Digital Control System Analysis and Design

Cover......Page 1
Dedication......Page 4
Contents......Page 5
Preface......Page 10
 1.1 Overview......Page 12
 1.2 Digital Control System......Page 13
 1.3 The Control Problem......Page 16
 1.4 Satellite Model......Page 17
 1.5 Servomotor System Model......Page 19
  Antenna Pointing System......Page 21
  Robotic Control System......Page 22
 1.6 Temperature Control System......Page 23
 1.7 Single-Machine Infinite Bus Power System......Page 25
 Problems......Page 28
 2.2 Discrete-Time Systems......Page 36
 2.3 Transform Methods......Page 38
  Multiplication by a Constant......Page 41
  Real Translation......Page 42
  Complex Translation......Page 44
  Final Value......Page 45
 2.5 Finding z-Transforms......Page 46
 2.6 Solution of Difference Equations......Page 49
  Power Series Method......Page 52
  Partial-Fraction Expansion Method......Page 53
  Inversion-Formula Method......Page 57
  Discrete Convolution......Page 58
 2.8 Simulation Diagrams and Flow Graphs......Page 60
 2.9 State Variables......Page 64
 2.10 Other State-Variable Formulations......Page 72
 2.11 Transfer Functions......Page 81
  Recursive Solution......Page 85
  z-Transform Method......Page 87
  Numerical Method via Digital Computer......Page 88
  Properties of the State Transition Matrix......Page 89
 2.13 Linear Time-Varying Systems......Page 90
 Problems......Page 91
 3.2 Sampled-Data Control Systems......Page 101
 3.3 The Ideal Sampler......Page 104
 3.4 Evaluation of E*(s)......Page 106
 3.5 Results from the Fourier Transform......Page 109
 3.6 Properties of E*(s)......Page 111
 3.7 Data Reconstruction......Page 114
  Zero-Order Hold......Page 115
  First-Order Hold......Page 119
  Fractional-Order Holds......Page 120
 References and Further Readings......Page 122
 Problems......Page 123
 4.2 The Relationship Between E(z) and E*(s)......Page 127
 4.3 The Pulse Transfer Function......Page 128
 4.4 Open-Loop Systems Containing Digital Filters......Page 134
 4.5 The Modified z-Transform......Page 137
 4.6 Systems with Time Delays......Page 140
 4.7 Nonsynchronous Sampling......Page 143
 4.8 State-Variable Models......Page 146
 4.9 Review of Continuous-Time State Variables......Page 147
 4.10 Discrete-Time State Equations......Page 151
 4.11 Practical Calculations......Page 155
 Problems......Page 157
 5.2 Preliminary Concepts......Page 168
 5.3 Derivation Procedure......Page 172
 5.4 State-Variable Models......Page 179
 References and Further Readings......Page 188
 Problems......Page 189
 6.2 System Time Response......Page 199
 6.3 System Characteristic Equation......Page 208
 6.4 Mapping the s-Plane into the z-Plane......Page 209
 6.5 Steady-State Accuracy......Page 216
 6.6 Simulation......Page 219
 6.8 Summary......Page 224
 Problems......Page 225
 7.2 Stability......Page 231
 7.3 Bilinear Transformation......Page 235
 7.4 The Routh–Hurwitz Criterion......Page 237
 7.5 Jury’s Stability Test......Page 240
 7.6 Root Locus......Page 245
 7.7 The Nyquist Criterion......Page 249
 7.8 The Bode Diagram......Page 258
 7.9 Interpretation of the Frequency Response......Page 260
 7.10 Closed-Loop Frequency Response......Page 262
 Problems......Page 271
 8.2 Control System Specifications......Page 280
  Transient Response......Page 281
  Relative Stability......Page 283
  Sensitivity......Page 284
  Disturbance Rejection......Page 285
 8.3 Compensation......Page 286
 8.4 Phase-Lag Compensation......Page 288
 8.5 Phase-Lead Compensation......Page 295
 8.6 Phase-Lead Design Procedure......Page 296
 8.7 Lag-Lead Compensation......Page 304
 8.8 Integration and Differentiation Filters......Page 308
 8.9 PID Controllers......Page 310
 8.10 PID Controller Design......Page 314
 8.11 Design by Root Locus......Page 322
 References and Further Readings......Page 335
 Problems......Page 336
 9.2 Pole Assignment......Page 344
  Observer Model......Page 353
  Error Dynamics......Page 355
  Controller Transfer Function......Page 360
  Closed-Loop Characteristic Equation......Page 363
  Closed-Loop State Equations......Page 364
 9.4 Reduced-Order Observers......Page 365
 9.5 Current Observers......Page 370
 9.6 Controllability and Observability......Page 375
 9.7 Systems with Inputs......Page 379
 9.8 Summary......Page 384
 Problems......Page 385
 10.1 Introduction......Page 391
 10.2 Identification of Static Systems......Page 392
 10.4 Black-Box Identification......Page 395
 10.5 Least-Squares System Identification......Page 402
 10.6 Estimating Transfer Functions with Partly Known Poles and Zeros......Page 408
 10.7 Recursive Least-Squares System Identification......Page 410
  Choice of Input......Page 413
  Choice of Signal Scaling......Page 414
 Problems......Page 415
 11.1 Introduction......Page 419
 11.2 The Quadratic Cost Function......Page 420
 11.3 The Principle of Optimality......Page 422
 11.4 Linear Quadratic Optimal Control......Page 425
 11.5 The Minimum Principle......Page 434
 11.6 Steady-State Optimal Control......Page 435
 11.7 Optimal State Estimation— Kalman Filters......Page 441
 11.9 Summary......Page 447
 References and Further Readings......Page 448
 Problems......Page 449
 12.1 Introduction......Page 455
 12.2 Servomotor System......Page 456
  System Model......Page 457
  Design......Page 460
 12.3 Environmental Chamber Control System......Page 462
  Temperature Control System......Page 464
 12.4 Aircraft Landing System......Page 468
  Design......Page 469
  Plant Transfer Function......Page 475
  Taube’s PID Controller......Page 477
  MATLAB pidtool PIDF Controllers......Page 478
 12.6 Topology Identification in Electric Power System Models......Page 485
 References......Page 489
 Appendix I: Design Equations......Page 491
 Appendix II: Mason’s Gain Formula......Page 492
  References......Page 496
 Appendix III: Evaluation of E*(s)......Page 497
  References......Page 501
 Appendix IV: Review of Matrices......Page 502
  Other Relationships......Page 506
  References......Page 508
  Introduction......Page 509
  Properties of the Laplace Transform......Page 514
  Differential Equations and Transfer Functions......Page 517
  Problems......Page 520
 Appendix VI: z-Transform Tables......Page 523
Index......Page 526