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Preface 13

1 An Overview and Brief History of Feedback Control 21

A Perspective on Feedback Control 21

Chapter Overview 22

1.1 A Simple Feedback System 23

1.2 A First Analysis of Feedback 26

1.3 Feedback System Fundamentals 30

1.4 A Brief History 31

1.5 An Overview of the Book 37

Summary 39

Review Questions 39

Problems 40

2 Dynamic Models 43

A Perspective on Dynamic Models 43

Chapter Overview 44

2.1 Dynamics of Mechanical Systems 44

2.1.1 Translational Motion 44

2.1.2 Rotational Motion 51

2.1.3 Combined Rotation and Translation 59

2.1.4 Complex Mechanical Systems （W） 62

2.1.5 Distributed Parameter Systems 62

2.1.6 Summary：Developing Equations of Motion for Rigid Bodies 64

2.2 Models of Electric Circuits 65

2.3 Models of Electromechanical Systems 70

2.3.1 Loudspeakers 70

2.3.2 Motors 72

2.3.3 Gears 76

2.4 Heat and Fluid-Flow Models 77

2.4.1 Heat Flow 78

2.4.2 Incompressible Fluid Flow 81

2.5 Historical Perspective 88

Summary 91

Review Questions 91

Problems 92

3 Dynamic Response 104

A Perspective on System Response 104

Chapter Overview 105

3.1 Review of Laplace Transforms 105

3.1.1 Response by Convolution 106

3.1.2 Transfer Functions and Frequency Response 111

3.1.3 The ？_ Laplace Transform 121

3.1.4 Properties of Laplace Transforms 123

3.1.5 Inverse Laplace Transform by Partial-Fraction Expansion 125

3.1.6 The Final Value Theorem 127

3.1.7 Using Laplace Transforms to Solve Differential Equations 129

3.1.8 Poles and Zeros 131

3.1.9 Linear System Analysis Using MatlabR 132

3.2 System Modeling Diagrams 138

3.2.1 The Block Diagram 138

3.2.2 Block-Diagram Reduction Using Matlab 142

3.2.3 Mason’s Rule and the Signal Flow Graph （W） 143

3.3 Effect of Pole Locations 143

3.4 Time-Domain Specifications 151

3.4.1 Rise Time 152

3.4.2 Overshoot and Peak Time 152

3.4.3 Settling Time 154

3.5 Effects of Zeros and Additional Poles 157

3.6 Stability 166

3.6.1 Bounded Input-Bounded Output Stability 167

3.6.2 Stability of LTI Systems 168

3.6.3 Routh’s Stability Criterion 169

3.7 Obtaining Models from Experimental Data：System Identification （W） 176

3.8 Amplitude and Time Scaling （W） 176

3.9 Historical Perspective 176

Summary 177

Review Questions 179

Problems 179

4 A First Analysis of Feedback 200

A Perspective on the Analysis of Feedback 200

Chapter Overview 201

4.1 The Basic Equations of Control 202

4.1.1 Stability 203

4.1.2 Tracking 204

4.1.3 Regulation 205

4.1.4 Sensitivity 206

4.2 Control of Steady-State Error to Polynomial Inputs：System Type 208

4.2.1 System Type for Tracking 209

4.2.2 System Type for Regulation and Disturbance Rejection 214

4.3 The Three-Term Controller：PID Control 216

4.3.1 Proportional Control （P） 216

4.3.2 Integral Control （I） 218

4.3.3 Derivative Control （D） 221

4.3.4 Proportional Plus Integral Control （PI） 221

4.3.5 PID Control 222

4.3.6 Ziegler-Nichols Tuning of the PID Controller 226

4.4 Feedforward Control by Plant Model Inversion 232

4.5 Introduction to Digital Control （W） 234

4.6 Sensitivity of Time Response to Parameter Change （W） 235

4.7 Historical Perspective 235

Summary 237

Review Questions 238

Problems 238

5 The Root-Locus Design Method 254

A Perspective on the Root-Locus Design Method 254

Chapter Overview 255

5.1 Root Locus of a Basic Feedback System 255

5.2 Guidelines for Determining a Root Locus 260

5.2.1 Rules for Determining a Positive （180°）Root Locus 262

5.2.2 Summary of the Rules for Determining a Root Locus 268

5.2.3 Selecting the Parameter Value 269

5.3 Selected Illustrative Root Loci 271

5.4 Design Using Dynamic Compensation 284

5.4.1 Design Using Lead Compensation 286

5.4.2 Design Using Lag Compensation 290

5.4.3 Design Using Notch Compensation 292

5.4.4 Analog and Digital Implementations （W） 294

5.5 A Design Example Using the Root Locus 295

5.6 Extensions of the Root-Locus Method 301

5.6.1 Rules for Plotting a Negative （0°）Root Locus 301

5.6.2 Consideration of Two Parameters 304

5.6.3 Time Delay （W） 306

5.7 Historical Perspective 307

Summary 309

Review Questions 310

Problems 311

6 The Frequency-Response Design Method 328

A Perspective on the Frequency-Response Design Method 328

Chapter Overview 329

6.1 Frequency Response 329

6.1.1 Bode Plot Techniques 337

6.1.2 Steady-State Errors 350

6.2 Neutral Stability 351

6.3 The Nyquist Stability Criterion 353

6.3.1 The Argument Principle 354

6.3.2 Application of The Argument Principle to Control Design 355

6.4 Stability Margins 368

6.5 Bode’s Gain-Phase Relationship 377

6.6 Closed-Loop Frequency Response 381

6.7 Compensation 383

6.7.1 PD Compensation 383

6.7.2 Lead Compensation （W） 384

6.7.3 PI Compensation 394

6.7.4 Lag Compensation 395

6.7.5 PID Compensation 401

6.7.6 Design Considerations 407

6.7.7 Specifications in Terms of the Sensitivity Function 409

6.7.8 Limitations on Design in Terms of the Sensitivity Function 414

6.8 Time Delay 418

6.8.1 Time Delay via the Nyquist Diagram （W） 420

6.9 Alternative Presentation of Data 420

6.9.1 Nichols Chart 420

6.9.2 The Inverse Nyquist Diagram （W） 424

6.10 Historical Perspective 424

Summary 425

Review Questions 428

Problems 428

State-Space Design 453

7 A Perspective on State-Space Design 453

Chapter Overview 454

7.1 Advantages of State-Space 454

7.2 System Description in State-Space 456

7.3 Block Diagrams and State-Space 462

7.4 Analysis of the State Equations 464

7.4.1 Block Diagrams and Canonical Forms 465

7.4.2 Dynamic Response from the State Equations 477

7.5 Control-Law Design for Full-State Feedback 483

7.5.1 Finding the Control Law 484

7.5.2 Introducing the Reference Input with Full-State Feedback 493

7.6 Selection of Pole Locations for Good Design 497

7.6.1 Dominant Second-Order Poles 497

7.6.2 Symmetric Root Locus （SRL） 499

7.6.3 Comments on the Methods 508

7.7 Estimator Design 509

7.7.1 Full-Order Estimators 509

7.7.2 Reduced-Order Estimators 515

7.7.3 Estimator Pole Selection 519

7.8 Compensator Design：Combined Control Law and Estimator （W） 521

7.9 Introduction of the Reference Input with the Estimator （W） 534

7.9.1 General Structure for the Reference Input 535

7.9.2 Selecting the Gain 544

7.10 Integral Control and Robust Tracking 545

7.10.1 Integral Control 546

7.10.2 Robust Tracking Control：The Error-Space Approach 548

7.10.3 Model-Following Design 559

7.10.4 The Extended Estimator 563

7.11 Loop Transfer Recovery 567

7.12 Direct Design with Rational Transfer Functions 572

7.13 Design for Systems with Pure Time Delay 576

7.14 Solution of State Equations （W） 579

7.15 Historical Perspective 579

Summary 582

Review Questions 585

Problems 586

8 Digital Control 610

A Perspective on Digital Control 610

Chapter Overview 611

8.1 Digitization 611

8.2 Dynamic Analysis of Discrete Systems 614

8.2.1 z-Transform 614

8.2.2 z-Transform Inversion 615

8.2.3 Relationship Between s and 617

8.2.4 Final Value Theorem 619

8.3 Design Using Discrete Equivalents 621

8.3.1 Tustin’s Method 622

8.3.2 Zero-Order Hold （ZOH） Method 625

8.3.3 Matched Pole-Zero （MPZ） Method 627

8.3.4 Modified Matched Pole-Zero（MMPZ） Method 631

8.3.5 Comparison of Digital Approximation Methods 632

8.3.6 Applicability Limits of the Discrete Equivalent Design Method 633

8.4 Hardware Characteristics 633

8.4.1 Analog-to-Digital （A/D） Converters 634

8.4.2 Digital-to-Analog Converters 634

8.4.3 Anti-Alias Prefilters 635

8.4.4 The Computer 636

8.5 Sample-Rate Selection 637

8.5.1 Tracking Effectiveness 638

8.5.2 Disturbance Rejection 638

8.5.3 Effect of Anti-Alias Prefilter 639

8.5.4 Asynchronous Sampling 640

8.6 Discrete Design 640

8.6.1 Analysis Tools 641

8.6.2 Feedback Properties 642

8.6.3 Discrete Design Example 643

8.6.4 Discrete Analysis of Designs 646

8.7 Discrete State-Space Design Methods （W） 648

8.8 Historical Perspective 648

Summary 649

Review Questions 651

Problems 651

9 Nonlinear Systems 657

A Perspective on Nonlinear Systems 657

Chapter Overview 658

9.1 Introduction and Motivation：Why Study Nonlinear Systems？ 659

9.2 Analysis by Linearization 661

9.2.1 Linearization by Small-Signal Analysis 661

9.2.2 Linearization by Nonlinear Feedback 666

9.2.3 Linearization by Inverse Nonlinearity 667

9.3 Equivalent Gain Analysis Using the Root Locus 668

9.3.1 Integrator Antiwindup 675

9.4 Equivalent Gain Analysis Using Frequency Response：Describing Functions 678

9.4.1 Stability Analysis Using Describing Functions 685

9.5 Analysis and Design Based on Stability 690

9.5.1 The Phase Plane 690

9.5.2 Lyapunov Stability Analysis 697

9.5.3 The Circle Criterion 703

9.6 Historical Perspective 710

Summary 711

Review Questions 711

Problems 712

10 Control System Design：Principles and Case Studies 723

A Perspective on Design Principles 723

Chapter Overview 724

10.1 An Outline of Control Systems Design 725

10.2 Design of a Satellite’s Attitude Control 731

10.3 Lateral and Longitudinal Control of a Boeing 747 749

10.3.1 Yaw Damper 753

10.3.2 Altitude-Hold Autopilot 761

10.4 Control of the Fuel-Air Ratio in an Automotive Engine 767

10.5 Control of the Read/Write Head Assembly of a Hard Disk 775

10.6 Control of RTP Systems in Semiconductor Wafer Manufacturing 783

10.7 Chemotaxis or How E.Coli Swims Away from Trouble 797

10.8 Historical Perspective 806

Summary 808

Review Questions 810

Problems 810

Appendix A Laplace Transforms 824

A.1 The？_ Laplace Transform 824

A.1.1 Properties of Laplace Transforms 825

A.1.2 Inverse Laplace Transform by Partial-Fraction Expansion 833

A.1.3 The Initial Value Theorem 836

A.1.4 Final Value Theorem 837

Appendix B Solutions to the Review Questions 839

Appendix C Matlab Commands 855

Bibliography 860

Index 868