Feedback control of dynamic systems

Cover......Page 1
Contents......Page 6
Preface......Page 14
 A Perspective on Feedback Control......Page 20
 Chapter Overview......Page 21
 1.1 A Simple Feedback System......Page 22
 1.2 A First Analysis of Feedback......Page 25
 1.3 A Brief History......Page 28
 1.4 An Overview of the Book......Page 33
 Review Questions......Page 35
 Problems......Page 36
 A Perspective on Dynamic Models......Page 39
  2.1.1 Translational Motion......Page 40
  2.1.2 Rotational Motion......Page 46
  2.1.3 Combined Rotation and Translation......Page 55
  2.1.4 Distributed Parameter Systems......Page 57
  2.1.5 Summary: Developing Equations of Motion for Rigid Bodies......Page 59
 2.2 Models of Electric Circuits......Page 60
 2.3 Models of Electromechanical Systems......Page 64
  2.4.1 Heat Flow......Page 69
  2.4.2 Incompressible Fluid Flow......Page 73
 2.5 Historical Perspective......Page 79
 Summary......Page 81
 Review Questions......Page 82
 Problems......Page 83
 A Perspective on System Response......Page 93
  3.1.1 Response by Convolution......Page 94
  3.1.2 Transfer Functions and Frequency Response......Page 99
  3.1.3 The L- Laplace Transform......Page 106
  3.1.4 Properties of Laplace Transforms......Page 108
  3.1.5 Inverse Laplace Transform by Partial-Fraction Expansion......Page 110
  3.1.6 The Final Value Theorem......Page 112
  3.1.7 Using Laplace Transforms to Solve Problems......Page 113
  3.1.8 Poles and Zeros......Page 115
  3.1.9 Linear System Analysis Using MATLAB......Page 116
  3.2.1 The Block Diagram......Page 121
  3.2.2 Block Diagram Reduction Using MATLAB......Page 126
 3.3 Effect of Pole Locations......Page 127
  3.4.1 Rise Time......Page 135
  3.4.2 Overshoot and Peak Time......Page 136
  3.4.3 Settling Time......Page 137
 3.5 Effects of Zeros and Additional Poles......Page 139
  3.6.1 Bounded Input–Bounded Output Stability......Page 149
  3.6.2 Stability of LTI Systems......Page 150
  3.6.3 Routh's Stability Criterion......Page 151
 3.7 Obtaining Models from Experimental Data......Page 159
  3.7.1 Models from Transient-Response Data......Page 161
  3.7.2 Models from Other Data......Page 165
  3.8.1 Amplitude Scaling......Page 166
  3.8.2 Time Scaling......Page 167
 3.9 Historical Perspective......Page 168
 Summary......Page 169
 Review Questions......Page 170
 Problems......Page 171
 A Perspective on the Analysis of Feedback......Page 189
 4.1 The Basic Equations of Control......Page 190
  4.1.1 Stability......Page 192
  4.1.3 Regulation......Page 193
  4.1.4 Sensitivity......Page 194
 4.2 Control of Steady-State Error to Polynomial Inputs: System Type......Page 197
  4.2.1 System Type for Tracking......Page 198
  4.2.2 System Type for Regulation and Disturbance Rejection......Page 202
 4.3 The Three-Term Controller: PID Control......Page 205
  4.3.2 Proportional Plus Integral Control (PI)......Page 206
  4.3.3 PID Control......Page 207
  4.3.4 Ziegler–Nichols Tuning of the PID Controller......Page 211
 4.4 Introduction to Digital Control......Page 217
 4.5 Historical Perspective......Page 222
 Summary......Page 224
 Review Questions......Page 225
 Problems......Page 226
 A Perspective on the Root-Locus Design Method......Page 239
 5.1 Root Locus of a Basic Feedback System......Page 240
 5.2 Guidelines for Determining a Root Locus......Page 245
  5.2.1 Rules for Plotting a Positive (180°) Root Locus......Page 247
  5.2.2 Summary of the Rules for Determining a Root Locus......Page 252
  5.2.3 Selecting the Parameter Value......Page 253
 5.3 Selected Illustrative Root Loci......Page 255
 5.4 Design Using Dynamic Compensation......Page 267
  5.4.1 Design Using Lead Compensation......Page 268
  5.4.2 Design Using Lag Compensation......Page 273
  5.4.3 Design Using Notch Compensation......Page 274
  5.4.4 Analog and Digital Implementations......Page 276
 5.5 A Design Example Using the Root Locus......Page 279
  5.6.1 Rules for Plotting a Negative (0°) Root Locus......Page 285
  5.6.2 Consideration of Two Parameters......Page 289
  5.6.3 Time Delay......Page 291
 5.7 Historical Perspective......Page 293
 Summary......Page 295
 Problems......Page 297
 A Perspective on the Frequency-Response Design Method......Page 315
 6.1 Frequency Response......Page 316
  6.1.1 Bode Plot Techniques......Page 323
  6.1.2 Steady-State Errors......Page 334
 6.2 Neutral Stability......Page 336
 6.3 The Nyquist Stability Criterion......Page 338
  6.3.1 The Argument Principle......Page 339
  6.3.2 Application to Control Design......Page 340
 6.4 Stability Margins......Page 353
 6.5 Bode's Gain–Phase Relationship......Page 360
 6.6 Closed-Loop Frequency Response......Page 365
 6.7 Compensation......Page 366
  6.7.2 Lead Compensation......Page 367
  6.7.4 Lag Compensation......Page 379
  6.7.5 PID Compensation......Page 384
  6.7.6 Design Considerations......Page 390
  6.7.7 Specifications in Terms of the Sensitivity Function......Page 392
  6.7.8 Limitations on Design in Terms of the Sensitivity Function......Page 396
 6.8 Time Delay......Page 400
  6.9.1 Nichols Chart......Page 401
 Summary......Page 405
 Review Questions......Page 407
 Problems......Page 408
 Chapter Overview......Page 432
 7.1 Advantages of State-Space......Page 433
 7.2 System Description in State-Space......Page 435
 7.3 Block Diagrams and State-Space......Page 440
  7.3.1 Time and Amplitude Scaling in State-Space......Page 443
  7.4.1 Block Diagrams and Canonical Forms......Page 444
  7.4.2 Dynamic Response from the State Equations......Page 455
 7.5 Control-Law Design for Full-State Feedback......Page 461
  7.5.1 Finding the Control Law......Page 462
  7.5.2 Introducing the Reference Input with Full-State Feedback......Page 470
 7.6 Selection of Pole Locations for Good Design......Page 474
  7.6.1 Dominant Second-Order Poles......Page 475
  7.6.2 Symmetric Root Locus (SRL)......Page 476
  7.7.1 Full-Order Estimators......Page 485
  7.7.2 Reduced-Order Estimators......Page 491
  7.7.3 Estimator Pole Selection......Page 495
 7.8 Compensator Design: Combined Control Law and Estimator......Page 497
 7.9 Introduction of the Reference Input with the Estimator......Page 510
  7.9.1 A General Structure for the Reference Input......Page 511
  7.9.2 Selecting the Gain......Page 520
 7.10 Integral Control and Robust Tracking......Page 521
  7.10.1 Integral Control......Page 522
  7.10.2 Robust Tracking Control: The Error-Space Approach......Page 524
  7.10.3 The Extended Estimator......Page 535
 7.11 Loop Transfer Recovery (LTR)......Page 538
 7.12 Direct Design with Rational Transfer Functions......Page 543
 7.13 Design for Systems with Pure Time Delay......Page 546
 7.14 Historical Perspective......Page 549
 Summary......Page 552
 Review Questions......Page 553
 Problems......Page 555
 A Perspective on Digital Control......Page 577
 8.1 Digitization......Page 578
  8.2.1 z-Transform......Page 580
  8.2.2 z-Transform Inversion......Page 581
  8.2.3 Relationship between s and z......Page 584
  8.2.4 Final Value Theorem......Page 585
 8.3 Design Using Discrete Equivalents......Page 587
  8.3.1 Matched Pole–Zero (MPZ) Method......Page 590
  8.3.3 Comparison of Digital Approximation Methods......Page 594
  8.3.4 Applicability Limits of the Discrete Equivalent Design Method......Page 595
  8.4.1 Analog-to-Digital (A/D) Converters......Page 596
  8.4.3 Anti-Alias Prefilters......Page 597
  8.4.4 The Computer......Page 598
 8.5 Sample-Rate Selection......Page 599
  8.5.2 Disturbance Rejection......Page 600
  8.5.3 Effect of Anti-Alias Prefilter......Page 601
  8.6.1 Analysis Tools......Page 602
  8.6.2 Feedback Properties......Page 604
  8.6.3 Discrete Design Example......Page 605
  8.6.4 Discrete Analysis of Designs......Page 607
 8.7 Historical Perspective......Page 609
 Summary......Page 610
 Review Questions......Page 611
 Problems......Page 612
 Perspective on Nonlinear Systems......Page 618
 9.1 Introduction and Motivation: Why Study Nonlinear Systems?......Page 619
 9.2 Analysis by Linearization......Page 621
  9.2.1 Linearization by Small-Signal Analysis......Page 622
  9.2.3 Linearization by Inverse Nonlinearity......Page 627
 9.3 Equivalent Gain Analysis Using the Root Locus......Page 628
  9.3.1 Integrator Antiwindup......Page 634
 9.4 Equivalent Gain Analysis Using Frequency Response: Describing Functions......Page 638
  9.4.1 Stability Analysis Using Describing Functions......Page 644
 9.5 Analysis and Design Based on Stability......Page 648
  9.5.1 The Phase Plane......Page 649
  9.5.2 Lyapunov Stability Analysis......Page 655
  9.5.3 The Circle Criterion......Page 661
 9.6 Historical Perspective......Page 667
 Summary......Page 668
 Problems......Page 669
 A Perspective on Design Principles......Page 679
 Chapter Overview......Page 680
 10.1 An Outline of Control Systems Design......Page 681
 10.2 Design of a Satellite's Attitude Control......Page 686
 10.3 Lateral and Longitudinal Control of a Boeing 747......Page 703
  10.3.1 Yaw Damper......Page 708
  10.3.2 Altitude-Hold Autopilot......Page 715
 10.4 Control of the Fuel–Air Ratio in an Automotive Engine......Page 721
 10.5 Control of the Read/Write Head Assembly of a Hard Disk......Page 728
 10.6 Control of RTP Systems in Semiconductor Wafer Manufacturing......Page 736
 10.7 Chemotaxis or How E. Coli Swims Away from Trouble......Page 750
 10.8 Historical Perspective......Page 758
 Summary......Page 760
 Review Questions......Page 761
 Problems......Page 762
  A.1.1 Properties of Laplace Transforms......Page 776
  A.1.2 Inverse Laplace Transform by Partial-Fraction Expansion......Page 785
  A.1.3 The Initial Value Theorem......Page 788
  A.1.4 Final Value Theorem......Page 789
Appendix B: Solutions to the Review Questions......Page 791
Appendix C: MATLAB Commands......Page 807
Bibliography......Page 812
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 E......Page 824
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 I......Page 826
 L......Page 827
 M......Page 828
 N......Page 829
 P......Page 830
 R......Page 832
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 T......Page 836
 Z......Page 838