#### Control Systems Engineering, 7th Edition

*By Norman S. Nise*

Control Systems Engineering, 7th Edition has become the top selling text for this course. It takes a practical approach, presenting clear and complete explanations. Real world examples demonstrate the analysis and design process, while helpful skill assessment exercises, numerous in-chapter examples, review questions and problems reinforce key concepts. A new progressive problem, a solar energy parabolic trough collector, is featured at the end of each chapter. Ten new simulated control lab experiments now complement the online resources that accompany the text. This edition also includes Hardware Interface Laboratory experiments for use on the MyDAQ platform from National Instruments. A tutorial for MyDAQ is included as Appendix D.

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Concept checkpoints help to reinforce learning

**Concept Check Questions** follow each reading section, helping students to reinforce and build upon the concepts they just learned.

Students develop problem-solving skills through guided exercises

**Control Solutions** for select Skill Assessment Exercises give students more problem-solving guidance in the form of hints, directions, and detailed solutions.

Students practice building the skills they need to succeed in the course

**Try It** exercises give students the opportunity to try programming solutions to problems themselves in MATLAB.

**Accessibly written.**Nise is noted for his clear writing and accessible presentation. Design Emphasis. Students are encouraged to go beyond a plug-and-chug approach through the use of design problems, progressive analysis and design problems, and examples and problems related to the case studies.**Real-world case studies.**The case studies (an autonomous submersible vehicle and an antenna position control system) are built up gradually throughout the chapters to demonstrate the analysis and design process.**Strong learning-by-example pedagogical approach.**Skill-assessment exercises demonstrate step-by-step techniques to solve most problems; cyber exploration labs show how to apply popular software tools (MATLAB®, LabVIEW®, and Simulink) to control engineering problems.**Clearly ties mathematics to physical reality.**Students can comprehend how theoretical concepts connect to actual system dynamics.**New Virtual Experiments.**The experiments (powered by Quanser) give students the opportunity to manipulate online simulations of real-world controls labs from their own computer.

#### What’s New

**Norman S. Nise** teaches in the Electrical and Computer Engineering Department at California State Polytechnic University, Pomona. In addition to being the author of Control Systems Engineering, Professor Nise has contributed to the CRC publications The Engineering Handbook, The Control Handbook, and The Electrical Engineering Handbook.

PREFACE, ix

1. INTRODUCTION, 1

1.1 Introduction, 2

1.2 A History of Control Systems, 4

1.3 System Configurations, 6

1.4 Analysis and Design Objectives, 9

1.5 The Design Process, 14

1.6 Computer-Aided Design, 19

1.7 The Control Systems Engineer, 20

Summary, 21

Review Questions, 22

Problems, 22

Cyber Exploration Laboratory, 29

Bibliography, 30

2. MODELING IN THE FREQUENCY DOMAIN, 33

2.1 Introduction, 34

2.2 Laplace Transform Review, 35

2.3 The Transfer Function, 44

2.4 Electrical Network Transfer Functions, 47

2.5 Translational Mechanical System Transfer Functions, 61

2.6 Rotational Mechanical System Transfer Functions, 69

2.7 Transfer Functions for Systems with Gears, 73

2.8 Electromechanical System Transfer Functions, 77

2.9 Electric Circuit Analogs, 83

2.10 Nonlinearities, 86

2.11 Linearization, 87

Case Studies, 92

Summary, 95

Review Questions, 95

Problems, 96

Cyber Exploration Laboratory, 107

Hardware Interface Laboratory, 110

Bibliography, 112

3. MODELING IN THE TIME DOMAIN, 115

3.1 Introduction, 116

3.2 Some Observations, 116

3.3 The General State-Space Representation, 120

3.4 Applying the State-Space Representation, 122

3.5 Converting a Transfer Function to State Space, 130

3.6 Converting from State Space to a Transfer Function, 136

3.7 Linearization, 138

Case Studies, 141

Summary, 145

Review Questions, 146

Problems, 146

Cyber Exploration Laboratory, 153

Bibliography, 155

4. TIME RESPONSE, 157

4.1 Introduction, 158

4.2 Poles, Zeros, and System Response, 158

4.3 First-Order Systems, 162

4.4 Second-Order Systems: Introduction, 164

4.5 The General Second-Order System, 169

4.6 Underdamped Second-Order Systems, 173

4.7 System Response with Additional Poles, 182

4.8 System Response With Zeros, 186

4.9 Effects of Nonlinearities Upon Time Response, 192

4.10 Laplace Transform Solution of State Equations, 194

4.11 Time Domain Solution of State Equations, 198

Case Studies, 202

Summary, 208

Review Questions, 209

Problems, 210

Cyber Exploration Laboratory, 223

Hardware Interface Laboratory, 227

Bibliography, 232

5. REDUCTION OF MULTIPLE SUBSYSTEMS, 235

5.1 Introduction, 236

5.2 Block Diagrams, 236

5.3 Analysis and Design of Feedback Systems, 245

5.4 Signal-Flow Graphs, 248

5.5 Mason’s Rule, 251

5.6 Signal-Flow Graphs of State Equations, 252

5.7 Alternative Representations in State Space, 256

5.8 Similarity Transformations, 264

Case Studies, 272

Summary, 278

Review Questions, 278

Problems, 279

Cyber Exploration Laboratory, 295

Bibliography, 297

6. STABILITY, 299

6.1 Introduction, 300

6.2 Routh-Hurwitz Criterion, 303

6.3 Routh-Hurwitz Criterion: Special Cases, 305

6.4 Routh-Hurwitz Criterion: Additional Examples, 31

6.5 Stability in State Space, 318

Case Studies, 321

Summary, 323

Review Questions, 323

Problems, 324

Cyber Exploration Laboratory, 332

Bibliography, 333

7. STEADY-STATE ERRORS, 335

7.1 Introduction, 336

7.2 Steady-State Error for Unity Feedback Systems, 339

7.3 Static Error Constants and System Type, 345

7.4 Steady-State Error Specifications, 348

7.5 Steady-State Error for Disturbances, 351

7.6 Steady-State Error for Nonunity Feedback Systems, 353

7.7 Sensitivity, 356

7.8 Steady-State Error for Systems in State Space, 359

Case Studies, 362

Summary, 365

Review Questions, 366

Problems, 367

Cyber Exploration Laboratory, 377

Bibliography, 379

8. ROOT LOCUS TECHNIQUES, 381

8.1 Introduction, 382

8.2 Defining the Root Locus, 386

8.3 Properties of the Root Locus, 388

8.4 Sketching the Root Locus, 390

8.5 Refining the Sketch, 395

8.6 An Example, 404

8.7 Transient Response Design via Gain Adjustment, 407

8.8 Generalized Root Locus, 411

8.9 Root Locus for Positive-Feedback Systems, 413

8.10 Pole Sensitivity, 415

Case Studies, 417

Summary, 422

Review Questions, 423

Problems, 423

Cyber Exploration Laboratory, 439

Hardware Interface Laboratory, 441

Bibliography, 447

9. DESIGN VIA ROOT LOCUS, 449

9.1 Introduction, 450

9.2 Improving Steady-State Error via Cascade Compensation, 453

9.3 Improving Transient Response via Cascade Compensation, 462

9.4 Improving Steady-State Error and Transient Response, 474

9.5 Feedback Compensation, 487

9.6 Physical Realization of Compensation, 495

Case Studies, 500

Summary, 504

Review Questions, 505

Problems, 506

Cyber Exploration Laboratory, 519

Hardware Interface Laboratory, 520

Bibliography, 523

10. FREQUENCY RESPONSE TECHNIQUES, 525

10.1 Introduction, 526

10.2 Asymptotic Approximations: Bode Plots, 531

10.3 Introduction to the Nyquist Criterion, 549

10.4 Sketching the Nyquist Diagram, 554

10.5 Stability via the Nyquist Diagram, 559

10.6 Gain Margin and Phase Margin via the Nyquist Diagram, 563

10.7 Stability, Gain Margin, and Phase Margin via Bode Plots, 565

10.8 Relation Between Closed-Loop Transient and Closed-Loop Frequency Responses, 569

10.9 Relation Between Closed- and Open-Loop Frequency Responses, 572

10.10 Relation Between Closed-Loop Transient and Open-Loop Frequency Responses, 577

10.11 Steady-State Error Characteristics from Frequency Response, 581

10.12 Systems with Time Delay, 585

10.13 Obtaining Transfer Functions Experimentally, 590

Case Study, 594

Summary, 595

Review Questions, 596

Problems, 597

Cyber Exploration Laboratory, 608

Bibliography, 609

11. DESIGN VIA FREQUENCY RESPONSE, 611

11.1 Introduction, 612

11.2 Transient Response via Gain Adjustment, 613

11.3 Lag Compensation, 616

11.4 Lead Compensation, 621

11.5 Lag-Lead Compensation, 627

Case Studies, 636

Summary, 638

Review Questions, 639

Problems, 639

Cyber Exploration Laboratory, 645

Bibliography, 646

12. DESIGN VIA STATE SPACE, 649

12.1 Introduction, 650

12.2 Controller Design, 651

12.3 Controllability, 658

12.4 Alternative Approaches to Controller Design, 661

12.5 Observer Design, 667

12.6 Observability, 674

12.7 Alternative Approaches to Observer Design, 677

12.8 Steady-State Error Design via Integral Control, 684

Case Study, 688

Summary, 693

Review Questions, 694

Problems, 695

Cyber Exploration Laboratory, 703

Bibliography, 704

13. DIGITAL CONTROL SYSTEMS, 707

13.1 Introduction, 707

13.2 Modeling the Digital Computer, 711

13.3 The z-Transform, 714

13.4 Transfer Functions, 719

13.5 Block Diagram Reduction, 723

13.6 Stability, 726

13.7 Steady-State Errors, 733

13.8 Transient Response on the z-Plane, 737

13.9 Gain Design on the z-Plane, 739

13.10 Cascade Compensation via the s-Plane, 742

13.11 Implementing the Digital

Compensator, 746

Case Studies, 749

Summary, 753

Review Questions, 754

Problems, 755

Cyber Exploration Laboratory, 762

Bibliography, 764

APPENDIX A List of Symbols, 767

APPENDIX B MATLAB Tutorial, 771

B.1 Introduction, 771

B.2 MATLAB Examples, 772

B.3 Command Summary, 814

Bibliography, 817

APPENDIX C MATLAB’s Simulink Tutorial, 819

C.1 Introduction, 819

C.2 Using Simulink, 819

C.3 Examples, 824

C.4 Using Simulink for Control System Design, 837

Summary, 846

Bibliography, 847

APPENDIX D LabVIEWTM Tutorial, 849

D.1 Introduction, 849

D.2 Control Systems Analysis, Design, and Simulation, 850

D.3 Using LabVIEW, 851

D.4 Analysis and Design Examples, 853

D.5 Simulation Examples, 865

D.6 Interfacing with External Hardware, 875

Summary, 879

Bibliography, 879

Online location is www.wiley.com/college/nise

GLOSSARY, 881

ANSWERS TO SELECTED PROBLEMS, 889

CREDITS, 895

INDEX

APPENDIX E MATLAB’s GUI Tools Tutorial (Online)

APPENDIX F MATLAB’s Symbolic Math Toolbox Tutorial (Online)

APPENDIX G Matrices, Determinants, and Systems of Equations (Online)

APPENDIX H Control System Computational Aids (Online)

APPENDIX I Derivation of a Schematic for a DC Motor (Online)

APPENDIX J Derivation of the Time Domain Solution of State Equations (Online)

APPENDIX K Solution of State Equations for t0≠0 (Online)

APPENDIX L Derivation of Similarity Transformations (Online)

APPENDIX M Root Locus Rules: Derivations (Online)

Control Systems Engineering Toolbox (Online)

Cyber Exploration Laboratory Experiments Covers Sheets (Online)

Lecture Graphics (Online)

Solutions to Assessment Exercises (Online)