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Textbook Trio
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n this issue we bring you reviews of three books that are directly relevant to the theme of the special section “Classical Control Revisited.” The first review, by Peter Dorato, discusses the unique aspects of the textbook by Kirsten Morris, who, incidentally, is a former associate editor for book reviews for IEEE Control Systems Magazine. In the next review, Daniel Davison describes the special features of the undergraduate control textbook by Goodwin, Graebe, and Salgado. Finally, Okko Bosgra provides us with a review of the second edition of the graduate textbook by Skogestand and Postlethwaite. If you are the author of a recently published book, please contact me about having your book reviewed in this department. Scott Ploen
[email protected]
Introduction to Feedback Control by KIRSTEN MORRIS
Most engineering programs in the United States include an introductory course on feedback control in their curriculum. In a 1990 survey of control systems education [1], 50% of programs granting a B.S.E.E. degree reported that an introHardcourt/Academic ductory control course was Press, 2001 required as part of their EE ISBN 0-12-507660-6 core. Although there is a current US$90.95, 512 pages. nationwide tendency toward reducing the number of required core courses, feedback control still constitutes an important component of most engineering disciplines. As noted in [2], automatic control can be viewed as the enabling technology of the 20th century. As a result, books that introduce feedback control are of great interest to both the academic and professional communities. The real issues concern which topics to cover in an introductory book and which prerequisites are needed to understand the theory. Most books labeled as classical introductory control books focus on control theory based on frequencydomain methods developed in the period 1930–1950. Ref-
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erence [3] is a good example, and the Nyquist stability criterion is a notable example of these methods. The key prerequisite for such classical control texts is some knowledge of complex analysis. In the 1960s, state-space methods such as Kalman filtering, optimal linear-quadratic-regulator (LQR) design, and stabilization by state feedback were introduced, and time-domain methods were added to classical frequencydomain methods. Many introductory control books started appearing in the 1970s with the term “modern control” in the title, with some state-space time-domain material mixed in with the “classical” frequency-domain material. Reference [4] is a good example of this trend. Linear algebra became an important prerequisite for understanding modern control theory. Between the mid 1970s and 1980s, a renaissance occurred in frequencydomain methods. In contrast to the frequency-domain design methods such as the Nyquist criterion, the new results were analytic results (also referred to as synthesis results) consisting of an existence theorem and a computable algorithm, which could find a solution when one existed. Examples of the new results include H∞ design theory and strong stabilization theory. Nevanlinna-Pick interpolation theory was used to design controllers. The 1985 monograph [5] includes most of the results available at the time for this new frequency-domain approach. It is interesting that a few years after the publication of [5], the H∞ design problem was solved by state-space techniques [6], leading to what is now known as the two-Riccati equation solution. Very few introductory control textbooks include theory developed after the state-space methods of the 1960s. Notable exceptions are [7] and the text reviewed here. Published in 2000, my monograph [8] was intended to supplement introductory textbooks with some of the analytic frequency-domain methods developed in the mid 1970s and 1980s. The texts [7] and the book under review are among the few examples where the post 1960s theory has been incorporated in an introductory text. To place this review in a proper context with respect to the current status of introductory control books, a list of topics covered in two introductory books, [9] and [10], is given. Since the material is more than can be covered in one semester, the topics are divided into two parts, assuming a two-semester sequence.
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First semester » modeling of physical systems (transfer functions and state-space equations) » dynamic response (linearization, transient response, and steady-state response) » stability (Routh-Hurwitz stability criterion) » root-locus methods » frequency-response methods (Nyquist stability criterion) » digital control (Introduction and transfer-function methods). Second semester » state-space design (state and state-estimate feedback, LQR design) » digital control (state-space design methods) » nonlinear systems (describing-function methods, linearization, and nonlinear stability concepts). In addition to covering these control topics, most introductory texts include appendices on matrices and complex variables.
CONTENTS OF INTRODUCTION TO FEEDBACK CONTROL The Morris text covers several topics normally included in most current introductory feedback control texts. For example, » transfer functions and state-space descriptions (Chapter II) » Routh-Hurwitz and Nyquist stability criteria (Chapter III) » state-feedback and linear-quadratic regulator theory (Chapter V). In addition to these standard topics, several topics from the post-1975 period are included. These topics, which have not yet been included in recent editions of introductory texts such as [9] and [10], include » robust stability and performance for unstructured perturbations (Chapters III and IV) » strong stabilization and Youla parameterization (Chapter VI) » generalized plants and H∞ design (chapters VII and VIII) H » ∞ optimization by model matching and interpolation theory (Chapter IX). Short appendices are included on normed linear spaces, matrix and abstract algebra, and state-space system manipulations. The material is well presented, with careful proofs of key results. Each chapter includes numerical examples, together with a good list of homework exercises. Some Matlab functions for computing numerical solution are mentioned, but the discussion of available computer software is limited.
CONCLUSIONS In the preface to her book, Kirsten Morris states, “This book is accessible to senior mathematics undergraduate
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students and to theoretically inclined engineering students.” This reviewer agrees with this statement, but of greater interest, especially to the academic engineering community, is the suitability of this introductory book as a text for a first engineering course in feedback control. Here there are some problems. One is that the mathematical level is too high, at least for most engineering programs in the United States. The survey [1] reports that only 23% of B.S.E.E programs, perhaps the most theoretical of all engineering degree programs, require a course in complex variables. Also reported in the above survey, less than 50% of electrical engineering programs require a linear algebra course. This figure limits accessibility of the Morris text for the majority of undergraduate engineering students. In addition, several standard topics associated with engineering courses on feedback control are not included, such as modeling of physical systems, root-locus analysis, digital control, and an introduction to nonlinear systems. If these topics had been included, and the level of mathematics reduced, this book would have been a major innovation for undergraduate control texts by including a significant amount of control theory developed after 1975. However, with its excellent treatment of the linearquadratic problem, the Youla parameterization, and H∞ theory, this book would make a very good text for a graduate engineering course in linear feedback control. Morris’s book could also be a valuable reference for graduate engineering students or applied mathematics students interested in becoming involved in research in the controls area. Finally, it should be noted that in many countries outside the United States, the mathematics preparation for engineering students is very rigorous. Thus the Morris text would be more accessible to students outside the United States. The difficulty in the United States in including more mathematics in the engineering curriculum is the time limit of a four-year bachelor’s degree. The American National Academy of Engineering has recently suggested that professional engineering education be extended to the master’s degree [11]. This extension would permit U.S. engineering students to be exposed to a deeper, more up-to-date treatment of control theory as presented by Morris and would be a welcome step in light of the recent globalization of engineering activities. Peter Dorato
REVIEWER INFORMATION Peter Dorato (
[email protected]) received the B.S.E.E. degree from the City College of New York in 1955, the M.S.E.E. degree from Columbia University in 1956, and the D.E.E. degree from the Polytechnic Institute of Brooklyn in 1961. He is currently professor emeritus in the Department of Electrical and Computer Engineering at the University of New Mexico. His research interests include robust control, linear feedback theory, analytic feedback design, and engineering education.
REFERENCES [1] P. Dorato, “A survey of control systems education in the United States,” IEEE Trans. Education, vol. 33, no. 3, pp. 306–310, 1990. [2] R.S. Kirby, S. Withington, A.B. Darling, and F.G. Kilgour, Engineering in Histor. New York: Dover Publications, 1990. [3] H. Chestnut and R. Mayer, Servomechanism and Regulating System Design. New York: Wiley, 1951. [4] K. Ogata, Modern Control Engineering, 1st ed. Upper Saddle River, NJ: Prentice Hall, 1970. [5] M. Vidyasagar, Control System Synthesis. A Factorization Approach. Cambridge, MA: MIT Press, 1985. [6] J.C. Doyle, K. Glover, P.P. Khargonekar, and B.A. Francis, “State-space
Control System Design by GRAHAM C. GOODWIN, STEFAN F. GRAEBE, and MARIO E. SALGADO
The origins of classical control engineering are fascinating. Largely motivated by military needs in World War II, research into controller analysis and design progressed to such an extent that, immediately after Prentice Hall, 2001 the end of the war, the first conISBN 0-13-958653-9 trol textbooks were published. 908 pages plus CD-ROM. By the mid 1950s, popular interest in automatic control was widespread, and the number of introductory textbooks mushroomed. An absorbing exposition of this early period is given in [1]. By the 1960s there were dozens of textbooks, including the representative books [2]–[17]. Today, when trying to choose a textbook for a first course in linear control, students and instructors alike can be overwhelmed by the options. For example, in addition to many of the older textbooks, my bookshelf alone has 17 recently published textbooks [18]–[34], and a library search indicates dozens of others. I examined the table of contents of [2]–[34], and it is remarkable to note that, with a few exceptions, the content of introductory control textbooks has not significantly changed over the years. Indeed, analysis and design based on Laplace transform techniques, the Nyquist stability criterion, root locus methods, and the Routh-Hurwitz stability test have been dominant topics for over 50 years. Curiously, even the features that distinguished textbooks in the 1950s and 1960s are similar to the features that distinguish books today: the balance between transfer function and state-space techniques, between continuous-time and discrete-time coverage, and between mathematical sophistication and practical engineering. The fact that largely the same material is taught today as was taught 50 years ago is not necessarily a sign that the present control curriculum is outdated; rather, in my opinion, it is reassuring to know that we really are teaching the fundamental principles and
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solutions to standard H2 and H∞ control problems,” IEEE Trans. Automat. Contr., vol. 34, no. 8, pp. 831–847, 1989. [7] P. B´elanger, Control Engineering: A Modern Approach. Fort Worth, TX: Saunders College Pub., 1995. [8] P. Dorato, Analytic Feedback System Design. An Interpolation Approach. Pacific Grove, CA: Brooks/Cole, 2000. [9] G.F. Franklin, J.D. Powell, and A. Emami-Naeimi, Feedback Control of Dynamic Systems, 5th ed. Upper Saddle River, NJ: Prentice Hall, 2006. [10] C.L. Phillips and R.D. Harbor, Feedback Control Systems, 4th ed. Upper Saddle River, NJ: Prentice Hall, 2000. [11] National Academy of Engineering, Educating the Engineer of 2020. Washington, DC: National Academies Press, 2005.
tools of control engineering, which do not change overnight. However, with all due respect to recent authors and publishers, it should be asked why so many new textbooks and new textbook editions are being written to teach the same introductory control material. A cynical reader would be justified in concluding that the only real differences between many new books and books from decades ago are the incorporation of Matlab, the introduction of color pages, and a significant increase in price! Despite similarities among introductory control textbooks, a few books stand out because they offer a different perspective. Control System Design by Goodwin, Graebe, and Salgado is such a book. The authors of Control System Design have decades of industrial control experience among them, with application areas as diverse as steel casting, distillation columns, and sugar processing. It is clear that the authors intended from the start to incorporate their practical experience into the book without compromising the mathematical rigor that has become standard in control academia. In my opinion they have succeeded in their objective.
THE BOOK’S PERSPECTIVE Control System Design reflects the practical experience of the authors in two ways. First, the book emphasizes several topics that are often neglected in control textbooks but are critical in many real-world problems. For example, the authors stress the importance of performance limitations in feedback control [34]–[36]. Both time- and frequency-domain performance limitations are carefully dealt with, first for singleinput, single-output (SISO) systems, and then for multi-input, multi-output (MIMO) systems. The book emphasizes the idea that it is important for the control engineer to assess, as early as possible in the design cycle, whether there are any properties of the plant—such as a time delay or a nonminimum-phase zero—that fundamentally limit the achievable closed-loop performance. Another example of a topic that receives little attention in typical textbooks is the choice of controller architecture. In Control System Design, the reader quickly learns to appreciate that the controller architecture affects the achievable closed-loop performance; for instance, it is shown that disturbance feed-
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forward, when feasible, can be used to overcome the limitations on disturbance rejection that arise in a pure feedback architecture. A third example of a practical topic that is often ignored is the nonlinear issue of actuator signal constraints. Constraints on both input amplitude and input rate of change are discussed. Techniques for dealing with the related issue of windup, the phenomenon whereby an integrator in the controller continues to integrate after an input hits a saturation limit, are also included. The second manner in which Control System Design reflects the industrial experience of the authors is in their choice of examples. More than a dozen case studies are included in the book and in the corresponding electronic resources. All of the case studies stem from recent real-world industrial systems in which the authors were involved. Some of the examples are revisited throughout the book, not only to illustrate analysis or design techniques but also to motivate why certain tools are needed in the first place. The examples are presented so that the reader can appreciate the basic issues without being overwhelmed with details. I found that the case studies make the book engaging by reminding me that modern control engineers, just like those from decades ago, can play a vital role in improving the efficiency and quality of industrial operations.
THE BOOK’S CONTENTS Control System Design covers a lot of material. The book has 26 chapters, divided into eight parts. The book starts in Part I with a brief history of control, an introduction to feedback principles, a discussion on modeling, and a review of signals and systems. In Part II, traditional classical control topics (Routh-Hurwitz, Nyquist theory, root locus, and PID control) are concisely covered, and a thorough treatment on pole placement is provided. Performance limitations, architecture issues, and control signal constraints in a SISO setting are included in Part III. The book then focuses on digital computer control in Part IV, where a unique feature of the presentation is the use of the delta operator as a tool for unifying the treatment of discrete-time and continuous-time theory [37]. The final section on SISO control, Part V, includes controller parameterizations, quadratically optimal control, statespace basics, and aspects of nonlinear control. Parts VI–VIII, the remainder of the book, deal with MIMO control. Topics include the exploitation of SISO methods in MIMO systems, linear-quadratic regulation, model predictive control, performance limitations, controller parameterizations, and decoupling techniques.
THE BOOK’S WRITING STYLE Control System Design is well written and a pleasure to read. Sections and chapters are nicely integrated, effective motivational and preview sections are provided regularly, and helpful summaries are included at the end of each chapter. The authors also manage to maintain the book’s practical
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flavor without grossly compromising mathematical integrity. Indeed, a theorem-proof format is used throughout most of the book to state main results. Having said this, not every result is justified by an appropriate theorem, but this lack of uniform rigor is understandable given realistic limits on the book size and the fact that some results, although useful in practice, are difficult to support theoretically. The book provides exercises at the end of each chapter, but I have not examined them carefully.
ELECTRONIC RESOURCES FOR THE BOOK The authors make extensive use of electronic resources to supplement their book. Most of the resources are available on a CD-ROM that is packaged with the book, but more up-to-date resources are available on a Web site. The Web site includes summaries of each chapter, appendices to the book (summarizing notation, Smith-McMillan forms, key results from analytic function theory, and some results on Riccati equations), interactive Java labs, Matlab programs for all examples used in the book, a comprehensive set of PowerPoint slides, an online book forum, errata, links to other relevant online resources, and even material for a Spanish introductory control course based on the book. I have reservations about the use of electronic media to supplement textbooks. One problem is that disk-drive hardware, data formats, and Internet addresses are constantly changing, making electronic data storage inherently short-lived. For example, Control System Design provides two Web links to the book’s Web page, but one link now leads to a Web page that has nothing to do with the book! Another disadvantage of electronic media is the inconvenience of needing to have a computer at hand while reading or studying from the book; when reading Control System Design at a cottage, I was frustrated more than once to discover that certain appendix material that is available only electronically would be helpful. Finally, I was disappointed to notice that the online forum, intended to be a venue for readers to discuss the book, was closed. Aside from the above inconveniences, a more serious concern arises: do the electronic resources have any educational value? Certainly the interactive Java labs are fun, but do they help students learn better than conventional methods, or do they help students learn material that cannot be taught in any other way? I am a skeptical on both counts. I am even more unconvinced about the benefits of the PowerPoint slides. Surely, effective teaching is possible only by careful personal preparation and study. Providing the slides tempts instructors to cut back on the preparation stage and may even deceive some instructors into thinking that they can effectively teach by simply reading the slides out loud to the class. Worse still, providing slides tempts students to skip lectures and may deceive some of them into thinking that memorizing the slides is equivalent to learning. I recognize that the authors put a great amount of thought and time into preparing the slides, but it is those
very ingredients that every teacher and student must personally put into the teaching and learning process. I am not alone in recognizing that the push to use technology in teaching may be a mixed blessing [38]–[40].
WHERE THE BOOK FITS IN It is not immediately obvious how Control System Design fits into a classical undergraduate curriculum. The authors suggest that the book can be used in four ways: as a text on signals and systems (using Part I), as a text on basic control theory (using parts I, II, and sections of III), as a text on digital control (using Part IV), or as a text for a second course on control (using sections of parts V–VIII). In my opinion, the book is written too concisely for the first three ways. For example, all of the material in a conventional classical control course is contained in Part II of the book, a mere 80 pages in length. The fourth suggested use of the book, as a second course on control, is not only realistic, but I believe that Control System Design is an excellent book for this purpose. The authors’ suggestion of using parts V–VIII to create a state-space course is one possibility. However, for students who have had a conventional first course in control systems, there are other ways to take advantage of the strengths of the book. For example, I can imagine an advanced classical control course based on parts III and V, or a digital control course based on parts III and IV, or an introductory multivariable control course based on Part III and selected sections from parts V–VIII.
FINAL RECOMMENDATION Control System Design is a well-written book that stands out to me because it provides a real-world perspective. Although the book is too concise for an introductory course, I recommend the book for a second course in control engineering and as a reference book. Finally, I especially recommend the book to all academic control researchers, particularly those who are so enveloped in theory that they have forgotten the exciting applied roots of control engineering. Daniel E. Davison
REVIEWER INFORMATION Daniel E. Davison (
[email protected]) received the B.A.Sc. degree in engineering science and the M.A.Sc. degree in electrical engineering from the University of Toronto in 1992 and 1994, respectively. He then obtained a Ph.D. in systems engineering from the University of Michigan in 1997. After working on an automotive emissions control project at the University of Cambridge, U.K., he accepted a position at the University of Waterloo, Canada, where he is now an associate professor in the Department of Electrical and Computer Engineering. He can be contacted at the Department of Electrical and Computer Engineering, University of Waterloo, Waterloo, Ontario, N2L 3G1 Canada.
REFERENCES [1] S. Bennett, A History of Control Engineering 1930–1955. Stevenage, U.K.: Peregrinus, 1993. [2] W.R. Ahrendt and J.F. Talpin, Automatic Feedback Control. New York: McGraw-Hill, 1951. [3] G.J. Thaler and R.G. Brown, Servomechanism Analysis. New York: McGraw-Hill, 1953. [4] W.R. Evans, Control-System Dynamics. New York: McGraw-Hill, 1954. [5] J.G. Truxal, Automatic Feedback Control System Synthesis. New York: McGraw-Hill, 1955. [6] G.H. Farrington, Fundamentals of Automatic Control. London, U.K.: Chapman & Hall, 1957. [7] G.J. Murphy, Basic Automatic Control Theory. New York: Van Nostrand, 1957. [8] D.P. Eckman, Automatic Process Control. New York: Wiley, 1958. [9] C.H. Wilts, Principles of Feedback Control. Reading, MA: Addison-Wesley, 1960. [10] F.H. Raven, Automatic Control Engineering. New York: McGraw-Hill, 1961. [11] A.E. De Barr, Automatic Control: An Introduction to the Theory of Feedback and Feedback Control Systems. New York: Reinhold, 1962. [12] R.N. Clark, Introduction to Automatic Control Systems. New York: Wiley, 1962. [13] B.C. Kuo, Automatic Control Systems. New York: Wiley, 1962. [14] M.A. Aizerman, Theory of Automatic Control (translated into English). New York: Pergamon, 1963. [15] B.E. DeRoy, Automatic Control Theory. New York: Wiley, 1966. [16] R.C. Dorf, Modern Control Systems. Reading, MA: Addison-Wesley, 1967. [17] M. Healey, Principles of Automatic Control. English Universities Press, 1967. [18] W.L. Brogan, Modern Control Theory, 3rd ed. Englewood, NJ: Prentice Hall, 1990. [19] C.E. Rohrs, J.L. Melsa, and D.G. Schultz, Linear Control Systems. New York: McGraw Hill, 1993. [20] J. Van de Vegte, Feedback Control Systems, 3rd ed. Englewood, NJ: Prentice Hall, 1994. [21] D.K. Anand and R.B. Zmood, Introduction to Control Systems, 3rd ed. London, U.K.: Butterworth-Heinemann, 1995. [22] M. Driels, Linear Control Systems Engineering. New York: McGraw Hill, 1996. [23] S.M. Shinners, Modern Control System Theory and Design, 2nd ed. New York: Wiley, 1998. [24] W. Bolton, Control Engineering, 2nd ed. Englewood, NJ: Prentice Hall, 1998. [25] C.L. Philips and R.D. Harbor, Feedback Control Systems, 4th ed. Englewood, NJ: Prentice Hall, 2000. [26] K. Ogata, Modern Control Engineering, 4th ed. Englewood, NJ: Prentice Hall, 2001. [27] R.N. Bateson, Introduction to Control System Technology, 7th ed. Englewood, NJ: Prentice-Hall, 2002. [28] J. Dorsey, Continuous and Discrete Control Systems: Modeling, Identification, Design, and Implementation. New York: McGraw Hill, 2002. [29] G.F. Franklin, J.D. Powell, and A. Emami-Naeini, Feedback Control of Dynamic Systems, 5th ed. Englewood, NJ: Prentice Hall, 2006. [30] R.T. Stefani, B. Shahian, C.J. Savant, Jr., and G.H. Hostetter, Design of Feedback Control Systems, 4th ed. Oxford, U.K.: Oxford Univ. Press, 2002. [31] B.C. Kuo and F. Golnaraghi, Automatic Control Systems, 8th ed. New York: Wiley, 2003. [32] N.S. Nise, Control Systems Engineering, 4th ed. New York: Wiley, 2004. [33] R.C. Dorf and R.H. Bishop, Modern Control Systems, 10th ed. Upper Saddle River, NJ: Pearson Prentice Hall, 2005. [34] S. Skogestad and I. Postlethwaite, Multivariable Feedback Control: Analysis and Design, 2nd ed. New York: Wiley, 2005. [35] J. Freudenberg, R. Middleton, and A. Stefanopoulou, “A survey of inherent design limitations,” in Proc. American Control Conf., Chicago, IL, 2000, pp. 2987–3001. [36] G. Stein, “Respect the unstable,” IEEE Contr. Syst. Mag., vol. 23, no. 4, pp. 12–25, 2003. [37] R.H. Middleton and G.C. Goodwin, Digital Control and Estimation: A Unified Approach. Englewood, NJ: Prentice-Hall, 1990. [38] D.S. Bernstein, “Chalk it up,” IEEE Contr. Syst. Mag., vol. 25, no. 4, pp. 6–8, 2005. [39] A. Lozano-Nieto, “How technology changes the way we teach—benefits and risks,” in Proc. IEEE Int. Professional Communication Conf., Quebec City, Canada, 1998, pp. 75–83, [40] D. Knipe and M. Lee, “The quality of teaching and learning via videoconferencing,” British J. Educational Technol., vol. 33, no. 3, pp. 301–311, 2002.
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Multivariable Feedback Control—Analysis and Design by SIGURD SKOGESTAD and IAN POSTLETHWAITE
Multivariable Feedback Control— Analysis and Design approaches multi-input, multi-output feedback control design for linear systems using the paradigms, theory, and tools of robust conWiley, 2005 trol that have arisen during the ISBN 0-470-01167-X past two decades. The book is US$145.00 (hardcover), aimed at graduate students and ISBN 0-470-01168-8 US$72.00 (softcover), practicing engineers who have a 608 pages. basic knowledge of classical control design and state-space control theory for linear systems. A basic knowledge of matrix theory and linear algebra is required to appreciate and digest the material offered. This edition is a revised and expanded version of the first edition, which was published in 1996. The size of the book has been increased, not by the number of pages, which decreased from 559 to 574, but by a 20% increase in the page size. The revision has left intact the original style, approach, and goals. This edition contains revisions of almost all chapters, including minor corrections, improvements, and new material. In chapters 5 and 6, recent results on fundamental performance limitations have been added. Chapter 10 has been reorganized, while Chapter 12 on linear matrix inequalities is new. All Matlab programs have been updated and made compatible with the Robust Control Toolbox. The book cohesively brings together three important conceptual achievements of the field of control: 1) multivariable feedback design, including a deep understanding of its achievements and limitations, 2) the concepts of uncertainty in plant behavior and uncertainty modeling as a natural part of a model-based approach to control design, and 3) the synthesis of feedback dealing with uncertainty models using H∞ and µ-synthesis tools. The book shows that the multivariable control design involves several phenomena not present in single-input, single output (SISO) control design, such as interaction among loops, directionality, and multivariable zeros. The incorporation of uncertainty in the design process can be seen as a major achievement, not only from a technical point of view but also as an educational issue. Uncertainty plays a major role in many fields of engineering, and the field of control is in the favorable position of having a theory available on how to make approximate uncertainty models and how to deal with them as part of the design of the feedback loop. The book teaches how to assemble the individual uncertainty models using the standard plant concept and shows that
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control design with H∞ and µ-synthesis tools is suited for dealing with the uncertainty concepts. These tools require a certain level of mathematics to define signal classes, norms, convexity, system factorizations, and the like, an effort well worth the price. The book provides the necessary insights and basic facts of knowledge, and yet the character of the book is design oriented, not mathematical. This format gives the book considerable strength. The main results are formulated with great precision in a theorem format, and a proof is included when the reasoning behind a proof amplifies understanding of the notions involved. Additional results are stated without proof, and reference is made to other sources such as [1]. This approach makes the book a fine example of how mathematical notions can be creatively used as building blocks in a design approach, where engineering students experience control design as a suite of mental steps. Many examples and exercises are scattered throughout the text, and Matlab m-files are provided for the main computational steps. The frequency-domain specification of uncertainty and performance weights in the H∞ and µsynthesis approaches take advantage of insights available in classical control design. As such, the concepts used in the book are easily grasped, and the use of classical control intuition is combined with computations that do the actual work. For almost all design steps discussed in the book, computational implementations are available in the Robust Control Toolbox. The authors have a strong background in research in the theory and application of multivariable and robust control. Sigurd Skogestad’s research work has concentrated on theoretical issues in the design of multivariable and robust control with applications to chemical reaction and separation processes. A second influence in the book is the successful British school of multivariable control at Manchester and Cambridge. The authors make clear that better theoretical understanding of key concepts of multivariable and robust control is the key toward better designs, and throughout the book this idea acts as a stimulus for the somewhat abstract and advanced ideas involved.
CONTENTS Multivariable Feedback Control—Analysis and Design begins with a chapter on classical control from a modern perspective, followed by a chapter dealing with basic properties of multivariable feedback systems. This chapter introduces many topics that are discussed more deeply in later chapters. The focus is on multivariable frequency response analysis using the singular value decomposition, sensitivity functions, relative gain analysis, and the role of multivariable right-half plane zeros. Two examples stress the relevance of input uncertainty in multivariable control. Chapter 4 on linear systems provides basic theory needed in the following chapters. For many readers this theory may be familiar material, but the selection of topics exactly
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fits the needs of the book. Chapters 5 and 6 go into detail by treating achievable control performance, depending on uncertainty and robustness properties. This topic is first considered for SISO systems by building intuitive knowledge about the concepts involved, followed by a more technical treatment dealing with the multivariable case. These chapters discuss feedback limitations imposed by time delay, phase lag, right-half-plane zeros, unstable poles, input constraints, and uncertainty. Although the uninitiated reader may have the impression that feedback has only limitations, the development creates important background knowledge for control law design part as well as issues such as sensor and actuator placement, control structure design, controller implementation, and embedded control structures. Chapters 7 and 8 discuss uncertainty modeling as well as the analysis of robust stability and robust performance. The generalized plant is a key concept in the analysis, and uncertainty is represented by real and complex perturbations. In the face of multiple perturbations, the structured singular value is shown to be the basic analysis tool. Using D-K iteration, the control analysis is extended to a control synthesis (design) step by solving a sequence of scaled H∞ problems. Chapter 9 is on controller design concentrating on tradeoffs in feedback design. The H∞ solution is given in several variants such as S/KS mixed sensitivity designs. Also linear quadratic Guassian design followed by loop transfer recovery is discussed. Also included is the Glover/McFarlane approach to H∞ loop-shaping design. Although chapters 7–9 form the culmination of the book, there are four additional chapters with material that broadens the approach. Chapter 10 discusses control structure design, which is an important subject from an applications point of view but difficult to present coherently and systematically in a single chapter since an underlying theory of structure selection is not available. Yet the authors have done a remarkable job explaining control layers, configuration selection, decentralized control, and classical structures such as cascade control. In addition, relations between structure selection and performance limitation indicators such as right-half-plane zeros are discussed. Chapter 11 considers model reduction, which is necessitated by the design methods presented in the book. In particular, µ synthesis yields controllers whose order is the sum of the orders of the model and weighting functions, which is generally impractically high. Consequently, this chapter focuses on truncation and residualization of balanced forms, as well as on Hankel-norm reduction. Chapter 12 provides an introduction to linear matrix inequalities (LMIs), which arise in the synthesis procedures. Although the chapter is short, it provides a basic introduction to the theory and a single example. Chapter 13 discusses applied control design for three case studies, namely, helicopter flight control, gas turbine control, and distillation process control. The book contains appendices
on matrix theory, signal and system norms, and subjects such as linear fractional transformations.
EVALUATION Multivariable Feedback Control—Analysis and Design provides a well-balanced, effective, and efficient treatment of robust multivariable control, well suited for graduate students and for engineers in industry. The book concentrates on creating an understanding of the underlying concepts and then formulates the problem in mathematical terms. This approach works well and creates synergy between building intuitive understanding and exploiting theoretical insight. The Matlab routines available in the Robust Control Toolbox are expected to handle all computations necessary in the various design steps. Because the book can rely on this toolbox, there is no need to have much material on computational algorithms in the book, although some numerical issues are discussed, such as the necessity of proper scaling and conditioning of model representations. However, for larger industrial robust control problems in high dimensions, solving the numerical issues is the key to success. Apart from being an excellent textbook, the book has several other merits that make it a valuable gem in the field of systems and control. The book combines high standards regarding precise formulations and mathematical correctness with being creatively design oriented and accessible for those having only a classical control background. The designs that the authors have in mind are fullscale industrial multivariable designs, where only the best concepts and tools bring success, and this message is heard throughout the book. The contents of the book can already be viewed as “classical robust control design,” and the book has contributed substantially toward bringing the field of control to this point. Finally, the book sets a firm international standard for the level of a graduate course in multivariable robust control. Okko H. Bosgra
REVIEWER INFORMATION Okko H. Bosgra obtained his M.S. degree with research diploma from Delft University of Technology, The Netherlands. From 1980–1985 he was professor of systems and control at Wageningen University, and since 1986 he has chaired the Mechanical Engineering Systems and Control Group at Delft University of Technology. Since 2003 he has held a joint appointment at Eindhoven University of Technology, The Netherlands. His research interests are in applications of robust control and system identification to the areas of process control and motion control.
REFERENCE [1] K. Zhou, J.C. Doyle, and K. Glover, Robust and Optimal Control. Englewood Cliffs, NJ: Prentice Hall, 1996.
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IEEE CONTROL SYSTEMS MAGAZINE 81