Feedback Control of Dynamic Systems

Cover......Page 1
Title Page......Page 2
Copyright Page......Page 3
Dedication......Page 4
Contents......Page 6
Preface......Page 14
A Perspective on Feedback Control......Page 22
Chapter Overview......Page 23
1.1 A Simple Feedback System......Page 24
1.2 A First Analysis of Feedback......Page 27
1.3 Feedback System Fundamentals......Page 31
1.4 A Brief History......Page 32
1.5 An Overview of the Book......Page 38
Review Questions......Page 40
Problems......Page 41
A Perspective on Dynamic Models......Page 44
2.1.1 Translational Motion......Page 45
2.1.2 Rotational Motion......Page 52
2.1.3 Combined Rotation and Translation......Page 60
2.1.5 Distributed Parameter Systems......Page 63
2.1.6 Summary: Developing Equations of Motion for Rigid Bodies......Page 65
2.2 Models of Electric Circuits......Page 66
2.3.1 Loudspeakers......Page 71
2.3.2 Motors......Page 73
2.3.3 Gears......Page 77
2.4 Heat and Fluid-Flow Models......Page 78
2.4.1 Heat Flow......Page 79
2.4.2 Incompressible Fluid Flow......Page 82
2.5 Historical Perspective......Page 89
Review Questions......Page 92
Problems......Page 93
A Perspective on System Response......Page 105
3.1 Review of Laplace Transforms......Page 106
3.1.1 Response by Convolution......Page 107
3.1.2 Transfer Functions and Frequency Response......Page 112
3.1.3 The L− Laplace Transform......Page 122
3.1.4 Properties of Laplace Transforms......Page 124
3.1.5 Inverse Laplace Transform by Partial-Fraction Expansion......Page 126
3.1.6 The Final Value Theorem......Page 128
3.1.7 Using Laplace Transforms to Solve Differential Equations......Page 130
3.1.8 Poles and Zeros......Page 132
3.1.9 Linear System Analysis Using Matlab......Page 133
3.2.1 The Block Diagram......Page 139
3.2.2 Block-Diagram Reduction Using Matlab......Page 143
3.3 Effect of Pole Locations......Page 144
3.4 Time-Domain Specifications......Page 152
3.4.2 Overshoot and Peak Time......Page 153
3.4.3 Settling Time......Page 155
3.5 Effects of Zeros and Additional Poles......Page 158
3.6 Stability......Page 167
3.6.1 Bounded Input–Bounded Output Stability......Page 168
3.6.2 Stability of LTI Systems......Page 169
3.6.3 Routh’s Stability Criterion......Page 170
3.9 Historical Perspective......Page 177
Summary......Page 178
Problems......Page 180
A Perspective on the Analysis of Feedback......Page 201
Chapter Overview......Page 202
4.1 The Basic Equations of Control......Page 203
4.1.1 Stability......Page 204
4.1.2 Tracking......Page 205
4.1.3 Regulation......Page 206
4.1.4 Sensitivity......Page 207
4.2 Control of Steady-State Error to Polynomial Inputs: System Type......Page 209
4.2.1 System Type for Tracking......Page 210
4.2.2 System Type for Regulation and Disturbance Rejection......Page 215
4.3.1 Proportional Control (P)......Page 217
4.3.2 Integral Control (I)......Page 219
4.3.4 Proportional Plus Integral Control (PI)......Page 222
4.3.5 PID Control......Page 223
4.3.6 Ziegler–Nichols Tuning of the PID Controller......Page 227
4.4 Feedforward Control by Plant Model Inversion......Page 233
4.5 Introduction to Digital Control (W)......Page 235
4.7 Historical Perspective......Page 236
Summary......Page 238
Problems......Page 239
A Perspective on the Root-Locus Design Method......Page 255
5.1 Root Locus of a Basic Feedback System......Page 256
5.2 Guidelines for Determining a Root Locus......Page 261
5.2.1 Rules for Determining a Positive (180˚) Root Locus......Page 263
5.2.2 Summary of the Rules for Determining a Root Locus......Page 269
5.2.3 Selecting the Parameter Value......Page 270
5.3 Selected Illustrative Root Loci......Page 272
5.4 Design Using Dynamic Compensation......Page 285
5.4.1 Design Using Lead Compensation......Page 287
5.4.2 Design Using Lag Compensation......Page 291
5.4.3 Design Using Notch Compensation......Page 293
5.4.4 Analog and Digital Implementations (W)......Page 295
5.5 A Design Example Using the Root Locus......Page 296
5.6.1 Rules for Plotting a Negative (0˚) Root Locus......Page 302
5.6.2 Consideration of Two Parameters......Page 305
5.6.3 Time Delay (W)......Page 307
5.7 Historical Perspective......Page 308
Summary......Page 310
Review Questions......Page 311
Problems......Page 312
A Perspective on the Frequency-Response Design Method......Page 329
6.1 Frequency Response......Page 330
6.1.1 Bode Plot Techniques......Page 338
6.1.2 Steady-State Errors......Page 351
6.2 Neutral Stability......Page 352
6.3 The Nyquist Stability Criterion......Page 354
6.3.1 The Argument Principle......Page 355
6.3.2 Application of The Argument Principle to Control Design......Page 356
6.4 Stability Margins......Page 369
6.5 Bode’s Gain–Phase Relationship......Page 378
6.6 Closed-Loop Frequency Response......Page 382
6.7.1 PD Compensation......Page 384
6.7.2 Lead Compensation (W)......Page 385
6.7.3 PI Compensation......Page 395
6.7.4 Lag Compensation......Page 396
6.7.5 PID Compensation......Page 402
6.7.6 Design Considerations......Page 408
6.7.7 Specifications in Terms of the Sensitivity Function......Page 410
6.7.8 Limitations on Design in Terms of the Sensitivity Function......Page 415
6.8 Time Delay......Page 419
6.9.1 Nichols Chart......Page 421
6.10 Historical Perspective......Page 425
Summary......Page 426
Problems......Page 429
A Perspective on State-Space Design......Page 454
7.1 Advantages of State-Space......Page 455
7.2 System Description in State-Space......Page 457
7.3 Block Diagrams and State-Space......Page 463
7.4 Analysis of the State Equations......Page 465
7.4.1 Block Diagrams and Canonical Forms......Page 466
7.4.2 Dynamic Response from the State Equations......Page 478
7.5 Control-Law Design for Full-State Feedback......Page 484
7.5.1 Finding the Control Law......Page 485
7.5.2 Introducing the Reference Input with Full-State Feedback......Page 494
7.6.1 Dominant Second-Order Poles......Page 498
7.6.2 Symmetric Root Locus (SRL)......Page 500
7.6.3 Comments on the Methods......Page 509
7.7.1 Full-Order Estimators......Page 510
7.7.2 Reduced-Order Estimators......Page 516
7.7.3 Estimator Pole Selection......Page 520
7.8 Compensator Design: Combined Control Law and Estimator (W)......Page 522
7.9 Introduction of the Reference Input with the Estimator (W)......Page 535
7.9.1 General Structure for the Reference Input......Page 536
7.9.2 Selecting the Gain......Page 545
7.10 Integral Control and Robust Tracking......Page 546
7.10.1 Integral Control......Page 547
7.10.2 Robust Tracking Control: The Error-Space Approach......Page 549
7.10.3 Model-Following Design......Page 560
7.10.4 The Extended Estimator......Page 564
7.11 Loop Transfer Recovery......Page 568
7.12 Direct Design with Rational Transfer Functions......Page 573
7.13 Design for Systems with Pure Time Delay......Page 577
7.15 Historical Perspective......Page 580
Summary......Page 583
Review Questions......Page 586
Problems......Page 587
A Perspective on Digital Control......Page 611
8.1 Digitization......Page 612
8.2.1 z-Transform......Page 615
8.2.2 z-Transform Inversion......Page 616
8.2.3 Relationship Between s and z......Page 618
8.2.4 Final Value Theorem......Page 620
8.3 Design Using Discrete Equivalents......Page 622
8.3.1 Tustin’s Method......Page 623
8.3.2 Zero-Order Hold (ZOH) Method......Page 626
8.3.3 Matched Pole–Zero (MPZ) Method......Page 628
8.3.4 Modified Matched Pole–Zero (MMPZ) Method......Page 632
8.3.5 Comparison of Digital Approximation Methods......Page 633
8.4 Hardware Characteristics......Page 634
8.4.2 Digital-to-Analog Converters......Page 635
8.4.3 Anti-Alias Prefilters......Page 636
8.4.4 The Computer......Page 637
8.5 Sample-Rate Selection......Page 638
8.5.2 Disturbance Rejection......Page 639
8.5.3 Effect of Anti-Alias Prefilter......Page 640
8.6 Discrete Design......Page 641
8.6.1 Analysis Tools......Page 642
8.6.2 Feedback Properties......Page 643
8.6.3 Discrete Design Example......Page 644
8.6.4 Discrete Analysis of Designs......Page 647
8.8 Historical Perspective......Page 649
Summary......Page 650
Problems......Page 652
A Perspective on Nonlinear Systems......Page 658
Chapter Overview......Page 659
9.1 Introduction and Motivation: Why Study Nonlinear Systems?......Page 660
9.2.1 Linearization by Small-Signal Analysis......Page 662
9.2.2 Linearization by Nonlinear Feedback......Page 667
9.2.3 Linearization by Inverse Nonlinearity......Page 668
9.3 Equivalent Gain Analysis Using the Root Locus......Page 669
9.3.1 Integrator Antiwindup......Page 676
9.4 Equivalent Gain Analysis Using Frequency Response: Describing Functions......Page 679
9.4.1 Stability Analysis Using Describing Functions......Page 686
9.5.1 The Phase Plane......Page 691
9.5.2 Lyapunov Stability Analysis......Page 698
9.5.3 The Circle Criterion......Page 704
9.6 Historical Perspective......Page 711
Review Questions......Page 712
Problems......Page 713
A Perspective on Design Principles......Page 724
Chapter Overview......Page 725
10.1 An Outline of Control Systems Design......Page 726
10.2 Design of a Satellite’s Attitude Control......Page 732
10.3 Lateral and Longitudinal Control of a Boeing 747......Page 750
10.3.1 Yaw Damper......Page 754
10.3.2 Altitude-Hold Autopilot......Page 762
10.4 Control of the Fuel–Air Ratio in an Automotive Engine......Page 768
10.5 Control of the Read/Write Head Assembly of a Hard Disk......Page 776
10.6 Control of RTP Systems in Semiconductor Wafer Manufacturing......Page 784
10.7 Chemotaxis or How E. Coli Swims Away from Trouble......Page 798
10.8 Historical Perspective......Page 807
Summary......Page 809
Problems......Page 811
A.1 The L− Laplace Transform......Page 825
A.1.1 Properties of Laplace Transforms......Page 826
A.1.2 Inverse Laplace Transform by Partial-Fraction Expansion......Page 834
A.1.3 The Initial Value Theorem......Page 837
A.1.4 Final Value Theorem......Page 838
Appendix B: Solutions to the Review Questions......Page 840
Appendix C: Matlab Commands......Page 856
Bibliography......Page 861
B......Page 869
C......Page 870
D......Page 871
F......Page 872
H......Page 873
L......Page 874
M......Page 875
P......Page 876
R......Page 877
S......Page 878
Z......Page 880
Inside Back Cover......Page 882