MODULE 1 INTRODUCTION TO FEEDBACK CONTROL 1
MODULE 2 TRANSFER FUNCTIONS AND BLOCK DIAGRAM ALGEBRA 22
Transfer Functions 22
Block Diagram Algebra 23
MODULE 3 FIRST-ORDER SYSTEMS 37
Impulse Response 39
Step Response 40
Ramp Response 41
Harmonic Response 41
First-Order Feedback Systems 43
Complex-Plane Representation：Poles and Zeros 45
Poles and Zeros of First-Order Systems 46
Dominant Poles 47
MODULE 4 SECOND-ORDER SYSTEMS 57
Second-Order Electrical System 63
Step Response 64
MODULE 5 SECOND-ORDER SYSTEM TIME-DOMAIN RESPONSE 75
Ramp Response 75
Harmonic Response 76
Relationship between System Poles and Transient Response 78
Time-Domain Performance Specifications 81
MODULE 6 SECOND-ORDER SYSTEMS: DISTURBANCE REJECTION AND RATE FEEDBACK 93
Open-and Closed-Loop Disturbance Rejection 96
Effect of Velocity Feedback 99
MODULE 7 HIGHER-ORDER SYSTEMS 111
Reduction to Lower-Order Systems 111
Third-Order Systems 112
Effect of a Closed-Loop Zero 114
Occurrence of Closed-Loop Zeros 117
MODULE 8 SYSTEM TYPE: STEADY-STATE ERRORS 125
Impulse Input 127
Step Input 128
Ramp Input 129
Acceleration Input 130
Non-Unity-Feedback Control Systems 132
MODULE 9 ROUTH’S METHOD, ROOT LOCUS: MAGNITUDE AND PHASE EQUATIONS 145
Routh’s Stability Criterion 145
Root Locus Method: Magnitude and Phase Equations 148
MODULE 10 RULES FOR PLOTTING THE ROOT LOCUS 173
MODULE 11 SYSTEM DESIGN USING THE ROOT LOCUS 199
MultiLoop System 199
System Design in the Complex Plane 202
Performance Requirements as Complex-Plane Constraints 203
Steady-State Error 204
Desirable Areas of Complex Plane for “Good” Response 205
MODULE 12 FREQUENCY RESPONSE AND NYQUIST DIAGRAMS 223
Frequency Response 224
Nyquist Diagrams from Transfer Functions 225
MODULE 13 NYQUIST STABILITY CRITERION 241
Conformal Mapping: Cauchy’s Theorem 241
Application to Stability 245
Some Comments on Nyquist Stability 252
Alternative Approach to Nyquist Stability Criterion 254
MODULE 14 NYQUIST ANALYSIS AND RELATIVE STABILITY 272
Conditional Stability 272
Gain and Phase Margins 274
MODULE 15 BODE DIAGRAMS 289
Bode Diagrams of Simple Transfer Functions 289
Bode Diagrams of Compound Transfer Functions 293
Elemental Bode Diagrams 297
MODULE 16 BODE ANALYSIS, STABILITY, AND GAIN AND PHASE MARGINS 319
Conditional Stability 319
Gain and Phase Margins in the Bode Diagram 321
System Type and Steady-State Error from Bode Diagrams 323
Further Discussion of Gain and Phase Margins 326
MODULE 17 TIME RESPONSE FROM FREQUENCY RESPONSE 341
Bode Diagram from the Root Locus 341
Closed-Loop Time Response from Open-Loop Phase Margin 344
Time Response of Higher-Order Systems 346
MODULE 18 FREQUENCY-DOMAIN SPECIFICATIONS AND CLOSED-LOOP FREQUENCY RESPONSE 361
Frequency-Domain Specifications 361
Closed-Loop Frequency Response from Nyquist Diagram 365
Closed-Loop Frequency Response from Bode Diagram 371
Gain for a Desired Mp from the Nyquist Diagram 374
Gain For a Desired Mp from the Nichols Chart 377
Non-Unity-Feedback Gain Systems 377
MODULE 19 PHASE LEAD COMPENSATION 396
Multiple-Design Constraints 396
Transfer Function of Phase Lead Element 399
Phase Lead Compensation Process 402
Comments on the Applicability and Results of Phase Lead Compensation 409
MODULE 20 PHASE LAG AND LEAD-LAG COMPENSATION 431
Transfer Function of Phase Lag Element 431
Phase Lag Compensation Process 433
Comments on Phase Lag Compensation 435
Lead-Lag Compensation 436
Transfer Function of a Lead-Lag Element 438
Lead-Lag Compensation Process 440
MODULE 21 MULTIMODE CONTROLLERS 463
Proportional Control 464
Proportional-Plus-Integral Control 466
Proportional-Plus-Derivative Control 468
Proportional-Plus-Integral-Plus-Derivative Control 471
MODULE 22 STATE-SPACE SYSTEM DESCRIPTIONS 487
State-Space Form Equations from Transfer Functions 492
Transfer Funoi?on from State-Space Form 495
Transformation of State Variable and Invariability of System Eigenvectors 496
Canonical Forms and Decoupled Systems 497
Relationship between Eigenvalues and System Poles 500
MODULE 23 STATE-SPACE SYSTEM RESPONSE, CONTROLLABILITY,AND OBSERVABILITY 515
Direct Numerical Solution of the State Equation 515
Solution Using State Transition Matrix 516
Solution Using Laplace Transforms 518
System Stability 518
Controllability and Observability 519
MODULE 24 STATE-SPACE CONTROLLER DESIGN 531
Direct Calculation of Gains by Comparison with Characteristic Equation 532
Pole Placement via Control Canonical Form of State Equations 534
Pole Placement via Ackermann’s Formula 539
MODULE 25 STATE-SPACE OBSERVER DESIGN 550
Observer Synthesis 550
Compensator Design 555
MODULE 26 WAVE ENERGY ABSORBTION DEVICE 569
MODULE 27 MISSILE ATTITUDE CONTROLLER 574
MODULE 28 ROBOTIC HAND DESIGN 582
MODULE 29 PUMPED STORAGE FLOW CONTROL SYSTEM 589
MODULE 30 SHIP STEERING CONTROL SYSTEM 597
MODULE 31 CRUISE MISSILE ALTITUDE CONTROL SYSTEM 605
MODULE 32 MACHINE TOOL POWER DRIVE SYSTEM WITH FLEXIBILITY 613
APPENDIX 1 REVIEW OF LAPLACE TRANSFORMS AND THEIR USE IN SOLVING DIFFERENTIAL EQUATIONS 620
Linear Properties 620
Shifting Theorem 620
Time Differentials 621
Final-Value Theorem 622
Inverse Transforms 622
Solving Linear Differential Equations 622
Index 625