Feedback Control of Dynamics Systems

Feedback Control of Dynamics Systems

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Overview

This introductory book provides an in-depth, comprehensive treatment of a collection of classical and state-space approaches to control system design—and ties the methods together so that a designer is able to pick the method that best fits the problem at hand. It includes case studies and comprehensive examples with close integration of MATLAB throughout the book. Chapter topics include an overview and brief history of feedback control, dynamic models, dynamic response, basic properties of feedback, the root-locus design method, the frequency-response design method, state-space design, digital control, and control-system design. A basic reference for control systems engineers.

Product Details

ISBN-13: 9780201115406
Publisher: Addison-Wesley
Publication date: 01/01/1986
Series: Addison-Wesley Series in Electrical Engineering
Pages: 580

Read an Excerpt

PREFACE:

As we planned the writing and production of a third edition of Feedback Control of Dynamic Systems we were guided by three central objectives. First we wanted to retain what was best about a basically good book. Second, we wanted to present the material in a way that would significantly improve its pedagogical effectiveness as a support for both students and teachers of feedback control. Finally, we wanted to enhance the book in ways that would reflect recent advances in the availability and use of computers in control system design.

The goals we have followed for each previous edition of this text serve as a basis for the third edition. These goals include developing insight into the problems of control and intuition about methods available to solve them, emphasizing design in parallel with analysis techniques, showing the unity among the several individual design techniques and synthesizing them into a "toolbox" of problem-solving methods, and presenting this interdisciplinary material in a way that is easily understood by students from any engineering background.

In order to meet these basic goals and to improve this edition's pedagogical effectiveness, we made a number of changes, including the addition of study aids to help students organize and review the large quantity of information in the book, as well as approximately three times as many problem-solving examples as the previous edition, ranging from basic drill to sophisticated design. We also provided expanded and clarified explanations of ideas and concepts that many students find difficult to understand. Finally we added computer commands for many operations and made available a MATLAB toolboxwith files that will reproduce many of the figures of the book. These figures can be studied to see exactly how a given design solution works and to explore alternatives.

In formulating these goals and developing these changes, we were guided by our own experiences and benefited from extensive and very detailed reviews provided by numerous other instructors who have used the book. We made a serious effort to incorporate each of the reviewers' suggested changes, provided the change was consistent with the book's overall goals. As a result, we feel that this third edition presents the material with more pedagogical support, motivation, and accessibility than ever before while remaining a solid foundation for meeting the educational challenges of a study of feedback control.

Addressing the Educational Challenges

Some of the educational challenges facing students of feedback control are long-standing; others have emerged in recent years. Some of the challenges remain for students across their entire engineering education; others are unique to this relatively sophisticated course. Whether they are old or new, general or particular, the educational challenges we perceived were critical to the evolution of this text. Here we will state several educational challenges and describe our approaches to each of them.

CHALLENGE: Students must master design as well as analysis techniques.

Design is central to all of engineering and especially so to control systems. Students find that design issues, with their corresponding opportunities to tackle practical applications, particularly motivating. But students also find design problems difficult because of the poorly posed problem statements and the lack of unique solutions. Because of both its inherent importance for and its motivational effect on students, design is emphasized throughout this text so that confidence in solving design problems is developed from the start.

The emphasis on design begins in Chapter 4 following the development of modeling and dynamic response. The basic idea of feedback is introduced first, showing its influence on disturbance rejection and tracking accuracy and robustness to parameter changes. The design orientation continues with a uniform treatment of the root locus, frequency response, and state feedback techniques. All the treatments are aimed at providing the knowledge necessary to find a good feedback control design with no more complex mathematical development than is essential to clear understanding.

Throughout the text, examples are used to compare and contrast the design techniques afforded by the different design methods and, in the capstone case studies of Chapter 9, complex real-world design problems are attached using all the methods in a unified way.

CHALLENGE: New ideas continue to be introduced into control. Control is an active field of research and hence there is a steady influx of new concepts, ideas, and techniques. In time, some of these elements develop to the point where they join the list of things every control engineer must know. This text is devoted to supporting students equally in their need to grasp both traditional and more modern topics.

Two of the modern aspects (1) balanced coverage of frequency response and state-space topics, and (2) an introduction to digital control area carried over from the earlier editions. The state-space methods are increasingly part of the well-prepared control engineer's toolbox, especially with the wide-spread availability of computer aids to carry out the computations associated with this method. Thus state-space ideas are introduced in the early chapters on models and state-space design methods are given equal emphasis (Chapter 7) with the s-plane (Chapter 5) and frequency-domain (Chapter 6) topics. Digital technology is used increasingly to implement controls and a preliminary description of digital design methods is presented in Chapter 8. However, the chapter is written in such a way that the basic ideas can be covered early in the course and can be applied throughout the book if desired.

New to the third edition is the integration of computer-aided methods. We recognize that this is a sensitive issue about which opinions vary from instructor to instructor. Some feel that time spent on computer assignments is time lost from learning basic concepts. Others feel that failure to teach computer-aided methods is a failure to prepare students properly for professional practice. We believe that computer aids are important and have included computer exercises and the ideas of Computer Aided Control System Design (CACSD) throughout the text. However, the inclusion of computer aids has been done in such a way that the main flow of the book does not depend on them and the book can be used by instructors who choose not to cover the computer-based methods at all. The computer aids are distinguished by a computer icon for easy identification.

CHALLENGE: Students need to manage a great deal of information. The vast array of systems to which feedback control is applied and the growing variety of techniques available for the solution of control problems means that today's student of feedback control must learn many new ideas. How do students keep their perspective as they plow through lengthy and complex textual passages? How do they identify highlights and draw conclusions? How do they review for exams? Helping students with these tasks was a criterion in developing several new features for the third edition. We outline these features below.

  • Chapter openers offer perspective and overview. They place the specific chapter topic in the context of the discipline as a whole and they briefly overview the chapter sections. See Chapter 3 opener, pp. 85-86.
  • Margin notes help students scan for chapter highlights. They point to important definitions, equations, and concepts. See Advantage of feedback, p. 174; root-locus guidelines, p. 260.
  • Bulleted chapter summaries help with student review and prioritization. These summaries briefly reiterate the key concepts and conclusions of the chapter. See Chapter 2 summary, p. 68-70.
  • The color blue is used (1) to highlight useful pedagogical features; (2) to highlight components under particular scrutiny within block diagrams; (3) to distinguish curves on graphs; and (4) to lend a more realistic look to figures of physical systems. See Figure 4.14, p. 188; Figure 3,22, p. 134; Figure 3.42, p. 158.

CHALLENGE: Students of feedback control come from a wide range of disciplines.

Feedback control is an interdisciplinary field in that control is applied to systems in every conceivable area of engineering. Consequently, some schools have separate introductory courses for control within the standard disciplines. However, to restrict the examples to one field is to miss much of the range and power of feedback. Covering the whole range of applications is overwhelming. In this book we aim to develop the interdisciplinary nature of the field and to provide review material for several of the most common technologies so that students from many disciplines will be comfortable with the presentation. For Electrical Engineering students who typically have a good background in transform analysis, we include in Chapter 2 an introduction to writing equations of motion for mechanical mechanisms. For mechanical engineers who typically have had a course in dynamics, we include in Chapter 3 a review of the Laplace Transform and dynamic response as needed in control. In addition, we introduce other technologies briefly and, from time to time, we present the equations of motion of a physical system without derivation but with enough physical description to be understood from a response point of view. Examples of some of the physical systems represented in the text include the read-write head for a computer disk drive, a satellite tracking system, the fuel-air ration in an automobile engine, and an airplane automatic pilot system. A quadruple diamond icon appears next to examples containing such real-world systems.

Outline of the Book

The contents of the book are organized into nine chapters and five appendixes. The chapters include some sections of advanced or enrichment material marked with a box that can be omitted without interfering with the flow of the material. The appendixes include background and reference material such as Laplace transform tables, review of complex variables, and a review of matrix theory.

In Chapter 1, the essential ideas of feedback and some of the key design issues are introduced. It also contains a brief history of control, from the ancient beginnings of process control to the contributions of flight control and electronic feedback amplifiers. This brief history intends to introduce the student to the origins of this field and the key figures who contributed to its development.

Chapter 2 is a short presentation of dynamic modeling and includes mechanical, electrical, electro-mechanical, fluid, and thermodynamic devices. It also discusses the state variable formulation of differential equations. This material can be omitted, used as the basis of review homework to smooth out the usual nonuniform preparation of students, or covered in depth.

Chapter 3 covers dynamic response. Again, much of this material may have been covered previously, especially by electrical engineering students. For many departments, the new material for a controls course concerns the correlation between pole locations and transient response and the effects of extra zeros and poles on dynamic response. This material needs to be covered carefully.

Chapter 4 introduces feedback in the most elementary context, permitting concentration on the essential effects of feedback on tracking accuracy, disturbance rejection, and sensitivity to model errors. Here, in the context of a first-order model for speed control, the concepts of proportional, derivative, and integral (PID) control are introduced. In this way, the student gets the idea of what control is all about before the tedious rules of root locus or the Nyquist Stability Criterion are developed. In this approach, the central issues of control design are brought forward and can remain in the foreground during the development of the necessary analysis that goes with construction of sophisticated design tools. The idea of steady-state tracking error, system type, and elementary stability ideas are also treated here.

Following the overview of feedback, the core of the book presents the design methods based on root locus, frequency response, and state variable feedback in Chapters 5, 6, and 7, respectively.

Chapter 8 develops the tools needed to design feedback control for implementation in a digital computer. The chapter is written so that the material can be used throughout the course. For example, a feedback control design found by using the root locus method in Chapter 5 could be implemented in a digital computer by covering Section 8.2. For a more in-depth treatment of the discrete case, Section 8.3 could be covered immediately after Chapter 3. Sections 8.4 and 8.5 might be covered after Chapter 5. However, for a complete treatment of feedback control using digital computers, the reader is referred to the companion text, Digital Control of Dynamic Systems, by Franklin, Powell, and Workman.

In Chapter 9 the three primary approaches are integrated in several case studies and a framework for design is described that includes a touch of the real-world context of practical control design.

Course Configurations

The material in this text can be covered flexibly. Most first-course students in controls will have some dynamics and Laplace transforms. Therefore, Chapter 2 and Section 3.2 would be a review for those students. In a ten-week quarter, it is possible to cover the remaining sections of Chapter 3, and all of Chapters 1, 4, 5, and 6. Most boxed sections should be omitted. In the second quarter, Chapters 7 and 9 can be covered comfortably including the boxed sections. Alternatively, some boxed sections could be omitted and selected portions of Chapter 8 included. A semester course should comfortably accommodate Chapters 1-7, including the review material of Chapters 2 and 3, if needed. If time remains after this core coverage, selected case studies from Chapter 9 or some introduction of digital control from Chapter 8 may be added.

Chapter 8 (digital control) may be included in several ways. The sequence shown in Fig. P.1 carries both continuous and discrete concepts along in parallel throughout the course. On the other hand, covering Section 8.2 after Chapter 5 simply gives an introduction on how to implement a controller in a digital computer without coverage of the z-transform. That material could also be used by the students for homework associated with Chapters 6 and 7. The entire book can also be used for a three-quarter sequence of courses consisting of modeling and dynamic response (Chapters 2 and 3), classical control (Chapters 4, 5, 6), and modern control (Chapters 7, 8, 9).

All the material in the book except Chapters 2 and 8 is now being used as the basic sequence of two ten-week quarter courses at Stanford University. This course sequence is taken by seniors and first-year graduate students, mostly in the departments of Aeronautics and Astronautics, Mechanical Engineering, and Electrical Engineering. The course sequence complements a graduate course in linear systems and is the prerequisite to courses in digital control, optimal control, flight control, and smart product design. Prerequisites for the course sequence include dynamics or circuit analysis and Laplace transforms.

Prerequisites to This Feedback Control Course

This book is for a first course at the senior level for all engineering majors. For the core topics in Chapters 4-7, prerequisite understanding of modeling and dynamic response is necessary. Many students will come into the course with sufficient background in those concepts from previous courses in physics, circuits, and dynamic response. For those needing review, Chapters 2 and 3 should fill in the gaps.

An elementary understanding of matrix algebra is necessary to understand the state-space material. While all students will have much of this in prerequisite math courses, a review of the basic relations is given in Appendix C and a brief treatment of particular material needed in control is given at the start of Chapter 7. The emphasis is on the relations between linear dynamic systems and linear algebra.

A Note on Computer Integration

Some of the most common CACSD software packages are MATLAB, a product of The MathWorks, Inc., MATRIX, from Integrated Systems, Inc., CTRL-C, a product of Systems Control Technology, Inc., and CC from Systems Technology, Inc. We assume that any engineer doing control design today will have access to one or more of these tools or their equivalent. We firmly believe that to use these tools effectively the engineer must understand the basics of the method being used so that the results from the computer can be evaluated and checked for reasonableness by independent analysis. We have chosen to embed MATLAB statements throughout the text to illustrate the use of a CACSD tool to aid in particular aspects of control system design. For those students using one of the other CACSD software tools, we have included a cross reference table (Table F.1 and the inside back cover) that allows the name of a particular function for any of the software told above to be determined easily.

As a further aid to students in quick and effective learning of CACSD tool use, all the graphical figures in the text were generated using MATLAB. These files are available at no cost by returning the card enclosed in the back of the book. The files are also available on the disk that is supplied with the instructor's manual. With these files, a user can duplicate the figure or edit the file to generate a similar figure with revised parameters or procedures. Our goal is to provide the student with sufficient resources to reap the rewards of computer calculations without the pain of reprogramming or learning complex program procedures. We do not intend to replace the software manual by the statements in the text. Rather, our goal is to guide the student to the appropriate place in the manual and to expedite the process of making full use of the power of the computer.

Supplements

An instructor's manual with complete solutions to homework problems, categorization of problems by subtopic, and disk with MATLAB M-files is available to adoptors of the third edition. The disk in the instructor's manual may be copied and distributed to students.

Acknowledgments

Finally, we wish to acknowledge our great debt to all those who have contributed to the development of feedback control into the exciting field it is today and specifically to the considerable help and education we have received from our students and our colleagues. In particular, we have benefited in this effort by many discussions with the following who taught introductory control at Stanford: A. E. Bryson, Jr., R. H. Cannon, Jr., D. B. Debra, and S. Rock. We also appreciate the comments and help of Profs. M. Anderson, J. Chiasson, S. Desa, and M. Rabins.

The thorough and thoughtful recommendations of the following reviewers were instrumental in improving the third edition: S. Centinkunt, University of Illinois at Chicago; R. I. Egbert, Wichita State University; T. Jordanides, California State University at Long Beach; J. Fleming, Texas A&M University; R. Langari, Texas A&M University; D. G. Meyere, University of Colorado at Boulder; C. P. Neuman, Carnegie-Mellon University; K. Passino, Ohio State University; and W. R. Perkins, University of Illinois at Urbana. Professors Egbert and Passino also contributed new homework problems. Special thanks go to A. L. Swindlehurst, Brigham Young University, for this thorough review, constructive suggestions, problem editing, and careful proofing of the third edition. We thank you all for your feedback and trust that our "loop compensation" has used it effectively!

The organization, editing, and guidance for addressing the needs of students provided to us by Laurie McGuire was an enormous help. Many thanks to her, Helen Wythe, and the rest of the Addison-Wesley staff.

G.F.F.M
J.D.P.
A.E.-N.
Stanford, California

Table of Contents

1. An Overview and Brief History of Feedback Control.
2. Dynamic Models.
3. Dynamic Response.
4. Basic Properties of Feedback.
5. The Root-Locus Design Method.
6. The Frequency-Response Design Method.
7. State-Space Design.
8. Digital Control.
9. Control-System Design: Principles and Case Studies.

Preface

In this fourth edition we again had the objectives of retaining the best of the previous editions, to rewrite key sections where we felt it was possible to improve the presentations and enhance the book's pedagogical effectiveness, and to take better advantage of the wide use of computers in control design, especially the toolboxes of MATLAB and Simulink, from The Mathworks, Inc.

The basic structure of the book is unchanged and we continue to combine analysis with design using the three approaches of the root locus, frequency response, and state variable equations. The text continues to include carefully worked out examples, many of them new to this edition, to illustrate the material. As a new feature, to assist the students in verifying that they have learned the material, we provide a set of review questions at the end of each chapter with answers in the back of the book. While modest changes were made throughout the entire book, special attention was given to the introduction of transforms in Chapter 3, to the introduction to feedback in Chapter 4, and to the organization and statements of the problems appearing at the end of each chapter.

In the three central chapters on the design methods, we continue to expect the students to learn how to perform the basic calculations by hand in order to be able to guide a design by understanding (and frequently by a quick sketch) rather than by computer rote. However, more than in previous editions, we de-emphasize the manual work and introduce computer tools early on in recognition of the universal use of these tools in control analysis and design. For example, we no longer mark certain problems asrequiring a computer but, rather, expect that the student has access to a computer in every case, as needed.

Furthermore, in recognition of the fact that, increasingly, controllers are implemented in embedded computers, we introduce digital control in Chapter 4 and in a number of cases compare the responses of feedback systems using analog controllers with those having a digital "equivalent" controller. As before, we have prepared a collection of all the MATLAB ".m" files used to produce the figures in the book and these are available at the companion web site for this title:

our site

or at the homepage for SC Solutions, Inc.:

our site

As representative applications of control, we again present extensive case studies in Chapter 9. In this edition we have added new studies of the control of the read-write head assembly of a computer hard disk and the temperature control of a silicon wafer in a Rapid Thermal Processor used in the fabrication of integrated circuits.

We feel that this fourth edition presents the material with good pedagogical support, provides strong motivation for the study of control, and represents a solid foundation for meeting the educational challenges of a study of feedback control.

Addressing the Educational Challenges

Some of the educational challenges facing students of feedback control are long-standing; others have emerged in recent years. Some of the challenges remain for students across their entire engineering education; others are unique to this relatively sophisticated course. Whether they are old or new, general or particular, the educational challenges we perceived were critical to the evolution of this text. Here we will state several educational challenges and describe our approaches to each of them.

  • CHALLENGE: Students must master design as well as analysis techniques.

Design is central to all of engineering and especially to control systems. Students find that design issues, with their corresponding opportunities to tackle practical applications, particularly motivating. But students also find design problems difficult because design problem statements are usually poorly posed and lack unique solutions. Because of both its inherent importance for and its motivational effect on students, design is emphasized throughout this text so that confidence in solving design problems is developed from the start.

The emphasis on design begins in Chapter 4, following the development of modeling and dynamic response. The basic idea of feedback is introduced first, showing its influence on disturbance rejection, tracking accuracy, and robustness to parameter changes. The design orientation continues with uniform treatments of the root locus, frequency response, and state variable feedback techniques. All of the treatments are aimed at providing the knowledge necessary to find a good feedback control design with no more complex mathematical development than is essential to clear understanding.

Throughout the text, examples are used to compare and contrast the design techniques afforded by the different design methods and, in the capstone case studies of Chapter 9, complex real-world design problems are tackled using all of the methods in a unified way.

  • CHALLENGE: New ideas continue to be introduced into control.

Control is an active field of research and hence there is a steady influx of new concepts, ideas, and techniques. In time, some of these elements develop to the point where they join the list of things every control engineer must know. This text is devoted to supporting students equally in their need to grasp both traditional and more modern topics.

In each of our previous editions we have tried to give equal time to root locus, frequency response, and state variable methods for design. In this edition we have shifted the emphasis from manual design methods augmented with computer tools to an emphasis on computer-aided methods augmented with a solid mastery of the underlying techniques. Included in this re-emphasis is the early introduction of sampling, which enables one to design digital controllers. While this material can be skipped to save time without disruption of the flow of the text, we feel that it is very important for students to recognize that digital control is being used increasingly and that the most basic techniques of digital control are easily mastered.

With regret we acknowledge that we are not able at this time to introduce the important topics of hybrid control or designs based on various optimization methods.

  • CHALLENGE: Students need to manage a great deal of information.

The vast array of systems to which feedback control is applied and the growing variety of techniques available for the solution of control problems means that today's student of feedback control must learn many new ideas. How do students keep their perspective as they plow through lengthy and complex textual passages? How do they identify highlights and draw conclusions? How do they review for exams? Helping students with these tasks was a criterion for the fourth edition. We outline these features in the accompanying table on page xiv.

  • CHALLENGE: Students of feedback control come from a wide range of disciplines.

Feedback control is an interdisciplinary field in that control is applied to systems in every conceivable area of engineering. Consequently, some schools have separate introductory courses for control within the standard disciplines and some, such as Stanford University, have a single set of courses taken by students from many disciplines. However, to restrict the examples to one field is to miss much of the range and power of feedback; but to cover the whole range of applications is overwhelming. In this book we develop the interdisciplinary nature of the field and provide review material for several of the most common technologies so that students from many disciplines will be comfortable with the presentation. For electrical engineering students who typically have a good background in transform analysis, we include an introduction to writing equations of motion for mechanical mechanisms in Chapter 2. For mechanical engineers, we include in Chapter 3 a review of the Laplace Transform and dynamic response as needed in control. In addition, we introduce other technologies briefly and, from time to time, we present the equations of motion of a physical system without derivation but with enough physical description to be understood from a response point of view. Examples of some of the physical systems represented in the text include the read-write head for a computer disk drive, a satellite tracking system, the fuel-air ratio in an automobile engine, and an airplane autopilot system.

Outline of the Book

The contents of the book is organized into nine chapters and seven appendixes. The chapters include some sections of advanced or enrichment material marked with a triangular blue icon that can be omitted without interfering with the flow of the material. Examples and problems based on this material are also marked with these icons. The appendixes include background and reference material such as Laplace transform tables, a review of complex variables, a review of matrix theory, and answers to the end-of-chapter review questions.

In Chapter 1, the essential ideas of feedback and some of the key design issues are introduced. The chapter also contains a brief history of control, from the ancient beginnings of process control to the contributions of flight control and electronic feedback amplifiers. It is hoped that this brief history will give a context for the field, introduce some of the key figures who contributed to its development, and provide motivation to the student for the studies to come.

Chapter 2 is a short presentation of dynamic modeling and includes mechanical, electrical, electro-mechanical, fluid, and thermodynamic devices. It also discusses the state variable formulation of differential equations. This material can be omitted, used as the basis for review homework to smooth out the usual non-uniform preparation of students, or covered in depth.

Chapter 3 covers dynamic response as used in control. Again, much of this material may have been covered previously, especially by electrical engineering students. For many students, the correlation between pole locations and transient response and the effects of extra zeros and poles on dynamic response is new material, as is the notion of stability of a closed-loop system. This material needs to be covered carefully.

Chapter 4 introduces feedback in the most elementary context, permitting concentration on the essential effects of feedback on tracking accuracy, disturbance rejection, and sensitivity to model errors. The basic equation and transfer functions of feedback are introduced along with the definitions of the sensitivity and complementary sensitivity functions. In the context of a first-order model for speed control, the concepts of proportional, integral, and derivative (PID) control are introduced. In this way, the student gets the idea of what control is all about before the tedious rules of root locus or the Nyquist Stability Criterion are developed. Finally, in this chapter the basic issues of digital control are introduced, along with the idea of a digital equivalent controller. In this approach, the central issues of control design are brought forward and can remain in the foreground during the development of the necessary analysis that goes with construction of sophisticated design tools. The concepts of steady-state tracking error and system type are also treated here.

Following the overview of feedback, the core of the book presents the design methods based on root locus, frequency response, and state variable feedback in Chapters 5, 6, and 7, respectively.

Chapter 8 develops in more detail the tools needed to design feedback control for implementation in a digital computer. However, for a complete treatment of feedback control using digital computers, the reader is referred to the companion text, Digital Control of Dynamic Systems, by Franklin, Powell, and Workman (Prentice Hall, 1998).

In Chapter 9, the three primary approaches are integrated in several case studies and a framework for design is described that includes a touch of the real-world context of practical control design.

Course Configurations

The material in this text can be covered flexibly. Most first-course students in controls will have some background in dynamics and Laplace transforms. Therefore, Chapter 2 and most of Chapter 3 would be a review for those students. In a 10-week quarter, it is possible to review Chapter 3, and cover all of Chapters 1, 4, 5, and 6. Most optional sections noted with a blue triangle should be omitted. In the second quarter, Chapters 7 and 9 can be covered comfortably including these optional sections. Alternatively, some optional sections could be omitted and selected portions of Chapter 8 included. A semester course should comfortably accommodate Chapters 1-7, including the review material of Chapters 2 and 3, if needed. If time remains after this core coverage, selected case studies from Chapter 9 or some introduction of digital control from Chapter 8 may be added.

The entire book can also be used for a three-quarter sequence of courses consisting of modeling and dynamic response (Chapters 2 and 3), classical control (Chapters 4-6), and modern control (Chapters 7-9).

Two basic 10-week courses are offered at Stanford and are taken by seniors and first-year graduate students who have not had a course in control, mostly in the Departments of Aeronautics and Astronautics, Mechanical Engineering, and Electrical Engineering. The first course reviews Chapters 2 and 3 and covers Chapters 4-6. The more advanced course is intended for graduate students and reviews Chapters 4-6 and covers Chapters 7-9. This sequence complements a graduate course in linear systems and is the prerequisite to courses in digital control, optimal control, flight control, and smart product design. Several of the subsequent courses include extensive laboratory experiments. Prerequisites for the course sequence include dynamics or circuit analysis and Laplace transforms.

Prerequisites to this Feedback Control Course

This book is for a first course at the senior level for all engineering majors. For the core topics in Chapters 4-7, prerequisite understanding of modeling and dynamic response is necessary. Many students will come into the course with sufficient background in those concepts from previous courses in physics, circuits, and dynamic response. For those needing review, Chapters 2 and 3 should fill in the gaps.

An elementary understanding of matrix algebra is necessary to understand the state-space material. While all students will have much of this in prerequisite math courses, a review of the basic relations is given in Appendix C and a brief treatment of particular material needed in control is given at the start of Chapter 7. The emphasis is on the relations between linear dynamic systems and linear algebra.

Supplements

An Instructor's Manual with complete solutions to homework problems is available to faculty who adopt the fourth edition. The web sites mentioned above include the .m files used to generate all of the MATLAB figures in the book.

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