动态系统反馈控制第六版

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"Feedback Control of Dynamic Systems" 是一本专为高级或研究生级别的控制分析与设计课程设计的教材，适用于工程、科学和管理等相关领域的学生和实践中的控制工程师。本书第六版在前几版的基础上进行了修订，以增强教师的教学灵活性和学生的可读性。书中的第四章“反馈的初步分析”经过大幅重写，以更合理和有效的方式呈现内容。新增的生物控制案例研究为学生引入了这个重要的新领域，每章都包含历史视角，以展示该领域的起源。与早期版本一样，本书的解决方案基于最新版本的MATLAB和SIMULINK。此外，一些较为复杂的话题被移到了配套网站FPE6e.com上。本书作者Gene F. Franklin是斯坦福大学的教授，他与J. David Powell和Abbas Emami-Naeini共同撰写此书。这本书的出版团队包括编辑、市场营销、版权管理等多个环节的专业人士，确保了书籍的高质量和专业性。在内容方面，"Feedback Control of Dynamic Systems"深入探讨了动态系统的反馈控制原理。通过对反馈概念的详细解析，读者可以理解如何通过反馈机制来稳定和优化系统性能。书中不仅涵盖了基础的控制系统理论，如根轨迹、频率响应和状态空间分析，还讨论了现代控制理论中的关键概念，如PID控制器的设计、离散时间系统以及线性时不变系统（LTI）的稳定性分析。 MATLAB和SIMULINK的集成使用，使得学生能够通过实际操作来加深对理论的理解。这些软件工具在控制系统设计和仿真中扮演着重要角色，帮助读者将理论知识应用于实际问题的解决。通过本书的学习，学生和工程师可以掌握分析和设计反馈控制系统的基本技能，为未来在自动化、航空航天、机器人技术、电力系统等领域的工作打下坚实的基础。此外，将一些较复杂的主题移至网上平台，既保持了教科书的简洁性，又为有兴趣深入学习的读者提供了额外的学习资源。这种安排体现了教育技术的发展趋势，适应了不同学习风格和进度的需求。 "Feedback Control of Dynamic Systems"是一部全面且深入的教材，旨在培养读者在动态系统控制领域的专业知识和实践能力，对于想要在这个领域保持竞争力的工程师来说，是一本不可或缺的参考书。

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 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 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 10, complex real-world design problems are attacked

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.

In each of our editions we have tried to give equal importance to root locus, frequency response, and state-variable

methods for design. In this edition we continue to emphasize solid mastery of the underlying techniques. coupled

with computer based methods for detailed calculation. We also provide an early introduction to data sampling and

discrete controllers in recognition of the major role played by digital controllers in our field. While this material can

be skipped to save time without harm to the flow of the text, we feel that it is very important for students to

understand that computer control is widely used and that the most basic techniques of computer control are easily

mastered.

• 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 appropriate conclusions? How do they review for exams? Helping students with these tasks was

a criterion for the Fourth and Fifth Editions and continues to be addressed in this Sixth Edition. We outline these

features below.

FEATURE

1. 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.

2. Margin notes help students scan for chapter highlights. They point to important definitions, equations, and

concepts.

3. Boxedhighlights identify key concepts within the running text. They also function to summarize important design

procedures.

4. Bulleted chapter summaries help with student review and prioritization. These summaries briefly reiterate the key

concepts and conclusions of the chapter.

5. Synopsis of design aids. Relationships used in design and throughout the book are collected inside the back cover

for easy reference.

6. 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.

7. Review questions at the end of each chapter with solutions in the back to guide the student in self-study

• 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, like Stanford, 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 in Chapter 2 an introduction to writing equations of motion for mechanical mechanisms. 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

automatic pilot system.

Outline of the Book

The contents of the book are organized into ten chapters and three appendixes. Optional sections of advanced or

enrichment material marked with a triangle (A) are included at the end of some chapters. There is additional

enrichment material on the website. Examples and problems based on this material are also marked with a triangle

(A). The appendices include background and reference material. The appendices in the book include Laplace

transform tables, answers to the end-of-chapter review questions, and a list of MATLAB commands. The appendixes

on the website include a review of complex variables, a review of matrix theory, some important results related to

State-Space design, a tutorial on RLTOOL for MATLAB, and optional material supporting or extending several of the

chapters.

In Chapter 1, the essential ideas of feedback and some of the key design issues are introduced. This chapter also

contains a brief history of control, from the ancient beginnings of process control to 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, electromechanical,

fluid, and thermodynamic devices. 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 depending on the needs of the students.

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 represent new material. Stability

of dynamic systems is also introduced in this Chapter. This material needs to be covered carefully.

Chapter 4 presents the basic equations and transfer functions of feedback along with the definitions of the

sensitivity function. With these tools, open-loop and closed-loop control are compared with respect to disturbance

rejection, tracking accuracy, and sensitivity to model errors. Classification of systems according to their ability to track

polynomial reference signals or to reject polynomial disturbances is described with the concept of system type.

Finally, the classical proportional, integral, and derivative (PID) control structure is introduced and the influence of

the controller parameters on a system’s characteristic equation is explored along with PID tuning methods. The end-

of-chapter optional section treats digital control.

Following the overview of feedback in Chapter 4, 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; Ellis-Kagle Press, 1998.

In Chapter 9 the nonlinear material includes techniques for the linearization of equations of motion, analysis of

zero memory nonlinearity as a variable gain, frequency response as a describing function, the phase plane, Lyapunov

stability theory, and the circle stability criterion.

In Chapter 10 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 most of Chapter 3 would be a review for those students. In a ten-week

quarter, it is possible to review 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, some introduction of digital control from Chapter 8, selected nonlinear issues from

Chapter 9 and some of the case studies from Chapter 10 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 7-10).

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 7-10. This sequence

complements a graduate course in linear systems and is the prerequisite to courses in digital control, nonlinear

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 WE

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

The Web site mentioned above includes the dot-m and dot-mdl files used to generate all the MATLAB figures in the

book and these may be copied and distributed to the students as desired. An instructor’s manual with complete

solutions to all homework problems is available. The Web site also includes advanced material and appendixes.

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, S. Rock, S.

Boyd, C. Tomlin, P. Enge, and C. Gerdes. Other colleagues who have helped us include D. Fraser, N. C. Emami, B.

Silver, M. Dorfman, D. Brennan, K. Rudie, L. Pao, F. Khorrami, K. Lorell, and P. D. Mathur.

Special thanks go to the many students who have provided almost all the solutions to the problems in the book.

G.F.F.

J.D.P.

A.E.-N.

Stanford, California

1 An Overview and Brief History of Feedback Control

A Perspective on Feedback Control

Feedback control of dynamic systems is a very old concept with many characteristics that have evolved over time.

The central idea is that a system’s output can be measured and fed back to a controller of some kind and used to

effect the control. It has been shown that signal feedback can be used to control a vast array of dynamic systems

including, for example, airplanes and hard-disk data storage devices. To achieve good control there are four basic

requirements.

• The system must be stable at all times

• The system output must track the command input signal

• The system output must be prevented from responding too much to disturbance inputs

• These goals must be met even if the model used in the design is not completely accurate or if the dynamics of the

physical system change over time or with environmental changes.

The requirement of stability is basic and may have two causes. In the first place, the system may be unstable. This

is illustrated by the Segway vehicle, which will simply fall over if the control is turned off. On the other hand, adding

feedback may itself drive the system unstable. In ordinary experience such an instability is called a “vicious circle,”

where the feedback signal that is circled back makes the situation worse rather than better.

There are many examples of the requirement of having the system’s output track a command signal. For example,

driving a car so that the vehicle stays in its lane is command tracking. Similarly, flying an airplane in the approach to

a landing strip requires that a glide path be accurately tracked.

Disturbance rejection is one of the very oldest applications of feedback control. In this case, the “command” is

simply a constant set point to which the output is to be held as the environment changes. A very common example

of this is the room thermostat whose job it is to hold the room temperature close to the set point as outside

temperature and wind change, and as doors and windows are opened and closed.

Finally, to design a controller for a dynamic system, it is necessary to have a mathematical model of the dynamic

response of the system in all but the simplest cases. Unfortunately, almost all physical systems are very complex and

often nonlinear. As a result, the design will usually be based on a simplified model and must be robust enough that

the system meets its performance requirements when applied to the real device. Furthermore, again in almost all

cases, as time and the environment change, even the best of models will be in error because the system dynamics

have changed. Again, the design must not be too sensitive to these inevitable changes and it must work well enough

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/** * Selects the type of motor that's to be used (ERM or LRA). * Utilizes the Feedback Control Register. * @param val Corresponding val for either ERM or LRA motor. */ void drv2605l_motor_select(uint8_t val) { drv2605l_write(FEEDBACK_REG, val); }

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