**CHAPTER ** **1 ** ** ***Introduction to Control Systems 1*

**1.1 **Introduction 2

**1.2 **Brief History of Automatic Control 5

**1.3 **Examples of Control Systems 10

**1.4 **Engineering Design 17

**1.5 **Control System Design 18

**1.6 **Mechatronic Systems 21

**1.7 **Green Engineering 25

**1.8 **The Future Evolution of Control Systems 27

**1.9 **Design Examples 28

**1.10 **Sequential Design Example: Disk Drive Read System 32

**1.11 **Summary 34

Skills Check 35

Exercises 37

Problems 39

Advanced Problems 44

Design Problems 46

Terms and Concepts 48

**CHAPTER ** **2 ** ** ***Mathematical Models of Systems 49*

**2.1 **Introduction 50

**2.2 **Differential Equations of Physical Systems 50

**2.3 **Linear Approximations of Physical Systems 55

**2.4 **The Laplace Transform 58

**2.5 **The Transfer Function of Linear Systems 65

**2.6 **Block Diagram Models 79

**2.7 **Signal-Flow Graph Models 84

**2.8 **Design Examples 90

**2.9 **The Simulation of Systems Using Control Design Software 113

**2.10 **Sequential Design Example: Disk Drive Read System 128

**2.11 **Summary 130

Skills Check 131

Exercises 135

Problems 141

Advanced Problems 153

Design Problems 155

Computer Problems 157

Terms and Concepts 159

**CHAPTER ** **3 ** ** ***State Variable Models 161*

**3.1 **Introduction 162

**3.2 **The State Variables of a Dynamic System 162

**3.3 **The State Differential Equation 166

**3.4 **Signal-Flow Graph and Block Diagram Models 171

**3.5 **Alternative Signal-Flow Graph and Block Diagram Models 182

**3.6 **The Transfer Function from the State Equation 187

**3.7 **The Time Response and the State Transition Matrix 189

**3.8 **Design Examples 193

**3.9 **Analysis of State Variable Models Using Control Design Software 206

**3.10 **Sequential Design Example: Disk Drive Read System 209

**3.11 **Summary 213

Skills Check 214

Exercises 217

Problems 220

Advanced Problems 227

Design Problems 230

Computer Problems 231

Terms and Concepts 232

**CHAPTER ** **4 ** ** ***Feedback Control System Characteristics 234*

**4.1 **Introduction 235

**4.2 **Error Signal Analysis 237

**4.3 **Sensitivity of Control Systems to Parameter Variations 239

**4.4 **Disturbance Signals in a Feedback Control System 242

**4.5 **Control of the Transient Response 247

**4.6 **Steady-State Error 250

**4.7 **The Cost of Feedback 253

**4.8 **Design Examples 254

**4.9 **Control System Characteristics Using Control Design Software 268

**4.10 **Sequential Design Example: Disk Drive Read System 273

**4.11 **Summary 277

Skills Check 279

Exercises 283

Problems 287

Advanced Problems 293

Design Problems 296

Computer Problems 300

Terms and Concepts 303

**CHAPTER ** **5 ** ** ***The Performance of Feedback Control Systems 304*

**5.1 **Introduction 305

**5.2 **Test Input Signals 305

**5.3 **Performance of Second-Order Systems 308

**5.4 **Effects of a Third Pole and a Zero on the Second-Order System

Response 314

**5.5 **The *s*-Plane Root Location and the Transient Response 320

**5.6 **The Steady-State Error of Feedback Control Systems 322

**5.7 **Performance Indices 330

**5.8 **The Simplification of Linear Systems 339

**5.9 **Design Examples 342

**5.10 **System Performance Using Control Design Software 356

**5.11 **Sequential Design Example: Disk Drive Read System 360

**5.12 **Summary 364

Skills Check 364

Exercises 368

Problems 371

Advanced Problems 377

Design Problems 379

Computer Problems 382

Terms and Concepts 384

**CHAPTER ** **6 ** ** ***The Stability of Linear Feedback Systems 386*

**6.1 **The Concept of Stability 387

**6.2 **The Routh—Hurwitz Stability Criterion 391

**6.3 **The Relative Stability of Feedback Control Systems 399

**6.4 **The Stability of State Variable Systems 401

**6.5 **Design Examples 404

**6.6 **System Stability Using Control Design Software 413

**6.7 **Sequential Design Example: Disk Drive Read System 421

**6.8 **Summary 424

Skills Check 425

Exercises 428

Problems 430

Advanced Problems 435

Design Problems 438

Computer Problems 440

Terms and Concepts 442

**CHAPTER ** **7 ** ** ***The Root Locus Method 443*

**7.1 **Introduction 444

**7.2 **The Root Locus Concept 444

**7.3 **The Root Locus Procedure 449

**7.4 **Parameter Design by the Root Locus Method 467

**7.5 **Sensitivity and the Root Locus 473

**7.6 **PID Controllers 480

**7.7 **Negative Gain Root Locus 492

**7.8 **Design Examples 496

**7.9 **The Root Locus Using Control Design Software 510

**7.10 **Sequential Design Example: Disk Drive Read System 516

**7.11 **Summary 518

Skills Check 522

Exercises 526

Problems 530

Advanced Problems 539

Design Problems 543

Computer Problems 549

Terms and Concepts 551

**CHAPTER ** **8 ** ** ***Frequency Response Methods 553*

**8.1 **Introduction 554

**8.2 **Frequency Response Plots 556

**8.3 **Frequency Response Measurements 577

**8.4 **Performance Specifications in the Frequency Domain 579

**8.5 **Log Magnitude and Phase Diagrams 582

**8.6 **Design Examples 583

**8.7 **Frequency Response Methods Using Control Design Software 596

**8.8 **Sequential Design Example: Disk Drive Read System 602

**8.9 **Summary 603

Skills Check 608

Exercises 613

Problems 616

Advanced Problems 626

Design Problems 628

Computer Problems 631

Terms and Concepts 633

**CHAPTER ** **9 ** ** ***Stability in the Frequency Domain 634*

**9.1 **Introduction 635

**9.2 **Mapping Contours in the *s*-Plane 636

**9.3 **The Nyquist Criterion 642

**9.4 **Relative Stability and the Nyquist Criterion 653

**9.5 **Time-Domain Performance Criteria in the Frequency Domain 661

**9.6 **System Bandwidth 668

**9.7 **The Stability of Control Systems with Time Delays 668

**9.8 **Design Examples 673

**9.9 **PID Controllers in the Frequency Domain 691

**9.10 **Stability in the Frequency Domain Using Control Design Software 692

**9.11 **Sequential Design Example: Disk Drive Read System 700

**9.12 **Summary 703

Skills Check 711

Exercises 715

Problems 721

Advanced Problems 731

Design Problems 735

Computer Problems 740

Terms and Concepts 742

**CHAPTER ** **10 ** ** ***The Design of Feedback Control Systems 743*

**10.1 **Introduction 744

**10.2 **Approaches to System Design 745

**10.3 **Cascade Compensation Networks 747

**10.4 **Phase-Lead Design Using the Bode Diagram 751

**10.5 **Phase-Lead Design Using the Root Locus 757

**10.6 **System Design Using Integration Networks 764

**10.7 **Phase-Lag Design Using the Root Locus 767

**10.8 **Phase-Lag Design Using the Bode Diagram 772

**10.9 **Design on the Bode Diagram Using Analytical Methods 776

**10.10 **Systems with a Prefilter 778

**10.11 **Design for Deadbeat Response 781

**10.12 **Design Examples 783

**10.13 **System Design Using Control Design Software 796

**10.14 **Sequential Design Example: Disk Drive Read System 802

**10.15 **Summary 804

Skills Check 806

Exercises 810

Problems 814

Advanced Problems 823

Design Problems 826

Computer Problems 831

Terms and Concepts 833

**CHAPTER ** **11 ** ** ***The Design of State Variable Feedback*

** ***Systems 834*

**11.1 **Introduction 835

**11.2 **Controllability and Observability 835

**11.3 **Full-State Feedback Control Design 841

**11.4 **Observer Design 847

**11.5 **Integrated Full-State Feedback and Observer 851

**11.6 **Reference Inputs 857

**11.7 **Optimal Control Systems 859

**11.8 **Internal Model Design 869

**11.9 **Design Examples 873

**11.10 **State Variable Design Using Control Design Software 882

**11.11 **Sequential Design Example: Disk Drive Read System 888

**11.12 **Summary 890

Skills Check 890

Exercises 894

Problems 896

Advanced Problems 900

Design Problems 903

Computer Problems 906

Terms and Concepts 908

**CHAPTER ** **12 ** ** ***Robust Control Systems 910*

**12.1 **Introduction 911

**12.2 **Robust Control Systems and System Sensitivity 912

**12.3 **Analysis of Robustness 916

**12.4 **Systems with Uncertain Parameters 918

**12.5 **The Design of Robust Control Systems 920

**12.6 **The Design of Robust PID-Controlled Systems 926

**12.7 **The Robust Internal Model Control System 932

**12.8 **Design Examples 935

**12.9 **The Pseudo-Quantitative Feedback System 952

**12.10 **Robust Control Systems Using Control Design Software 953

**12.11 **Sequential Design Example: Disk Drive Read System 958

**12.12 **Summary 960

Skills Check 961

Exercises 965

Problems 967

Advanced Problems 971

Design Problems 974

Computer Problems 980

Terms and Concepts 982

**CHAPTER ** **13 ** ** ***Digital Control Systems 984*

**13.1 **Introduction 985

**13.2 **Digital Computer Control System Applications 985

**13.3 **Sampled-Data Systems 987

**13.4 **The *z*-Transform 990

**13.5 **Closed-Loop Feedback Sampled-Data Systems 995

**13.6 **Performance of a Sampled-Data, Second-Order System 999

**13.7 **Closed-Loop Systems with Digital Computer Compensation 1001

**13.8 **The Root Locus of Digital Control Systems 1004

**13.9 **Implementation of Digital Controllers 1008

**13.10 **Design Examples 1009

**13.11 **Digital Control Systems Using Control Design Software 1018

**13.12 **Sequential Design Example: Disk Drive Read System 1023

**13.13 **Summary 1025

Skills Check 1025

Exercises 1029

Problems 1031

Advanced Problems 1033

Design Problems 1034

Computer Problems 1036

Terms and Concepts 1037

**APPENDIX ** **A ** ** ***MATLAB Basics 1038*

** ***References 1056*

** ***Index 1071*

**WEB RESOURCES**

**APPENDIX ** **B ** ** ***MathScript RT Module Basics*

**APPENDIX ** **C ** ** ***Symbols, Units, and Conversion Factors*

**APPENDIX ** **D ** ** ***Laplace* ** *** Transform Pairs*

**APPENDIX ** **E ** ** ***An Introduction to Matrix Algebra*

**APPENDIX ** **F ** ** ***Decibel Conversion*

**APPENDIX ** **G ** ** ***Complex Numbers*

**APPENDIX ** **H ** ** ***z-Transform Pairs Preface*

**APPENDIX ** **I ** ** ***Discrete-Time Evaluation of the Time Response*