Control System Analysis and Design

Cover......Page 1
Preface......Page 6
Contents......Page 8
 1.1 Introduction......Page 16
  Closed loop control system (feedback control system)......Page 17
 1.2 Effects of Feedback......Page 18
  Electrical systems......Page 25
  Mechanical system......Page 26
 1.4 Mathematical Modelling of Translational/Rotational Mechanical System......Page 28
  Force-voltage (f-v) analogy......Page 33
  Procedure to construct analogous electrical system using f-v analogy......Page 35
  Procedure to construct analogous electrical system using f-i analogy......Page 36
 1.6 Gear Train and its Electrical Analog......Page 37
  Electrical analog of gear train......Page 39
 1.7 Transfer Function......Page 41
  Transfer function model of system......Page 42
  Zero state response......Page 44
  Transfer function of a system with multi inputs and multi outputs......Page 45
  Time varying and time invariant systems......Page 47
  Causal system......Page 48
 Problems and Solutions......Page 49
 Drill Problems......Page 56
 Multiple Choice Questions......Page 58
 Answers and Hints to Multiple Choice Questions......Page 65
 2.1 Introduction......Page 68
 2.2 Standard Test Signals......Page 69
  Unit step response of first order system......Page 70
  Unit ramp response of first order system......Page 72
  Unit impulse response of first order system......Page 73
  Illustrative examples......Page 74
  Unit step response of a general second order control system......Page 75
  Transient response specifications......Page 77
  The characteristic equation roots and corresponding time response......Page 80
  Unit impulse response of a general second order system......Page 85
 2.5 Steady State Performance of Linear System......Page 87
  Type number of a system......Page 88
  Steady state error due to step input......Page 89
  Steady state error due to ramp input (velocity input)......Page 90
  Steady state error due to parabolic input (acceleration input)......Page 91
 2.6 The Error Series......Page 93
 2.7 Higher Order Systems......Page 94
  Technique to cast away insignificant poles......Page 95
  Addition of a zero to closed loop transfer function......Page 96
  Addition of a pole to open loop transfer function......Page 97
  Addition of pole to closed loop transfer function......Page 98
 Problems and Solutions......Page 99
 Drill Problems......Page 110
 Multiple Choice Questions......Page 112
 Answers and Hints to Multiple Choice Questions......Page 125
 3.1 Block Diagrams......Page 130
  Block diagram development......Page 131
  Block diagram reduction......Page 132
 3.2 Signal Flow Graph......Page 134
  Important definitions......Page 135
  Construction of signal flow graph for electrical network......Page 138
  Mason’s gain rule......Page 139
 Problems and Solutions......Page 140
 Drill Problems......Page 163
 Multiple Choice Question......Page 169
 Answers and Hints to Multiple Choice Questions......Page 175
  Impulse response stability......Page 178
  Bounded input bounded output (BIBO) stability......Page 179
 4.2 Coefficient Test for Stability......Page 181
 4.3 Routh's Stability Test......Page 182
 4.4 Left Column Zero of Array......Page 184
 4.5 Premature Termination of Array......Page 186
 4.6 Relative Stability Analysis......Page 190
 4.7 Routh's Stability Test in Control System Analysis......Page 191
 Problems and Solutions......Page 192
 Drill Problems......Page 209
 Multiple Choice Questions......Page 212
 Answers and Hints to Multiple Choice Questions......Page 217
 5.1 Introduction......Page 221
 5.2 Root Locus for Feedback Systems......Page 223
  Graphical evaluation of angle and magnitude of G(s) H(s)......Page 225
 5.3 Root Locus Construction......Page 228
  Some root locus plots......Page 241
 5.4 Root Loci for Systems with Other Forms......Page 243
 5.5 Root Loci for Systems with Positive Feedback......Page 245
 5.6 Root Locus of a G(s) H(s) Product with Pole-zero Cancellation......Page 249
  Addition of poles......Page 250
  Addition of zeros......Page 251
 5.8 Effects of Delay on Root Locus......Page 252
 5.9 Root Contours (Multiple Parameter Variation)......Page 254
 Problems and Solutions......Page 256
 Drill Problems......Page 280
 Multiple Choice Questions......Page 283
 Answers and Hints to Multiple Choice Questions......Page 290
  Strengths of frequency response approach......Page 293
  Steady state sinusoidal response......Page 294
  Graphical evaluation of frequency response......Page 296
 6.3 Correlation Between Time Response and Frequency Response......Page 297
  Frequency response specifications......Page 298
  Polar plot construction......Page 302
  Addition of poles at origin......Page 317
  Addition of finite non-origin poles......Page 319
 6.5 The Nyquist Stability Criterion......Page 320
  Mapping......Page 321
  Nyquist stability criterion......Page 325
  Nyquist procedure for minimum phase system......Page 327
  Relative stability using Nyquist procedure......Page 328
  The measures of relative stability: Gain margin and phase margin......Page 330
  Generating complete Nyquist plot and interpretting stability......Page 336
  The product terms of G( jω) H( jω)......Page 342
  Poles and zeros at origin of s plane......Page 343
  Real axis poles or zeros......Page 346
  Sketching magnitude (dB) plot......Page 351
  Sketching phase plot......Page 352
  Gain margin and phase margin from Bode plot......Page 354
  Evaluation of Kp from Bode plot......Page 356
  Evaluation of Kv from Bode plot......Page 357
  Evaluation of Ka from Bode plot......Page 358
  All pass systems......Page 364
  Effect of variation in gain K on Bode plot......Page 365
  Effect of presence of delay in system on Bode plot......Page 366
  Finding transfer function models......Page 367
  Imaginary axis zeros and poles......Page 369
 6.7 Closed Loop Frequency Response of Unity Feedback System......Page 370
  Constant magnitude loci (M circles)......Page 372
 Problems and Solutions......Page 379
 Drill Problems......Page 421
 Multiple Choice Questions......Page 426
 Answers and Hints to Multiple Choice Questions......Page 446
 7.1 Introduction......Page 454
  State space......Page 455
  Phase variable form of state model......Page 460
  Dual phase variable form of state model......Page 462
  State model for systems with single input and multiple outputs......Page 463
  State model for systems with multiple inputs and single output......Page 464
  Other ways of modelling......Page 466
  State space model using canonical variables......Page 470
 7.3 Modelling Electrical and Mechanical Systems......Page 474
 7.4 Finding Transfer Function from State Space Model......Page 476
  First order systems......Page 479
  State transition matrix......Page 480
  Properties of STM......Page 481
  Higher order systems......Page 482
 7.6 Controllability and Observability......Page 483
  Test of state controllability for diagonal systems......Page 484
  Test of observability for diagonal systems......Page 487
  Causes of uncontrollability and/or unobservability......Page 488
  Principle of duality......Page 490
 7.7 Finding Decoupled State Equations (Diagonalisation)......Page 491
 7.8 State Feedback and Pole Placement......Page 496
 7.9 Observer Design......Page 499
 Problems and Solutions......Page 503
 Drill Problems......Page 532
 Multiple Choice Questions......Page 537
 Answers and Hints to Multiple Choice Questions......Page 543
 8.2 Controller Configurations......Page 547
  Two position/on-off control......Page 549
  Proportional control......Page 550
  Integral control......Page 551
  Proportional plus Integral control (PI)......Page 552
  Proportional plus Derivative control (PD)......Page 554
  Proportional plus Integral plus Derivative control (PID)......Page 556
  PI controller......Page 558
  PID controller......Page 560
  Phase lead compensator......Page 561
  Phase lag-compensator......Page 566
  Lag-lead compensator......Page 570
 8.6 Root Locus Design......Page 572
  PI compensator design......Page 574
  Lag-compensator design......Page 576
  Cascade compensator design for improving transient response......Page 579
  PD compensator design......Page 580
  Lead compensator design......Page 583
  PID controller design......Page 586
  Lag-lead compensator design......Page 589
 8.7 Frequency Response Design......Page 592
  Lag-compensator design......Page 593
  Lead compensator design......Page 597
  Phase lag-lead compensator design......Page 601
 8.8 Rate Feedback Compensator Design......Page 605
  Minor loop feedback compensation......Page 608
 Problems and Solutions......Page 611
 Drill Problems......Page 641
 Multiple Choice Questions......Page 644
 Answers and Hints to Multiple Choice Questions......Page 649
 9.1 Introduction......Page 651
 9.2 Potentiometer......Page 652
  Potentiometer performance indices......Page 656
  Types of potentiometer......Page 657
  Synchro transmitter (ST)......Page 658
  Synchro control transformer (CT)......Page 659
  Armature controlled DC servo motor......Page 662
  Field controlled DC servo motor......Page 666
  AC servo motor......Page 668
  DC tachometer......Page 672
  AC tachometer......Page 673
 9.6 Servo Amplifier......Page 674
  Amplidyne......Page 675
 9.7 Stepper Motor......Page 678
  Incremental encoder......Page 688
  Absolute encoder......Page 690
 9.9 Mechanical Arrangements to Convert Rotational Motion into Corresponding Linear Motion......Page 691
 9.10 Belt or Chain Drive and Lever System......Page 692
 Problems and Solutions......Page 693
 Drill Problems......Page 705
 Multiple Choice Questions......Page 709
 Answers and Hints to Multiple Choice Questions......Page 713
Index......Page 714