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Feedback Systems: An Introduction for Scientists and Engineers

Åström, Karl Johan and Murray, Richard M. (2008) Feedback Systems: An Introduction for Scientists and Engineers. Princeton University Press , Princeton, NJ. ISBN 978-0-691-13576-2 http://resolver.caltech.edu/CaltechBOOK:2008.003

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Abstract

This book provides an introduction to the basic principles and tools for the design and analysis of feedback systems. It is intended to serve a diverse audience of scientists and engineers who are interested in understanding and utilizing feedback in physical, biological, information and social systems.We have attempted to keep the mathematical prerequisites to a minimum while being careful not to sacrifice rigor in the process. We have also attempted to make use of examples from a variety of disciplines, illustrating the generality of many of the tools while at the same time showing how they can be applied in specific application domains. A major goal of this book is to present a concise and insightful view of the current knowledge in feedback and control systems. The field of control started by teaching everything that was known at the time and, as new knowledge was acquired, additional courses were developed to cover new techniques. A consequence of this evolution is that introductory courses have remained the same for many years, and it is often necessary to take many individual courses in order to obtain a good perspective on the field. In developing this book, we have attempted to condense the current knowledge by emphasizing fundamental concepts. We believe that it is important to understand why feedback is useful, to know the language and basic mathematics of control and to grasp the key paradigms that have been developed over the past half century. It is also important to be able to solve simple feedback problems using back-of-the-envelope techniques, to recognize fundamental limitations and difficult control problems and to have a feel for available design methods. This book was originally developed for use in an experimental course at Caltech involving students from a wide set of backgrounds. The course was offered to undergraduates at the junior and senior levels in traditional engineering disciplines, as well as first- and second-year graduate students in engineering and science. This latter group included graduate students in biology, computer science and physics. Over the course of several years, the text has been classroom tested at Caltech and at Lund University, and the feedback from many students and colleagues has been incorporated to help improve the readability and accessibility of the material. Because of its intended audience, this book is organized in a slightly unusual fashion compared to many other books on feedback and control. In particular, we introduce a number of concepts in the text that are normally reserved for second-year courses on control and hence often not available to students who are not control systems majors. This has been done at the expense of certain traditional topics, which we felt that the astute student could learn independently and are often explored through the exercises. Examples of topics that we have included are nonlinear dynamics, Lyapunov stability analysis, the matrix exponential, reachability and observability, and fundamental limits of performance and robustness. Topics that we have deemphasized include root locus techniques, lead/lag compensation and detailed rules for generating Bode and Nyquist plots by hand. Several features of the book are designed to facilitate its dual function as a basic engineering text and as an introduction for researchers in natural, information and social sciences. The bulk of the material is intended to be used regardless of the audience and covers the core principles and tools in the analysis and design of feedback systems. Advanced sections, marked by the “dangerous bend” symbol shown here, contain material that requires a slightly more technical background, of the sort that would be expected of senior undergraduates in engineering. A few sections are marked by two dangerous bend symbols and are intended for readers with more specialized backgrounds, identified at the beginning of the section. To limit the length of the text, several standard results and extensions are given in the exercises, with appropriate hints toward their solutions. To further augment the printed material contained here, a companion web site has been developed and is available from the publisher’s web page: http://press.princeton.edu/titles/8701.html The web site contains a database of frequently asked questions, supplemental examples and exercises, and lecture material for courses based on this text. The material is organized by chapter and includes a summary of the major points in the text as well as links to external resources. The web site also contains the source code for many examples in the book, as well as utilities to implement the techniques described in the text. Most of the code was originally written using MATLAB M-files but was also tested with LabView MathScript to ensure compatibility with both packages. Many files can also be run using other scripting languages such as Octave, SciLab, SysQuake and Xmath. The first half of the book focuses almost exclusively on state space control systems. We begin in Chapter 2 with a description of modeling of physical, biological and information systems using ordinary differential equations and difference equations. Chapter 3 presents a number of examples in some detail, primarily as a reference for problems that will be used throughout the text. Following this, Chapter 4 looks at the dynamic behavior of models, including definitions of stability and more complicated nonlinear behavior. We provide advanced sections in this chapter on Lyapunov stability analysis because we find that it is useful in a broad array of applications and is frequently a topic that is not introduced until later in one’s studies. The remaining three chapters of the first half of the book focus on linear systems, beginning with a description of input/output behavior in Chapter 5. In Chapter 6, we formally introduce feedback systems by demonstrating how state space control laws can be designed. This is followed in Chapter 7 by material on output feedback and estimators. Chapters 6 and 7 introduce the key concepts of reachability and observability, which give tremendous insight into the choice of actuators and sensors, whether for engineered or natural systems. The second half of the book presents material that is often considered to be from the field of “classical control.” This includes the transfer function, introduced in Chapter 8, which is a fundamental tool for understanding feedback systems. Using transfer functions, one can begin to analyze the stability of feedback systems using frequency domain analysis, including the ability to reason about the closed loop behavior of a system from its open loop characteristics. This is the subject of Chapter 9, which revolves around the Nyquist stability criterion. In Chapters 10 and 11, we again look at the design problem, focusing first on proportional-integral-derivative (PID) controllers and then on the more general process of loop shaping. PID control is by far the most common design technique in control systems and a useful tool for any student. The chapter on frequency domain design introduces many of the ideas of modern control theory, including the sensitivity function. In Chapter 12, we combine the results from the second half of the book to analyze some of the fundamental trade-offs between robustness and performance. This is also a key chapter illustrating the power of the techniques that have been developed and serving as an introduction for more advanced studies. The book is designed for use in a 10- to 15-week course in feedback systems that provides many of the key concepts needed in a variety of disciplines. For a 10-week course, Chapters 1–2, 4–6 and 8–11 can each be covered in a week’s time, with the omission of some topics from the final chapters. A more leisurely course, spread out over 14–15 weeks, could cover the entire book, with 2 weeks on modeling (Chapters 2 and 3) — particularly for students without much background in ordinary differential equations — and 2 weeks on robust performance (Chapter 12). The mathematical prerequisites for the book are modest and in keeping with our goal of providing an introduction that serves a broad audience. We assume familiarity with the basic tools of linear algebra, including matrices, vectors and eigenvalues. These are typically covered in a sophomore-level course on the subject, and the textbooks by Apostol [10], Arnold [13] and Strang [187] can serve as good references. Similarly, we assume basic knowledge of differential equations, including the concepts of homogeneous and particular solutions for linear ordinary differential equations in one variable. Apostol [10] and Boyce and DiPrima [42] cover this material well. Finally, we also make use of complex numbers and functions and, in some of the advanced sections, more detailed concepts in complex variables that are typically covered in a junior-level engineering or physics course in mathematical methods. Apostol [9] or Stewart [186] can be used for the basic material, with Ahlfors [6], Marsden and Hoffman [146] or Saff and Snider [172] being good references for the more advanced material. We have chosen not to include appendices summarizing these various topics since there are a number of good books available. One additional choice that we felt was important was the decision not to rely on a knowledge of Laplace transforms in the book. While their use is by far the most common approach to teaching feedback systems in engineering, many students in the natural and information sciences may lack the necessary mathematical background. Since Laplace transforms are not required in any essential way, we have included them only in an advanced section intended to tie things together for students with that background. Of course, we make tremendous use of transfer functions, which we introduce through the notion of response to exponential inputs, an approach we feel is more accessible to a broad array of scientists and engineers. For classes in which students have already had Laplace transforms, it should be quite natural to build on this background in the appropriate sections of the text. Acknowledgments: The authors would like to thank the many people who helped during the preparation of this book. The idea for writing this book came in part from a report on future directions in control [155] to which Stephen Boyd, Roger Brockett, John Doyle and Gunter Stein were major contributors. Kristi Morgansen and Hideo Mabuchi helped teach early versions of the course at Caltech on which much of the text is based, and Steve Waydo served as the head TA for the course taught at Caltech in 2003–2004 and provided numerous comments and corrections. Charlotta Johnsson and Anton Cervin taught from early versions of the manuscript in Lund in 2003–2007 and gave very useful feedback. Other colleagues and students who provided feedback and advice include Leif Andersson, John Carson, K. Mani Chandy, Michel Charpentier, Domitilla Del Vecchio, Kate Galloway, Per Hagander, Toivo Henningsson Perby, Joseph Hellerstein, George Hines, Tore Hägglund, Cole Lepine, Anders Rantzer, Anders Robertsson, Dawn Tilbury and Francisco Zabala. The reviewers for Princeton University Press and Tom Robbins at NI Press also provided valuable comments that significantly improved the organization, layout and focus of the book. Our editor, Vickie Kearn, was a great source of encouragement and help throughout the publishing process. Finally, we would like to thank Caltech, Lund University and the University of California at Santa Barbara for providing many resources, stimulating colleagues and students, and pleasant working environments that greatly aided in the writing of this book.


Item Type:Book
Additional Information:Copyright ©2008 by Princeton University Press. Reprinted with permission. Welcome to AMwiki <http://www.cds.caltech.edu/~murray/amwiki>. This is the wiki for the text Feedback Systems by Karl J. Åström and Richard M. Murray. On this site you will find the complete text of the book as well as additional examples, exercises, and frequently asked questions. Contents Preface ix Chapter 1. Introduction 1 1.1 What Is Feedback? 1 1.2 What Is Control? 3 1.3 Feedback Examples 5 1.4 Feedback Properties 17 1.5 Simple Forms of Feedback 23 1.6 Further Reading 25 Exercises 25 Chapter 2. System Modeling 27 2.1 Modeling Concepts 27 2.2 State Space Models 34 2.3 Modeling Methodology 44 2.4 Modeling Examples 51 2.5 Further Reading 61 Exercises 61 Chapter 3. Examples 65 3.1 Cruise Control 65 3.2 Bicycle Dynamics 69 3.3 Operational Amplifier Circuits 71 3.4 Computing Systems and Networks 75 3.5 Atomic Force Microscopy 81 3.6 Drug Administration 84 3.7 Population Dynamics 89 Exercises 91 Chapter 4. Dynamic Behavior 95 4.1 Solving Differential Equations 95 4.2 Qualitative Analysis 98 4.3 Stability 102 4.4 Lyapunov Stability Analysis 110 4.5 Parametric and Nonlocal Behavior 120 4.6 Further Reading 126 Exercises 126 Chapter 5. Linear Systems 131 5.1 Basic Definitions 131 5.2 The Matrix Exponential 136 5.3 Input/Output Response 145 5.4 Linearization 158 5.5 Further Reading 163 Exercises 164 Chapter 6. State Feedback 167 6.1 Reachability 167 6.2 Stabilization by State Feedback 175 6.3 State Feedback Design 183 6.4 Integral Action 195 6.5 Further Reading 197 Exercises 197 Chapter 7. Output Feedback 201 7.1 Observability 201 7.2 State Estimation 206 7.3 Control Using Estimated State 211 7.4 Kalman Filtering 215 7.5 A General Controller Structure 219 7.6 Further Reading 226 Exercises 226 Chapter 8. Transfer Functions 229 8.1 Frequency Domain Modeling 229 8.2 Derivation of the Transfer Function 231 8.3 Block Diagrams and Transfer Functions 242 8.4 The Bode Plot 250 8.5 Laplace Transforms 259 8.6 Further Reading 262 Exercises 262 Chapter 9. Frequency Domain Analysis 267 9.1 The Loop Transfer Function 267 9.2 The Nyquist Criterion 270 9.3 Stability Margins 278 9.4 Bode’s Relations and Minimum Phase Systems 283 9.5 Generalized Notions of Gain and Phase 285 9.6 Further Reading 290 Exercises 290 Chapter 10. PID Control 293 10.1 Basic Control Functions 293 10.2 Simple Controllers for Complex Systems 298 10.3 PID Tuning 302 10.4 Integrator Windup 306 10.5 Implementation 308 10.6 Further Reading 312 Exercises 313 Chapter 11. Frequency Domain Design 315 11.1 Sensitivity Functions 315 11.2 Feedforward Design 319 11.3 Performance Specifications 322 11.4 Feedback Design via Loop Shaping 326 11.5 Fundamental Limitations 331 11.6 Design Example 340 11.7 Further Reading 343 Exercises 344 Chapter 12. Robust Performance 347 12.1 Modeling Uncertainty 347 12.2 Stability in the Presence of Uncertainty 352 12.3 Performance in the Presence of Uncertainty 358 12.4 Robust Pole Placement 361 12.5 Design for Robust Performance 369 12.6 Further Reading 374 Exercises 374 Bibliography 377 Index 387
Subject Keywords:Chemical Engineering, Control and Dynamical Systems, Electrical Engineering, Mechanical Engineering
Record Number:CaltechBOOK:2008.003
Persistent URL:http://resolver.caltech.edu/CaltechBOOK:2008.003
Official Citation:Karl Johan Åström and Richard M. Murray. Feedback systems : an introduction for scientists and engineers. Princeton University Press, Princeton, NJ, 2008. http://resolver.caltech.edu/CaltechBOOK:2008.003
Usage Policy:You are granted permission for individual, educational, research and non-commercial reproduction, distribution, display and performance of this work in any format.
ID Code:25062
Collection:CaltechBOOK
Deposited By: Imported from CaltechBOOK
Deposited On:06 Feb 2008
Last Modified:26 Dec 2012 13:36

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