. Using Laplace Transforms to Solve Problems, 94
3.1.8. Poles and Zeros, 96
3.1.9. Linear System Analysis Using MATLAB, 97
3.2. System Modeling Diagrams, 102
3.2.1. The Block Diagram, 102
3.2.2. Block Diagram Reduction Using MATLAB, 107
3.3. Effect of Pole Locations, 108
3.4. Time-Domain Specifications, 116
3.4.1. Rise Time, 116
3.4.2. Overshoot and Peak Time, 117
3.4.3. Settling Time, 118
3.5. Effects of Zeros and Additional Poles, 120
3.6. Stability, 130
3.6.1. Bounded Input–Bounded Output Stability, 130
3.6.2. Stability of LTI Systems, 131
3.6.3. Routh’s Stability Criterion, 132
3.7. Obtaining Models from Experimental Data, 140
3.7.1. Models from Transient-Response Data, 142
3.7.2. Models from Other Data, 146
3.8. Amplitude and Time Scaling, 147
3.8.1. Amplitude Scaling, 147
3.8.2. Time Scaling, 148
3.9. Historical Perspective, 149
Summary, 150
Review Questions, 151
Problems, 152
4. A First Analysis of Feedback, 170
A Perspective on the Analysis of Feedback, 170
Chapter Overview, 171
4.1. The Basic Equations of Control, 171
4.1.1. Stability, 173
4.1.2. Tracking, 174
4.1.3. Regulation, 174
4.1.4. Sensitivity, 175
4.2. Control of Steady-State Error to Polynomial Inputs: System Type, 178
4.2.1. System Type for Tracking, 179
4.2.2. System Type for Regulation and Disturbance Rejection, 183
4.3. The Three-Term Controller: PID Control, 186
4.3.1. Proportional Control (P), 187
4.3.2. Proportional Plus Integral Control (PI), 187
4.3.3. PID Control, 188
4.3.4. Ziegler–Nichols Tuning of the PID Controller, 192
4.4. Introduction to Digital Control, 198
4.5. Historical Perspective, 203
Summary, 205
Review Questions, 206
Problems, 207
5. The Root-Locus Design Method, 220
A Perspective on the Root-Locus Design Method, 220
Chapter Overview, 221
5.1. Root Locus of a Basic Feedback System, 221
5.2. Guidelines for Determining a Root Locus, 226
5.2.1. Rules for Plotting a Positive (180°) Root Locus, 228
5.2.2. Summary of the Rules for Determining a Root Locus, 233
5.2.3. Selecting the Parameter Value, 234
5.3. Selected Illustrative Root Loci, 236
5.4. Design Using Dynamic Compensation, 248
5.4.1. Design Using Lead Compensation, 249
5.4.2. Design Using Lag Compensation, 254
5.4.3. Design Using Notch Compensation, 255
5.4.4. Analog and Digital Implementations, 257
5.5. A Design Example Using the Root Locus, 260
5.6. Extensions of the Root-Locus Method, 266
5.6.1. Rules for Plotting a Negative (0°) Root Locus, 266
5.6.2. Consideration of Two Parameters, 270
5.6.3. Time Delay, 272
5.7. Historical Perspective, 274
Summary, 276
Review Questions, 278
Problems, 278
6. The Frequency-Response Design Method, 296
A Perspective on the Frequency-Response Design Method, 296
Chapter Overview, 297
6.1. Frequency Response, 297
6.1.1. Bode Plot Techniques, 304
6.1.2. Steady-State Errors, 315
6.2. Neutral Stability, 317
6.3. The Nyquist Stability Criterion, 319
6.3.1. The Argument Principle, 320
6.3.2. Application to Control Design, 321
6.4. Stability Margins, 334
6.5. Bode’s Gain–Phase Relationship, 341
6.6. Closed-Loop Frequency Response, 346
6.7. Compensation, 347
6.7.1. PD Compensation, 348
6.7.2. Lead Compensation, 348
6.7.3. PI Compensation, 360
6.7.4. Lag Compensation, 360
6.7.5. PID Compensation, 365
6.7.6. Design Considerations, 371
6.7.7. Specifications in Terms of the Sensitivity Function, 373
6.7.8. Limitations on Design in Terms of the Sensitivity Function, 377
6.8. Time Delay, 381
6.9. Alternative Presentation of Data, 382
6.9.1. Nichols Chart, 382
6.10. Historical Perspective, 386
Summary, 386
Review Questions, 388
Problems, 389
7. State-Space Design, 413
A Perspective on State-Space Design, 413
Chapter Overview, 413
7.1. Advantages of State-Space, 414
7.2. System Description in State-Space, 416
7.3. Block Diagrams and State-Space, 421
7.3.1. Time and Amplitude Scaling in State-Space, 424
7.4. Analysis of the State Equations, 425
7.4.1. Block Diagrams and Canonical Forms, 425
7.4.2. Dynamic Response from the State Equations, 436
7.5. Control-Law Design for Full-State Feedback, 442
7.5.1. Finding the Control Law, 443
7.5.2. Introducing the Reference Input with Full-State Feedback, 451
7.6. Selection of Pole Locations for Good Design, 455
7.6.1. Dominant Second-Order Poles, 456
7.6.2. Symmetric Root Locus (SRL), 457
7.6.3. Comments on the Methods, 466
7.7. Estimator Design, 466
7.7.1. Full-Order Estimators, 466
7.7.2. Reduced-Order Estimators, 472
7.7.3. Estimator Pole Selection, 476
7.8. Compensator Design: Combined Control Law and Estimator, 478
7.9. Introduction of the Reference Input with the Estimator, 491
7.9.1. A General Structure for the Reference Input, 492
7.9.2. Selecting the Gain, 501
7.10. Integral Control and Robust Tracking, 502
7.10.1. Integral Control, 503
7.10.2. Robust Tracking Control: The Error-Space Approach, 505
7.10.3. The Extended Estimator, 516
7.11. Loop Transfer Recovery (LTR), 519
7.12. Direct Design with Rational Transfer Functions, 524
7.13. Design for Systems with Pure Time Delay, 527
7.14. Historical Perspective, 530
Summary, 533
Review Questions, 534
Problems, 536
8. Digital Control, 558
A Perspective on Digital Control, 558
Chapter Overview, 559
8.1. Digitization, 559
8.2. Dynamic Analysis of Discrete Systems, 561
8.2.1. z-Transform, 561
8.2.2. z-Transform Inversion, 562
8.2.3. Relationship between s and z, 565
8.2.4. Final Value Theorem, 566
8.3. Design Using Discrete Equivalents, 568
8.3.1. Matched Pole–Zero (MPZ) Method, 571
8.3.2. Modified Matched Pole–Zero (MMPZ) Method, 575
8.3.3. Comparison of Digital Approximation Methods, 575
8.3.4. Applicability Limits of the Discrete Equivalent Design Method, 576
8.4. Hardware Characteristics, 577
8.4.1. Analog-to-Digital (A/D) Converters, 577
8.4.2. Digital-to-Analog (D/A) Converters, 578
8.4.3. Anti-Alias Prefilters, 578
8.4.4. The Computer, 579
8.5. Sample-Rate Selection, 580
8.5.1. Tracking Effectiveness, 581
8.5.2. Disturbance Rejection, 581
8.5.3. Effect of Anti-Alias Prefilter, 582
8.5.4. Asynchronous Sampling, 583
8.6. Discrete Design, 583
8.6.1. Analysis Tools, 583
8.6.2. Feedback Properties, 585
8.6.3. Discrete Design Example, 586
8.6.4. Discrete Analysis of Designs, 588
8.7. Historical Perspective, 590
Summary, 591
Review Questions, 592
Problems, 593
9. Nonlinear Systems, 599
Perspective on Nonlinear Systems, 599
Chapter Overview, 600
9.1. Introduction and Motivation: Why Study Nonlinear Systems?, 600
9.2. Analysis by Linearization, 602
9.2.1. Linearization by Small-Signal Analysis, 603
9.2.2. Linearization by Nonlinear Feedback, 608
9.2.3. Linearization by Inverse Nonlinearity, 608
9.3. Equivalent Gain Analysis Using the Root Locus, 609
9.3.1. Integrator Antiwindup, 615
9.4. Equivalent Gain Analysis Using Frequency Response: Describing Functions, 619
9.4.1. Stability Analysis Using Describing Functions, 625
9.5. Analysis and Design Based on Stability, 629
9.5.1. The Phase Plane, 630
9.5.2. Lyapunov Stability Analysis, 636
9.5.3. The Circle Criterion, 642
9.6. Historical Perspective, 648
Summary, 649
Review Questions, 650
Problems, 650
10. Control System Design: Principles and Case Studies, 660
A Perspective on Design Principles, 660
Chapter Overview, 661
10.1. An Outline of Control Systems Design, 662
10.2. Design of a Satellite’s Attitude Control, 667
10.3. Lateral and Longitudinal Control of a Boeing 747, 684
10.3.1. Yaw Damper, 689
10.3.2. Altitude-Hold Autopilot, 696
10.4. Control of the Fuel–Air Ratio in an Automotive Engine, 702
10.5. Control of the Read/Write Head Assembly of a Hard Disk, 709
10.6. Control of RTP Systems in Semiconductor Wafer Manufacturing, 717
10.7. Chemotaxis or How E. Coli Swims Away from Trouble, 731
10.8. Historical Perspective, 739
Summary, 741
Review Questions, 742
Problems, 743
Appendix A. Laplace Transforms, 757
A.1. The L- Laplace Transform, 757
A.1.1. Properties of Laplace Transforms, 757
A.1.2. Inverse Laplace Transform by Partial-Fraction Expansion, 766
A.1.3. The Initial Value Theorem, 769
A.1.4. Final Value Theorem, 770
Appendix B. Solutions to the Review Questions, 772
Appendix C. MATLAB Commands, 788
Bibliography, 793
Index, 801
Table of Laplace Transforms, EP-1
Chronological History of Feedback Control, EP-2
MATLAB Functions, EP-3
Design Aids, EP-4

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