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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 Function 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

CONTROL SYSTEM DESIGN: CASE STUDIES 569

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