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More About This Textbook
Overview
Modern Control Systems, 12e, is ideal for an introductory undergraduate course in control systems for engineering students.
Written to be equally useful for all engineering disciplines, this text is organized around the concept of control systems theory as it has been developed in the frequency and time domains. It provides coverage of classical control, employing root locus design, frequency and response design using Bode and Nyquist plots. It also covers modern control methods based on state variable models including pole placement design techniques with fullstate feedback controllers and fullstate observers. Many examples throughout give students ample opportunity to apply the theory to the design and analysis of control systems. Incorporates computeraided design and analysis using MATLAB and LabVIEW MathScript.
This bestselling text, renowned for its practical applications and design problems, has been revised to make greater use of MATLAB integration, and features a new chapter on digital controls. The book includes more practical applications and contexts than any other book in the field.
Editorial Reviews
Booknews
Organized around the concepts of control system theory as they have been developed in the frequency and time domains, this senior level engineering textbook stresses physical system modeling and practical control system designs with realistic system specifications. The ninth edition integrates a companion web site and the use of Simulink. Annotation c. Book News, Inc., Portland, OR (booknews.com)Product Details
Related Subjects
Meet the Author
Richard C. Dorf is a Professor of Electrical and Computer Engineering at the University of California, Davis. Known as an instructor who is highly concerned with the discipline of electrical engineering and its application to social and economic needs, Professor Dorf has written and edited several successful engineering textbooks and handbooks, including the best selling Engineering Handbook, second edition and the third edition of the Electrical Engineering Handbook. Professor Dorf is also co author of Technology Ventures, a leading textbook on technology entrepreneurship. Professor Dorf is a Fellow of the IEEE and a Fellow of the ASEE. He is active in the fields of control system design and robotics. Dr. Dorf holds a patent for the PIDA controller.
Robert H. Bishop is the OPUS Dean of Engineering at Marquette University and is a Professor in the Department of Electrical and Computer Engineering. Prior to coming to Marquette University, he was a Professor of Aerospace Engineering and Engineering Mechanics at The University of Texas at Austin for 20 years where he held the Joe J. King Professorship and was a Distinguished Teaching Professor. Professor Bishop started his engineering career as a member of the technical staff at the MIT Charles Stark Draper Laboratory. He authors the wellknown textbook for teaching graphical programming entitled Learning with LabVIEW and is also the editorinchief of the Mechatronics Handbook. A talented educator, Professor Bishop has been recognized with numerous teaching awards including the coveted Lockheed Martin Tactical Aircraft Systems Award for Excellence in Engineering Teaching. He also received the John Leland Atwood Award by the American Society of Engineering Educators (ASEE) and the American Institute of Aeronautics and Astronautics (AIAA) that is given periodically to “a leader who has made lasting and significant contributions to aerospace engineering education.” He is a Fellow of the AIAA, a Fellow of the American Astronautical Society (AAS), and active in ASEE and in the Institute of Electrical and Electronics Engineers (IEEE).
Read an Excerpt
Preface
MODERN CONTROL SYSTEMS—THE BOOK
The Mars Pathfinder spacecraft was sent aloft aboard a Delta II expendable launch vehicle on December 4,1996 to begin a sevenmonth journey to the Red Planet. The Pathfinder mission, one of the first of the NASA Discoveryclass missions, was the first mission to land on Mars since the successful Viking spacecraft over two decades ago. After traveling over 497,418,000 km, the spacecraft impacted the Martian surface on July 4,1997 with a velocity of about 18 m/s. Upon impact the spacecraft bounced up approximately 15 meters, then continued to bounce another 15 times and rolled to a stop about 1 km from the initial impact point. The landing site is known as the Sagan Memorial Station and is located in the Ares Vallis region at 19.33 N, 33.55 W. Pathfinder deployed the firstever autonomous rover vehicle, known as the Sojourner, to explore the landing site area. The mobile Sojourner had a mass of 10.5 kilograms and was designed to roam in a 300m^{2} area for around 30 days. The 0.25m^{2} solar array provided 16 watthours of peak power and the primary battery provided about 150 watthours of power. The steering control of this vehicle had to be accurate and had to limit the power consumption. Control engineers play a critical role in the success of the planetary exploration program. The role of autonomous vehicle spacecraft control systems will continue to increase as flight computer hardware and operating systems improve. In fact, Pathfinder used a commercially produced, multitasking computer operating system hosted in a 32bit radiationhardened workstation with1gigabyte storage, programmable in C. This is quite an advancement over the Apollo computers with a fixed (readonly) memory of 36,864 words (one word was 16 bits) together with an erasable memory of 2,048 words. The Apollo "programming language" was a pseudocode notation encoded and stored as a list of data words "interpreted" and translated into a sequence of subroutine links. Interesting realworld problems, such as planetary mobile rovers like Sojourner, are used as illustrative examples throughout the book. For example, a mobile rover design problem is discussed in the Design Example in Section 4.8.
Control engineering is an exciting and a challenging field. By its very nature, control engineering is a multidisciplinary subject, and it has taken its place as a core course in the engineering curriculum. It is reasonable to expect different approaches to mastering and practicing the art of control engineering. Since the subject has a strong mathematical foundation, one might approach it from a strictly theoretical point of view, emphasizing theorems and proofs. On the other hand, since the ultimate objective is to implement controllers in real systems, one might take an ad hoc approach relying only on intuition and handson experience when designing feedback control systems. Our approach is to present a control engineering methodology that, while based on mathematical fundamentals, stresses physical system modeling and practical control system designs with realistic system specifications.
We believe that the most important and productive approach to learning is for each of us to rediscover and recreate anew the answers and methods of the past. Thus the ideal is to present the student with a series of problems and questions and point to some of the answers that have been obtained over the past decades. The traditional method—to confront the student not with the problem but with the finished solution—is to deprive the student of all excitement, to shut off the creative impulse, to reduce the adventure of humankind to a dusty heap of theorems. The issue, then, is to present some of the unanswered and important problems that we continue to confront, for it may be asserted that what we have truly learned and understood, we discovered ourselves.
The purpose of this book is to present the structure of feedback control theory and to provide a sequence of exciting discoveries as we proceed through the text and problems. If this book is able to assist the student in discovering feedback control system theory and practice, it will have succeeded.
THE AUDIENCE
This text is designed for an introductory undergraduate course in control systems for engineering students. There is very little demarcation between aerospace, chemical, electrical, industrial, and mechanical engineering in control system practice; therefore this text is written without any conscious bias toward one discipline. Thus it is hoped that this book will be equally useful for all engineering disciplines and, perhaps, will assist in illustrating the utility of control engineering. The numerous problems and examples represent all fields, and the examples of the sociological, biological, ecological, and economic control systems are intended to provide the reader with an awareness of the general applicability of control theory to many facets of life. We believe that exposing students of one discipline to examples and problems from other disciplines will provide them with the ability to see beyond their own field of study. Many students pursue careers in engineering fields other than their own. For example, many electrical and mechanical engineers find themselves in the aerospace industry working alongside aerospace engineers. We hope this introduction to control engineering will give students a broader understanding of control system design and analysis.
In its first eight editions, Modern Control Systems has been used in seniorlevel courses for engineering students at more than 400 colleges and universities. It also has been used in courses for engineering graduate students with no previous background in control engineering.
THE NINTH EDITION
A companion website has been developed for students and faculty using the ninth edition. The website contains practice exercises and exam problems, all the MATLAB mfiles and Simulink simulations in the book, Laplace and ztransform tables, written materials on matrix algebra, complex numbers, and symbols, units, and conversion factors. An icon will appear in the book margin whenever there is additional related material on the website. Also, since the website provides a mechanism for continuously updating and adding control related materials of interest to students and professors, it is advisable to visit the website regularly during the semester or quarter when taking the course. The MCS website address is ...
Table of Contents
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 SignalFlow 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 SignalFlow Graph and Block Diagram Models 171
3.5 Alternative SignalFlow 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 SteadyState 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 SecondOrder Systems 308
5.4 Effects of a Third Pole and a Zero on the SecondOrder System
Response 314
5.5 The sPlane Root Location and the Transient Response 320
5.6 The SteadyState 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 sPlane 636
9.3 The Nyquist Criterion 642
9.4 Relative Stability and the Nyquist Criterion 653
9.5 TimeDomain 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 PhaseLead Design Using the Bode Diagram 751
10.5 PhaseLead Design Using the Root Locus 757
10.6 System Design Using Integration Networks 764
10.7 PhaseLag Design Using the Root Locus 767
10.8 PhaseLag 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 FullState Feedback Control Design 841
11.4 Observer Design 847
11.5 Integrated FullState 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 PIDControlled Systems 926
12.7 The Robust Internal Model Control System 932
12.8 Design Examples 935
12.9 The PseudoQuantitative 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 SampledData Systems 987
13.4 The zTransform 990
13.5 ClosedLoop Feedback SampledData Systems 995
13.6 Performance of a SampledData, SecondOrder System 999
13.7 ClosedLoop 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 zTransform Pairs Preface
APPENDIX I DiscreteTime Evaluation of the Time Response
Preface
Preface
MODERN CONTROL SYSTEMS—THE BOOK
The Mars Pathfinder spacecraft was sent aloft aboard a Delta II expendable launch vehicle on December 4,1996 to begin a sevenmonth journey to the Red Planet. The Pathfinder mission, one of the first of the NASA Discoveryclass missions, was the first mission to land on Mars since the successful Viking spacecraft over two decades ago. After traveling over 497,418,000 km, the spacecraft impacted the Martian surface on July 4,1997 with a velocity of about 18 m/s. Upon impact the spacecraft bounced up approximately 15 meters, then continued to bounce another 15 times and rolled to a stop about 1 km from the initial impact point. The landing site is known as the Sagan Memorial Station and is located in the Ares Vallis region at 19.33 N, 33.55 W. Pathfinder deployed the firstever autonomous rover vehicle, known as the Sojourner, to explore the landing site area. The mobile Sojourner had a mass of 10.5 kilograms and was designed to roam in a 300m^{2} area for around 30 days. The 0.25m^{2} solar array provided 16 watthours of peak power and the primary battery provided about 150 watthours of power. The steering control of this vehicle had to be accurate and had to limit the power consumption. Control engineers play a critical role in the success of the planetary exploration program. The role of autonomous vehicle spacecraft control systems will continue to increase as flight computer hardware and operating systems improve. In fact, Pathfinder used a commercially produced, multitasking computer operating system hosted in a 32bit radiationhardened workstationwith1gigabyte storage, programmable in C. This is quite an advancement over the Apollo computers with a fixed (readonly) memory of 36,864 words (one word was 16 bits) together with an erasable memory of 2,048 words. The Apollo "programming language" was a pseudocode notation encoded and stored as a list of data words "interpreted" and translated into a sequence of subroutine links. Interesting realworld problems, such as planetary mobile rovers like Sojourner, are used as illustrative examples throughout the book. For example, a mobile rover design problem is discussed in the Design Example in Section 4.8.
Control engineering is an exciting and a challenging field. By its very nature, control engineering is a multidisciplinary subject, and it has taken its place as a core course in the engineering curriculum. It is reasonable to expect different approaches to mastering and practicing the art of control engineering. Since the subject has a strong mathematical foundation, one might approach it from a strictly theoretical point of view, emphasizing theorems and proofs. On the other hand, since the ultimate objective is to implement controllers in real systems, one might take an ad hoc approach relying only on intuition and handson experience when designing feedback control systems. Our approach is to present a control engineering methodology that, while based on mathematical fundamentals, stresses physical system modeling and practical control system designs with realistic system specifications.
We believe that the most important and productive approach to learning is for each of us to rediscover and recreate anew the answers and methods of the past. Thus the ideal is to present the student with a series of problems and questions and point to some of the answers that have been obtained over the past decades. The traditional method—to confront the student not with the problem but with the finished solution—is to deprive the student of all excitement, to shut off the creative impulse, to reduce the adventure of humankind to a dusty heap of theorems. The issue, then, is to present some of the unanswered and important problems that we continue to confront, for it may be asserted that what we have truly learned and understood, we discovered ourselves.
The purpose of this book is to present the structure of feedback control theory and to provide a sequence of exciting discoveries as we proceed through the text and problems. If this book is able to assist the student in discovering feedback control system theory and practice, it will have succeeded.
THE AUDIENCE
This text is designed for an introductory undergraduate course in control systems for engineering students. There is very little demarcation between aerospace, chemical, electrical, industrial, and mechanical engineering in control system practice; therefore this text is written without any conscious bias toward one discipline. Thus it is hoped that this book will be equally useful for all engineering disciplines and, perhaps, will assist in illustrating the utility of control engineering. The numerous problems and examples represent all fields, and the examples of the sociological, biological, ecological, and economic control systems are intended to provide the reader with an awareness of the general applicability of control theory to many facets of life. We believe that exposing students of one discipline to examples and problems from other disciplines will provide them with the ability to see beyond their own field of study. Many students pursue careers in engineering fields other than their own. For example, many electrical and mechanical engineers find themselves in the aerospace industry working alongside aerospace engineers. We hope this introduction to control engineering will give students a broader understanding of control system design and analysis.
In its first eight editions, Modern Control Systems has been used in seniorlevel courses for engineering students at more than 400 colleges and universities. It also has been used in courses for engineering graduate students with no previous background in control engineering.
THE NINTH EDITION
A companion website has been developed for students and faculty using the ninth edition. The website contains practice exercises and exam problems, all the MATLAB mfiles and Simulink simulations in the book, Laplace and ztransform tables, written materials on matrix algebra, complex numbers, and symbols, units, and conversion factors. An icon will appear in the book margin whenever there is additional related material on the website. Also, since the website provides a mechanism for continuously updating and adding control related materials of interest to students and professors, it is advisable to visit the website regularly during the semester or quarter when taking the course. The MCS website address is ...