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Ⅰ THE ELEMENTS 1

Ⅰ THE ELEMENTS 1

PREVIEW 3

1 THE EXCITEMENT OF CONTROL ENGINEERING 5

1．2 Motivation for Control Engineering 5

1．1 Preview 5

1 The Excitement of Control Engineering 5

1．3 Historical Periods of Control Theory 9

1．4 Types of Control-System Design 10

1．5 System Integration 11

1．6 Summary 18

1．7 Further Reading 19

2 Introduction to the Principles of Feedback 21

2 INTRODUCTION TO THE PRINCIPLES OF FEEDBACK 21

2．1 Preview 21

2．2 The Principal Goal of Control 21

2．3 A Motivating Industrial Example 22

2．4 Definition of the Problem 27

2．5 Prototype Solution to the Control Problem via Inversion 29

2．6 High-Gain Feedback and Inversion 32

2．7 From Open-to Closed-Loop Architectures 34

2．9 Measurements 36

2．8 Trade-offs Involved in Choosing the Feedback Gain 36

2．10 Summary 38

2．11 Further Reading 39

3 MODELING 41

3．1 Preview 41

3．2 The Raison d être for Models 41

3 Modeling 41

3．3 Model Complexity 42

3．4 Building Models 44

3．5 Model Structures 45

3．6 State Space Models 45

3．7 Solution of Continuous-Time State Space Models 49

3．8 High-Order Differential and Difference-Equation Models 50

3．9 Modeling Errors 50

3．10 Linearization 52

3．11 Case Studies 57

3．12 Summary 58

3．13 Further Reading 60

3．14 Problems for the Reader 61

4 Continuous-Time Signals and Systems 65

4．2 Linear Continuous-Time Models 65

4 CONTINUOUS-TIME SIGNALS AND SYSTEMS 65

4．1 Preview 65

4．3 Laplace Transforms 66

4．4 Laplace Transform．Properties and Examples 67

4．5 Transfer Functions 70

4．6 Stability of Transfer Functions 74

4．7 Impulse and Step Responses of Continuous-Time Linear Systems 74

4．8 Poles，Zeros：and Time Responses 76

4．9 Frequency Response 85

4．10 Fourier Transform 92

4．11 Models Frequently Encountered 97

4．12 Modeling Errors for Linear Systems 99

4．13 Bounds for Modeling Errors 103

4．14 Summary 104

4．15 Further Reading 108

4．16 Problems for the Reader 110

Ⅱ SISO CONTROL ESSENTIALS 117

Ⅱ SISO CONTROL ESSENTIALS 117

PREVIEW 119

5 ANALYSIS OF SISO CONTROL LOOPS 121

5．1 Preview 121

5．2 Feedback Structures 121

5 Analysis of SISO Control Loops 121

5．3 Nominal Sensitivity Functions 125

5．4 Closed-Loop Stability Based on the Characteristic Polynomial 127

5．5 Stability and Polynomial Analysis 128

5．6 Root Locus（RL） 134

5．7 Nominal Stability using Frequency Response 138

5．8 Relative Stability：Stability Margins and Sensitivity Peaks 143

5．9 Robustness 145

5．10 Summary 150

5．11 Further Reading 152

5．12 Problems for the Reader 154

6 Classical PID Control 159

6 CLASSICAL PID CONTROL 159

6．1 Preview 159

6．2 PID Structure 159

6．3 Empirical Tuning 162

6．4 Ziegler-Nichols（Z-N）Oscillation Method 162

6．5 Reaction Curve Based Methods 166

6．6 Lead-Lag Compensators 170

6．7 Distillation Column 171

6．8 Summary 174

6．9 Further Reading 175

6．10 Problems for the Reader 176

7 SYNTHESIS OF SISO CONTROLLERS 179

7．1 Preview 179

7．2 Polynomial Approach 179

7 Synthesis of SISO Controllers 179

7．3 PI and PID Synthesis Revisited by using Pole Assignment 187

7．4 Smith Predictor 189

7．5 Summary 191

7．6 Further Reading 192

7．7 Problems for the Reader 193

Ⅲ SISO CONTROL DESIGN 197

Ⅲ SISO CONTROL DESIGN 197

PREVIEW 199

8 Fundamental Limitations in SISO Control 201

8 FUNDAMENTAL LIMITATIONS IN SISO CONTROL 201

8．1 Preview 201

8．2 Sensors 202

8．3 Actuators 203

8．5 Model-Error Limitations 206

8．4 Disturbances 206

8．6 Structural Limitations 207

8．7 An Industrial Application（Hold-Up Effect in Reversing Mill） 222

8．8 Remedies 225

8．9 Design Homogeneity，Revisited 232

8．10 Summary 232

8．11 Further Reading 235

8．12 Problems for the Reader 237

9 Frequency-Domain Design Limitations 241

9 FREQUENCY-DOMAIN DESIGN LIMITATIONS 241

9．1 Preview 241

9．2 Bode s Integral Constraints on Sensitivity 242

9．3 Integral Constraints on Complementary Sensitivity 246

9．4 Poisson Integral Constraint on Sensitivity 249

9．5 Poisson Integral Constraint on Complementary Sensitivity 254

9．6 Example of Design Trade-offs 256

9．7 Summary 259

9．8 Further Reading 260

9．9 Problems for the Reader 263

10 Architectural Issues in SISO Control 265

10 ARCHITECTURAL ISSUES IN SISO CONTROL 265

10．2 Models for Deterministic Disturbances and References 265

10．1 Preview 265

10．3 Internal Model Principle for Disturbances 267

10．4 Internal Model Principle for Reference Tracking 271

10．5 Feedforward 271

10．6 Industrial Applications of Feedforward Control 279

10．7 Cascade Control 281

10．8 Summary 285

10．9 Further Reading 288

10．10 Problems for the Reader 289

11 Dealing with Constraints 293

11 DEALING WITH CONSTRAINTS 293

11．1 Preview 293

11．2 Wind-Up 294

11．3 Anti-Wind-up Scheme 295

11．4 State Saturation 301

11．5 Introduction to Model Predictive Control 306

11．6 Summary 306

11．7 Further Reading 307

11．8 Problems for the Reader 309

Ⅳ DIGITAL COMPUTER CONTROL 315

Ⅳ DIGITAL COMPUTER CONTROL 315

PREVIEW 317

12 Models for Sampled-Data Systems 319

12．1 Preview 319

12 MODELS FOR SAMPLED-DATA SYSTEMS 319

12．2 Sampling 319

12．3 Signal Reconstruction 321

12．4 Linear Discrete-Time Models 322

12．5 The Shift Operator 322

12．6 Z-Transform 323

12．7 Discrete Transfer Functions 324

12．8 Discrete Delta-Domain Models 328

12．9 Discrete Delta-Transform 331

12．10 Discrete Transfer Functions（Delta Form） 335

12．12 Discrete System Stability 336

12．11 Transfer Functions and Impulse Responses 336

12．13 Discrete Models for Sampled Continuous Systems 337

12．14 Using Continuous State Space Models 340

12．15 Frequency Response of Sampled-Data Systems 342

12．16 Summary 345

12．17 Further Reading 348

12．18 Problems for the Reader 349

13 DIGITAL CONTROL 353

13．1 Preview 353

13．2 Discrete-Time Sensitivity Functions 353

13 Digital Control 353

13．3 Zeros of Sampled-Data Systems 355

13．4 Is a Dedicated Digital Theory Really Necessary? 357

13．5 Approximate Continuous Designs 358

13．6 At-Sample Digital Design 362

13．7 Internal Model Principle for Digital Control 372

13．8 Fundamental Performance Limitations 376

13．9 Summary 380

13．10 Further Reading 381

13．11 Problems for the Reader 383

14 HYBRID CONTROL 387

14．1 Preview 387

14．2 Hybrid Analysis 387

14．3 Models for Hybrid Control Systems 387

14 Hybrid Control 387

14．4 Analysis of Intersample Behavior 391

14．5 Repetitive Control Revisited 393

14．6 Poisson Summation Formula 394

14．7 Summary 396

14．8 Further Reading 397

14．9 Problems for the Reader 398

Ⅴ ADVANCED SISO CONTROL 403

Ⅴ ADVANCED SISO CONTROL 403

PREVIEW 405

15 SISO Controller Parameterizations 407

15 SISO CONTROLLER PARAMETERIZATIONS 407

15．1 Preview 407

15．2 Open-Loop Inversion Revisited 407

15．3 Affine Parameterization：The Stable Case 408

15．4 PID Synthesis by using the Affine Parameterization 418

15．5 Affine Parameterization for Systems Having Time Delays 427

15．6 Undesirable Closed-Loop Poles 430

15．7 Affine Parameterization：The Unstable Open-Loop Case 438

15．8 Discrete-Time Systems 446

15．9 Summary 447

15．10 Further reading 451

15．11 Problems for the Reader 453

16 Control Design based on Optimization 457

16 CONTROL DESIGN BASED ON OPTIMIZATION 457

16．1 Preview 457

16．2 Optimal Q（Affine）Synthesis 458

16．3 Robust Control Design with Confidence Bounds 464

16．4 Cheap Control Fundamental Limitations 478

16．5 Frequency-Domain Limitations Revisited 480

16．6 Summary 482

16．7 Further Reading 483

16．8 Problems for the Reader 486

17 Linear State Space Models 491

17．1 Preview 491

17．2 Linear Continuous-Time State Space Models 491

17 LINEAR STATE SPACE MODELS 491

17．3 Similarity Transformations 492

17．4 Transfer Functions Revisited 494

17．5 From Transfer Function to State Space Representation 496

17．6 Controllability and Stabilizability 498

17．7 Observability and Detectability 508

17．8 Canonical Decomposition 513

17．9 Pole-Zero Cancellation and System Properties 516

17．10 Summary 519

17．11 Further Reading 521

17．12 Problems for the Reader 523

18 Synthesis via State Space Methods 527

18．1 Preview 527

18．2 Pole Assignment by State Feedback 527

18 SYNTHESIS VIA STATE SPACE METHODS 527

18．3 Observers 531

18．4 Combining State Feedback with an Observer 537

18．5 Transfer-Function Interpretations 539

18．6 Reinterpretation of the Affine Parameterization of all Stabilizing Controllers 545

18．7 State Space Interpretation of Internal Model Principle 546

18．8 Trade-Offs in State Feedback and Observers 551

18．9 Dealing with Input Constraints in the Context of State-Estimate Feedback 552

18．10 Summary 553

18．11 Further Reading 555

18．12 Problems for the Reader 556

19 Introduction to Nonlinear Control 559

19 INTRODUCTION TO NONLINEAR CONTROL 559

19．1 Preview 559

19．2 Linear Control of a Nonlinear Plant 559

19．3 Switched Linear Controllers 564

19．4 Control of Systems with Smooth Nonlinearities 567

19．5 Static Input Nonlinearities 567

19．6 Smooth Dynamic Nonlinearities for Stable and Stably Invertible Models 568

19．7 Disturbance Issues in Nonlinear Control 575

19．8 More General Plants with Smooth Nonlinearities 580

19．9 Nonsmooth Nonlinearities 583

19．10 Stability of Nonlinear Systems 585

19．11 Generalized Feedback Linearization for nonstability-Invertible Plants 595

19．12 Summary 603

19．13 Further Reading 604

19．14 Problems for the Reader 607

Ⅵ MIMO CONTROL ESSENTIALS 609

Ⅵ MIMO CONTROL ESSENTIALS 609

PREVIEW 611

20 ANALYSIS OF MIMO CONTROL LOOPS 613

20．1 Preview 613

20．2 Motivational Examples 613

20 Analysis of MIMO Control Loops 613

20．3 Models for Multivariable Systems 615

20．4 The Basic MIMO Control Loop 624

20．5 Closed-Loop Stability 626

20．6 Steady-State Response for Step Inputs 630

20．7 Frequency-Domain Analysis 631

20．8 Robustness Issues 641

20．9 Summary 644

20．10 Further Reading 646

20．11 Problems for the Reader 648

21 Exploiting SISO Techniques in MIMO Control 653

21．1 Preview 653

21．2 Completely Decentralized Control 653

21 EXPLOITING SISO TECHNIQUES IN MIMO CONTROL 653

21．3 Pairing of Inputs and Outputs 657

21．4 Robustness Issues in Decentralized Control 660

21．5 Feedforward Action in Decentralized Control 662

21．6 Converting MIMO Problems to SISO Problems 664

21．7 Industrial Case Study（Strip Flatness Control） 666

21．8 Summary 670

21．9 Further Reading 671

21．10 Problems for the Reader 672

Ⅶ MIMO CONTROL DESIGN 675

Ⅶ MIMO CONTROL DESIGN 675

PREVIEW 677

22 DESIGN VIA OPTIMAL CONTROL TECHNIQUES 679

22．1 Preview 679

22 Design via Optimal Control Techniques 679

22．2 State-Estimate Feedback 679

22．3 Dynamic Programming and Optimal Control 682

22．4 The Linear Quadratic Regulator（LQR） 685

22．5 Properties of the Linear Quadratic Optimal Regulator 687

22．6 Model Matching Based on Linear Quadratic Optimal Regulators 692

22．7 Discrete-Time Optimal Regulators 695

22．8 Connections to Pole Assignment 696

22．9 Observer Design 698

22．10 Linear Optimal Filters 699

22．11 State-Estimate Feedback 713

22．12 Transfer-Function Interpretation 713

22．13 Achieving Integral Action in LQR Synthesis 716

22．14 Industrial Applications 718

22．15 Summary 730

22．16 Further Reading 733

22．17 Problems for the Reader 736

23 Model Predictive Control 739

23．1 Preview 739

23 MODEL PREDICTIVE CONTROL 739

23．2 Anti-Wind-Up Revisited 740

23．3 What is Model Predictive Control? 744

23．4 Stability 748

23．5 Linear Models with Quadratic Cost Function 751

23．6 State Estimation and Disturbance Prediction 756

23．7 Rudder Roll Stabilization of Ships 758

23．8 Summary 762

23．9 Further Reading 763

23．10 Problems for the Reader 766

24 Fundamental Limitations in MIMO Control 771

24 FUNDAMENTAL LIMITATIONS IN MIMO CONTROL 771

24．1 Preview 771

24．2 Closed-Loop Transfer Function 772

24．4 The Cost of the Internal Model Principle 773

24．3 MIMO Internal Model Principle 773

24．5 RHP Poles and Zeros 774

24．6 Time-Domain Constraints 775

24．7 Poisson Integral Constraints of MIMO Complementary Sensitivity 780

24．8 Poisson Integral Constraints on MIMO Sensitivity 782

24．9 Interpretation 783

24．10 An Industrial Application：Sugar Mill 785

24．11 Nonsquare Systems 796

24．12 Discrete-Time Systems 800

24．13 Summary 800

24．14 Further Reading 802

24．15 Problems for the Reader 804

Ⅷ ADVANCED MIMO CONTROL 807

Ⅷ ADVANCED MIMO CONTROL 807

PREVIEW 809

25．1 Preview 811

25 MIMO CONTROLLER PARAMETERIZATIONS 811

25．2 Affine Parameterization：Stable MIMO Plants 811

25 MIMO Controller Parameterizations 811

25．3 Achieved Sensitivities 813

25．4 Dealing with Model Relative Degree 813

25．5 Dealing with NMP Zeros 824

25．6 Affine Parameterization：Unstable MIMO Plants 841

25．7 State Space Implementation 844

25．8 Summary 847

25．9 Further Reading 848

25．10 Problems for the Reader 850

26 Decoupling 851

26 DECOUPLING 853

26．1 Preview 853

26．2 Stable Systems 854

26．3 Pre-and PostDiagonalization 861

26．4 Unstable Systems 863

26．5 Zeros of Decoupled and Partially Decoupled Systems 873

26．6 Frequency-Domain Constraints for Dynamically Decoupled Systems 876

26．7 The Cost of Decoupling 878

26．8 Input Saturation 882

26．9 MIMO Anti-Wind-Up Mechanism 883

26．10 Summary 891

26．11 Further Reading 893

26．12 Problems for the Reader 895