《LINEAR CONTROL SYSTEMS ENGINEERING》

MODULE 1INTRODUCTION TO FEEDBACK CONTROL1

MODULE 2TRANSFER FUNCTIONS AND BLOCK DIAGRAM ALGEBRA22

Transfer Functions22

Block Diagram Algebra23

MODULE 3FIRST-ORDER SYSTEMS37

Impulse Response39

Step Response40

Ramp Response41

Harmonic Response41

First-Order Feedback Systems43

Complex-Plane Representation: Poles and Zeros45

Poles and Zeros of First-Order Systems46

Dominant Poles47

MODULE 4SECOND-ORDER SYSTEMS57

Second-Order Electrical System63

Step Response64

MODULE 5SECOND-ORDER SYSTEM TIME-DOMAIN RESPONSE75

Ramp Response75

Harmonic Response76

Relationship between System Poles and Transient Response78

Time-Domain Performance Specifications81

MODULE 6SECOND-ORDER SYSTEMS: DISTURBANCE REJECTION AND RATE FEEDBACK93

Open- and Closed-Loop Disturbance Rejection96

Effect of Velocity Feedback99

MODULE 7HIGHER-ORDER SYSTEMS111

Reduction to Lower-Order Systems111

Third-Order Systems112

Effect of a Closed-Loop Zero114

Occurrence of Closed-Loop Zeros117

MODULE 8SYSTEM TYPE: STEADY-STATE ERRORS125

Impulse Input127

Step Input128

Ramp Input129

Acceleration Input130

Non-Unity-Feedback Control Systems132

MODULE 9ROUTH'S METHOD, ROOT LOCUS: MAGNITUDE AND PHASE EQUATIONS145

Routh's Stability Criterion145

Root Locus Method: Magnitude and Phase Equations148

MODULE 10 RULES FOR PLOTTING THE ROOT LOCUS173

MODULE 11SYSTEM DESIGN USING THE ROOT LOCUS199

MultiLoop System199

System Design in the Complex Plane202

Performance Requirements as Complex-Plane Constraints203

Steady-State Error204

Desirable Areas of Complex Plane for “Good” Response205

MODULE 12 FREQUENCY RESPONSE AND NYQUIST DIAGRAMS223

Frequency Response224

Nyquist Diagrams from Transfer Functions225

MODULE 13 NYQUIST STABILITY CRITERION241

Conformal Mapping: Cauchy's Theorem241

Application to Stability245

Some Comments on Nyquist Stability252

Alternative Approach to Nyquist Stability Criterion254

MODULE 14 NYQUIST ANALYSIS AND RELATIVE STABILITY272

Conditional Stability272

Gain and Phase Margins274

MODULE 15 BODE DIAGRAMS289

Bode Diagrams of Simple Transfer Functions289

Bode Diagrams of Compound Transfer Functions293

Elemental Bode Diagrams297

MODULE 16 BODE ANALYSIS, STABILITY, AND GAIN AND PHASE MARGINS319

Conditional Stability319

Gain and Phase Margins in the Bode Diagram321

System Type and Steady-State Error from Bode Diagrams323

Further Discussion of Gain and Phase Margins326

MODULE 17 TIME RESPONSE FROM FREQUENCY RESPONSE341

Bode Diagram from the Root Locus341

Closed-Loop Time Response from Open-Loop Phase Margin344

Time Response of Higher-Order Systems346

MODULE 18 FREQUENCY-DOMAIN SPECIFICATIONS AND CLOSED-LOOP FREQUENCY RESPONSE361

Frequency-Domain Specifications361

Closed-Loop Frequency Response from Nyquist Diagram365

Closed-Loop Frequency Response from Bode Diagram371

Gain for a Desired Mp from the Nyquist Diagram374

Gain For a Desired Mp from the Nichols Chart377

Non-Unity-Feedback Gain Systems377

MODULE 19 PHASE LEAD COMPENSATION396

Multiple-Design Constraints396

Transfer Function of Phase Lead Element399

Phase Lead Compensation Process402

Comments on the Applicability and Results of Phase Lead Compensation409

MODULE 20 PHASE LAG AND LEAD-LAG COMPENSATION431

Transfer Function of Phase Lag Element431

Phase Lag Compensation Process433

Comments on Phase Lag Compensation435

Lead-Lag Compensation436

Transfer Function of a Lead-Lag Element438

Lead-Lag Compensation Process440

MODULE 21MULTIMODE CONTROLLERS463

Proportional Control464

Proportional-Plus-Integral Control466

Proportional-Plus-Derivative Control468

Proportional-Plus-Integral-Plus-Derivative Control471

MODULE 22 STATE-SPACE SYSTEM DESCRIPTIONS487

State-Space Form Equations from Transfer Functions492

Transfer Function from State-Space Form495

Transformation of State Variable and Invariability of System Eigenvectors496

Canonical Forms and Decoupled Systems497

Relationship between Eigenvalues and System Poles500

MODULE 23 STATE-SPACE SYSTEM RESPONSE, CONTROLLABILITY,AND OBSERVABILITY515

Direct Numerical Solution of the State Equation515

Solution Using State Transition Matrix516

Solution Using Laplace Transforms518

System Stability518

Controllability and Observability519

MODULE 24 STATE-SPACE CONTROLLER DESIGN531

Direct Calculation of Gains by Comparison with Characteristic Equation532

Pole Placement via Control Canonical Form of State Equations534

Pole Placement via Ackermann's Formula539

MODULE 25 STATE-SPACE OBSERVER DESIGN550

Observer Synthesis550

Compensator Design555

CONTROL SYSTEM DESIGN: CASE STUDIES569

MODULE 26 WAVE ENERGY ABSORBTION DEVICE569

MODULE 27 MISSILE ATTITUDE CONTROLLER574

MODULE 28 ROBOTIC HAND DESIGN582

MODULE 29 PUMPED STORAGE FLOW CONTROL SYSTEM589

MODULE 30 SHIP STEERING CONTROL SYSTEM597

MODULE 31CRUISE MISSILE ALTITUDE CONTROL SYSTEM605

MODULE 32 MACHINE TOOL POWER DRIVE SYSTEM WITH FLEXIBILITY613

APPENDIX 1 REVIEW OF LAPLACE TRANSFORMS AND THEIR USE IN SOLVING DIFFERENTIAL EQUATIONS620

Linear Properties620

Shifting Theorem620

Time Differentials621

Final-Value Theorem622

Inverse Transforms622

Solving Linear Differential Equations622

Index625