Modern Control Systems (Addison-Wesley Series in Electrical Engineering)

For more than twenty years, Modern Control Systems has set the standard of excellence for undergraduate control systems textbooks. It has remained a bestseller because Richard Dorf and Robert Bishop have been able to take complex control theory and make it exciting and accessible to students. The book presents a control engineering methodology that, while based on mathematical fundamentals, stresses physical system modeling and practical control system designs with realistic system specifications.

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 seven-month journey to the Red Planet. The Pathfinder mission, one of the first of the NASA Discovery-class 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 first-ever 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 300-m2 area for around 30 days. The 0.25-m2 solar array provided 16 watt-hours of peak power and the primary battery provided about 150 watt-hours 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 32-bit radiation-hardened workstation with 1-gigabyte storage, programmable in C. This is quite an advancement over the Apollo computers with a fixed (read-only) 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 real-world 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 hands-on 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 senior-level 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 m-files and Simulink simulations in the book, Laplace and z-transform 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 prenhall/dorf.

With the ninth edition we continue to evolve the design emphasis that historically has characterized Modern Control Systems. Using the real-world engineering problems associated with designing a controller for a disk drive read system, we present the Sequential Design Example (identified by an arrow icon in the text), which is considered sequentially in each chapter using the methods and concepts in that chapter. Disk drives are used in computers of all sizes and they represent an important application of control engineering. Various aspects of the design of controllers for the disk drive read system are considered in each chapter. For example, in Chapter 1 we identify the control goals, identify the variables to be controlled, write the control specifications, and establish the preliminary system configuration for the disk drive. Then in Chapter 2 we obtain models of the process, sensors, and actuators. In the remaining chapters we continue the design process, stressing the main points of the chapters.

In the same spirit as the Sequential Design Example, we present a design problem that we call the Continuous Design Problem (identified by a triple arrow icon in the text) to give students the opportunity to build upon a design problem from chapter to chapter. High-precision machinery places stringent demands on table slide systems. In the Continuous Design Problem, students apply the techniques and tools presented in each chapter to the development of a design solution that meets the specified requirements.

The computer-aided design and analysis component of the book continues to evolve and improve. The MATLAB end-of-chapter problem set are identified by the graphical icon in the text. Also, many of the solutions to various components of the Sequential Design Example utilize MATLAB with corresponding scripts included in the figures.

In the ninth edition, we introduce the use of Simulink as an efficient way for MATLAB users to model, simulate, and analyze feedback control systems. Since Simulink is an interactive tool utilizing graphical interfaces effectively, we believe that the best way to learn about it is to jump right in and use it. Appendix B is devoted to the basics of Simulink where the student can walk through a sequence of steps to construct and simulate a simple system. We attempt to provide basic information about Simulink that is as loosely tied to specific releases of the software as possible. At the time of this ninth edition, the latest version is Simulink 3.0. As different versions of Simulink are released, previous introductions to Simulink Basics will be posted on the MCS website—check there if you are having compatibility problems with the Simulink models in this book.

Simulink examples are presented in Chapters 5 and 11. In Chapter 5, aircraft roll control is investigated using Simulink. In Chapter 11, a Simulink simulation is developed to study a system in state variable form. Pedagogy

The book is organized around the concepts of control system theory as they have been developed in the frequency and time domains. A real attempt has been made to make the selection of topics, as well as the systems discussed in the examples and problems, modern in the best sense. Therefore this book includes discussions on robust control systems and system sensitivity, state variable models, controllability and observability, computer control systems, internal model control, robust PID controllers, and computer-aided design and analysis, to name a few. However, the classical topics of control theory that have proved to be so very useful in practice have been retained and expanded.

Building Basic Principles: From Classical to Modern. Our goal is to present a clear exposition of the basic principles of frequency- and time-domain design techniques. The classical methods of control engineering are thoroughly covered: Laplace transforms and transfer functions; root locus design; Routh-Hurwitz stability analysis; frequency response methods, including Bode, Nyquist, and Nichols; steady-state error for standard test signals; second-order system approximations; and phase and gain margin and bandwidth. In addition, coverage of the state variable method is significant. Fundamental notions of controllability and observability for state variable models are discussed. Full state feedback design with Ackermann's formula for pole placement is presented, along with a discussion on the limitations of state variable feedback.

Upon this strong foundation of basic principles, the book provides many opportunities to explore topics beyond the traditional. Advances in robust control theory are introduced in Chapter 12. The implementation of digital computer control systems is discussed in Chapter 13. Each chapter but the first uses a MATLAB section to introduce the student to the notion of computer-aided design and analysis. The book concludes with an extensive References section, divided by chapter, to guide the student to further sources of information on control engineering.

Progressive Development of Problem-Solving Skills. Reading the chapters, attending lectures and taking notes, and working through the illustrated examples are all part of the learning process. But the real test comes at the end of the chapter with the problems. The book takes the issue of problem solving seriously. In each chapter, there are five problem types:

Exercises Problems Advanced Problems Design Problems MATLAB Problems

For example, the problem set for State Variable Models, Chapter 3 (see page 159) includes 19 exercises, 36 problems, 6 advanced problems, 5 design problems, and 7 MATLAB problems. The exercises permit the students to utilize readily the concepts and methods introduced in each chapter by solving relatively straightforward exercises before attempting the more complex problems. Answers to one-third of the exercises are provided. The problems require an extension of the concepts of the chapter to new situations. Introduced in the seventh edition to the problem set, the advanced problems represent problems of increasing complexity. The design problems emphasize the design task; the MATLAB problems give the student practice with problem solving using computers. In total, the book contains more than 800 problems. Also, the MCS website contains practice exercises that are instantly graded providing quick feedback for students. The abundance of problems of increasing complexity gives students confidence in their problem-solving ability as they work their way from the exercises to the design and MATLAB problems. A complete instructor manual, available for all adopters of the text for course use, contains complete solutions to all end-of-chapter problems.

A set of M-files, the Modern Control Systems Toolbox, has been developed by the authors to supplement the text. The M-files contain the scripts from each MATLAB and Simulink example in the text. You may retrieve the M-files from Prentice Hall at prenhall/dorf

Design Emphasis Without Compromising Basic Principles. The all-important topic of design of real-world, complex control systems is a major theme throughout the text. Emphasis on design for real-world applications addresses interest in design by ABET and industry. Each chapter contains at least one design example, including the following:

insulin delivery control (Sec. 1.11, page 22) low-pass filter (Sec. 2.9, page 72) printer belt drive (Sec. 3.9, page 147) Mars rover vehicle (Sec. 4.8, page 194) Hubble Space Telescope pointing control (Sec. 5.11, page 259) tracked vehicle turning control (Sec. 6.5, page 307) laser manipulator control system (Sec. 7.8, page 368) engraving machine control system (Sec. 8.7, page 435) remotely controlled reconnaissance vehicle (Sec. 9.8, page 505) x-y plotter (Sec. 10.13, page 595) automatic test system (Sec. 11.9, page 655) ultra-precision diamond turning machine (Sec. 12.12, page 710) worktable motion control system (Sec. 13.9, page 762)

The MATLAB sections assist students in utilizing computer-aided design and analysis concepts and rework many of the design examples. In Chapter 5, the Sequential Design Example: Disk Drive Read System is analyzed using MATLAB. A MATLAB script that can be used to analyze the design is presented in Figure 5.53, p. 274. In general, each script is annotated with comment boxes that highlight important aspects of the script. The accompanying output of the script (generally a graph) also contains comment boxes pointing out significant elements. The scripts can also be utilized_ with modifications as the foundation for solving other related problems.

Learning Enhancement. Each chapter begins with a chapter Preview describing the topics the student can expect to encounter. The chapters conclude with an end-of-cha...