- Email: [email protected]
Optimal control: Linear quadratic methods
1068
Book Reviews
of a particular control law (self-tuning in this case) is not adequate for its successful application. Experimental results in this chapter demonstrate that judicious use of wellestablished techniques may provide very respectable solutions to large complex control problems. The book contains two chapters on power plant control.
ems", provides an overview of computer applications in various parts of a railway network (passenger addressing, power substation, train routing and headway control). This is an interesting area where control probably forms the core of operation yet remains transparent to the bulk of the end
Chapter 9. (M. Uchida.) "'An advanced control of thermal
Having read the book, I was somewhat bewildered by its scope and the spectrum of techniques covered within 515 pages of text. In most chapters, the depth of treatment is low and many of the applications (exceptions being Chapters 7, 8 and 11) do not really provide a carefully laid out introduction to the inexperienced control or computer engineer. With this in mind, I think that the book is likely to be of benefit to practising control engineers as a reference rather than a design source book. Some senior postgraduates in control/computer engineering may find the book useful in a peripheral way. Because of the lack of a continuous theme, I do not think that it is helpful for class room teaching. I would definitely recommend it for all technical reference libraries, but at £89, I hesitate to recommend its purchase by individual readers unless there is a specific chapter which relates directly to their work. One major problem with all edited books is that the individual chapters come in various shapes, sizes and fonts. Having been written by 20 authors from six countries, variations in style, notation and emphasis are to be expected. Despite this, and the occasional chapters not blending in well with its neighbours, the editors have succeeded in providing a collection of topics within a reasonably unified framework, albeit on a fairly introductory level. My only comment against the book is that much of the computing techniques covered are dated, e.g. no mention of multiple instruction multiple data (MIMD), transputers or occam; reference to shared memory appears only briefly (p. 60). I personally feel that by leaving out much of the late 1980s advances on concurrent processing and communicating sequential processes, the editors may have reduced the active life-span of this very well-organized and carefully edited book.
power plants" provides comprehensive background information on various areas of power plant control leading to a general description of LQG techiques for steam temperature control. Various aspects of monitoring, including diagnostic features, are briefly covered.
Chapter 10. (H. Nakamura.)"Status report on real-time control in industries: electric power systems", previews the hierarchical aspects of power systems. Various aspects of controlling load frequency, load dispatch and reactive power control are then briefly described. This chapter concludes with some remarks on control in abnormal conditions. The last four chapters of the book cover four different sectors of industry: steel plant, gas pipeline, cement production and the railway network. Chapter 11. (K. Saito.) "Status report on real-time control in steel industry", provides a historical background and the evolution of computer control in steel industry, which in many ways pioneered some of the early implementation of feedback techniques. Dr Saito's review is perhaps a timely reminder that at the end of the day, the designer must have a thorough understanding of the control problems if his solutions are to be taken up by industry. The most interesting feature of this chapter is the way the author has managed to embed the control laws within the overall operational context. This chapter should motivate engineers whose sole aim is to see a working system rather than getting involved with the intricacies of mathematical derivation which so often blurs the application potential of many new techniques.
Chapter 12. (G. Lappus and G. Schmidt.) "Process monitoring and control of gas pipeline networks", provides an interesting overview of method for collection, analysis, management and display of gas flow data in real-time. A number of issues related to fault detection and diagnosis, as well as the detection of measurement faults, are highlighted towards the end of this chapter. Chapter 13. (S. Kawai and Y. Kioke.) "Real-time computer control of cement industry", brings in the methods of various stages in cement production (kiln and blending, in particular) in the context of their control using auto-tuning PID control. A number of experimental results are included. Here again, the authors have successfully combined some of the recent advances in control theory with real-life design requirements. Chapter 14. (H. lhara and M. Nohmi.) "Current status of microcomputer applications on railway transportation syst-
users.
About the reviewer Pradip Sinha received his D.Phil in control engineering from the University of Sussex, Brighton, U.K. in 1974. He was a postdoctoral research fellow at Sussex during 1974-1977 and a lecturer in engineering at the University of Warwick, Coventry, U.K. during 1977-1985. He is now Professor of Electronic Engineering and Head of the Electronic and Control Engineering Division within the Department of Engineering, University of Reading, U.K. He is the author of Multivariable Control--An Introduction (Marcel Dekker, 1984), Microprocessors for Engineers (Ellis Horwood/Prentice Hall, 1987) and Electromagnetic Suspension: Dynamics and Control (IEE/Peter Peregrinus, 1987). His current research interests are multivariable systems, fault tolerant control, and algorithms for high-speed precision visually-guided robots.
Optimal Control: Linear Quadratic Methods* Brian D. O. Anderson and John B. Moore
Reviewer: VLADIM[R K U ~ E R A Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, P.O.B. 18, 18208 Prague, Czechoslovakia.
* Optimal Control: Linear Quadratic Methods by B. D. O. Anderson and J. B. Moore. Prentice-Hall, Englewood Cliffs, NJ (1990). ISBN-0-13-638560-5.
OPTIMAL CONTROL is a branch of modern control theory that provides analytical designs of systems that are supposed to be the best possible ones within a particular class. Linear optimal control is a special sort of optimal control that restricts attention to linear systems and linear control laws. This constraint is justified: many engineering systems are linear and linear optimal controls have readily computable solutions, are simple to implement and will frequently
Book Reviews suffice. Furthermore, the linear results may often be applied to nonlinear systems as well. Linear optimal controls are achieved by working with quadratic performance indices. Such methods are termed linear-quadratic (LQ) methods and there is a vast body of literature on this subject. One of the recent additions is Optimal Control: Linear Quadratic Methods by Brian D. O. Anderson and John B. Moore. It is a major revision of their earlier work, Linear Optimal Control, published by Prentice-Hall in 1971. In revising the original text, the authors omitted material on relay control systems, dual-mode controllers, and so-called specific optimal regulator problems; added material on second variation theory, frequency shaping, loop recovery, and controller reduction; included new Appendices and changed the title to focus on LQ methods, as opposed to H~ and L 1 methods now being developed. The aim of the book is to construct bridges that are required for the student and practising control engineer between the familiar classical control methods and those of modern control theory. It attempts to do so by consistently adopting the viewpoint that many modern control results have interpretation in terms of classical control notions; many modern control results do have practical engineering significance, as distinct from applied mathematical significance; classical design insights and modern control tools are synergistic in achieving practical designs. The text is intended for the first or later year graduate student. The background assumed of the reader is an elementary control course and an elementary introduction to linear algebra and linear systems. Exposure to a prior or concurrent course in optimal control is not assumed. The book contains three major parts. Part One introduces and outlines the basic theory of the optimal regulator. Chapter 1 is introductory. Chapter 2 sets up the problem by translating into mathematical terms the physical requirements on a regulator. The derivation of the optimal control law is via the Hamilton-Jacobi equation which is introduced using the Principle of Optimality. The infinite-time interval problem is studied in Chapter 3, which includes the stability properties of the optimal regulators. Chapter 4 considers tracking problems by building on the regulator theory. Part Two outlines the engineering properties of the optimal regulator. Degree of stability, gain and phase margins, tolerance of time-delay and effect of nonlinearities are studied in Chapter 5. Also frequency domain formulas are derived to deduce sensitivity and robustness properties. In Chapter 6, the relationship between quadratic index weight selection and closed-loop properties is studied with
1069
emphasis on the asymptotic properties as the control cost weight approaches infinity or zero. Part Three considers state estimation and linear-quadraticGaussian (LQG) design. Chapter 7 deals with state estimation, including the case when measurements are noisy, by exploiting to some extent the theory of Parts One and Two. Chapter 8 deals with control law synthesis when the states of the system to be controlled are not available. When the system is precisely known, then in the LQG case, certainty equivalence is the optimal approach, resulting in the separation of state estimation and state feedback. Otherwise, there can be poor robustness properties, unless loop transmission recovery and frequency shaping techniques are adopted, as shown in Chapter 8 and 9. Controller reduction methods are studied in Chapter 10. Finally, in Chapter 11, some practical aspects concerning implementation of controllers via digital computers are studied. The Appendices summarize results in matrix theory, linear system theory, the Minimum Principle, stability theory and Riccati equations relevant to the material in the book. Author Index and Subject Index are included for the reader's convenience. There are dozens of problems to be found at the end of the sections, which extend and complete the theoretical material. The solutions are available in a separate "Solutions Manual", There are also open-ended problems which require computer studies. In summary, the book is an up-to-date revision of the earlier successful text. It explores linear optimal control theory as seen from the engineering viewpoint. It is extremely well written, with chapter outlines, step-by-step explanations, main point summaries of each section and numerous illustrative and practical examples. The overall appearance is also very good, resulting in a pleasant reading and easy orientation in the text. The book will be appreciated by both the student and the teacher, and will be a valuable acquisition for everybody's library.
About the reviewer Vladimir Ku~era is Director of the Institute of Information Theory and Automation in Prague, Czechoslovakia. He graduated from Czech Technical University, Prague with degrees in electrical engineering and automatic control. He contributed to the theory of Riccati equations, to the design of deadbeat controllers, and pioneered the use of polynomial equations in linear control systems. He is a member of the IFAC Council, a senior member of the IEEE, and serves on the editorial boards of a number of journals.
System Identification* Torsten
S6derstr6m
Reviewer: H. G. NATKE Universit~it Hannover, CurtRisch Institut fiir Dynamik, Schali- und MeBtechnik, Appelstr. 9A, 3000 Hannover, Germany. SYSTEM IOErCn~CATIOr~(SI) is an important field, not only in engineering. It can be called test and computer aided modelling and also experimental analysis. These terms provide an impression of the interdisciplinary character of SI. It combines testing (excitation and measurement) and analysis, deterministic and stochastic processes and systems. Analysis here means the theoretical handling of the system as well as the analysis of the system itself. Applications are manifold; they begin with economic problems, include
* System Identification by Torsten S6derstr6m and Petre Stoica. Prentice Hall, Englewood Cliffs NJ (1989). $75.95. AUTO 28:5-N
and Petre
Stoica
biological tasks, and do not end with engineering problems. The book to be reviewed gives an introduction to the subject. This contains mention of some problems and some definitions, and seems to be adequate to the purpose. Next to the Introduction, the Introductory Examples inform the reader of the contents of the remaining chapters. Here concepts are introduced like system, process, model structure, ID methods and the experimental condition. "System" is defined as a mathematical description of the process and not as the object under test. Among these concepts the reviewer finds no reference to model definition or any statements on the model building process dependent on the aim, etc. and model structure (parametrization) is a part of this. Apart from this criticism both introductory chapters are an excellent contribution towards motivating the reader and taking him close to the problems arising in SI.
Book Reviews
of a particular control law (self-tuning in this case) is not adequate for its successful application. Experimental results in this chapter demonstrate that judicious use of wellestablished techniques may provide very respectable solutions to large complex control problems. The book contains two chapters on power plant control.
ems", provides an overview of computer applications in various parts of a railway network (passenger addressing, power substation, train routing and headway control). This is an interesting area where control probably forms the core of operation yet remains transparent to the bulk of the end
Chapter 9. (M. Uchida.) "'An advanced control of thermal
Having read the book, I was somewhat bewildered by its scope and the spectrum of techniques covered within 515 pages of text. In most chapters, the depth of treatment is low and many of the applications (exceptions being Chapters 7, 8 and 11) do not really provide a carefully laid out introduction to the inexperienced control or computer engineer. With this in mind, I think that the book is likely to be of benefit to practising control engineers as a reference rather than a design source book. Some senior postgraduates in control/computer engineering may find the book useful in a peripheral way. Because of the lack of a continuous theme, I do not think that it is helpful for class room teaching. I would definitely recommend it for all technical reference libraries, but at £89, I hesitate to recommend its purchase by individual readers unless there is a specific chapter which relates directly to their work. One major problem with all edited books is that the individual chapters come in various shapes, sizes and fonts. Having been written by 20 authors from six countries, variations in style, notation and emphasis are to be expected. Despite this, and the occasional chapters not blending in well with its neighbours, the editors have succeeded in providing a collection of topics within a reasonably unified framework, albeit on a fairly introductory level. My only comment against the book is that much of the computing techniques covered are dated, e.g. no mention of multiple instruction multiple data (MIMD), transputers or occam; reference to shared memory appears only briefly (p. 60). I personally feel that by leaving out much of the late 1980s advances on concurrent processing and communicating sequential processes, the editors may have reduced the active life-span of this very well-organized and carefully edited book.
power plants" provides comprehensive background information on various areas of power plant control leading to a general description of LQG techiques for steam temperature control. Various aspects of monitoring, including diagnostic features, are briefly covered.
Chapter 10. (H. Nakamura.)"Status report on real-time control in industries: electric power systems", previews the hierarchical aspects of power systems. Various aspects of controlling load frequency, load dispatch and reactive power control are then briefly described. This chapter concludes with some remarks on control in abnormal conditions. The last four chapters of the book cover four different sectors of industry: steel plant, gas pipeline, cement production and the railway network. Chapter 11. (K. Saito.) "Status report on real-time control in steel industry", provides a historical background and the evolution of computer control in steel industry, which in many ways pioneered some of the early implementation of feedback techniques. Dr Saito's review is perhaps a timely reminder that at the end of the day, the designer must have a thorough understanding of the control problems if his solutions are to be taken up by industry. The most interesting feature of this chapter is the way the author has managed to embed the control laws within the overall operational context. This chapter should motivate engineers whose sole aim is to see a working system rather than getting involved with the intricacies of mathematical derivation which so often blurs the application potential of many new techniques.
Chapter 12. (G. Lappus and G. Schmidt.) "Process monitoring and control of gas pipeline networks", provides an interesting overview of method for collection, analysis, management and display of gas flow data in real-time. A number of issues related to fault detection and diagnosis, as well as the detection of measurement faults, are highlighted towards the end of this chapter. Chapter 13. (S. Kawai and Y. Kioke.) "Real-time computer control of cement industry", brings in the methods of various stages in cement production (kiln and blending, in particular) in the context of their control using auto-tuning PID control. A number of experimental results are included. Here again, the authors have successfully combined some of the recent advances in control theory with real-life design requirements. Chapter 14. (H. lhara and M. Nohmi.) "Current status of microcomputer applications on railway transportation syst-
users.
About the reviewer Pradip Sinha received his D.Phil in control engineering from the University of Sussex, Brighton, U.K. in 1974. He was a postdoctoral research fellow at Sussex during 1974-1977 and a lecturer in engineering at the University of Warwick, Coventry, U.K. during 1977-1985. He is now Professor of Electronic Engineering and Head of the Electronic and Control Engineering Division within the Department of Engineering, University of Reading, U.K. He is the author of Multivariable Control--An Introduction (Marcel Dekker, 1984), Microprocessors for Engineers (Ellis Horwood/Prentice Hall, 1987) and Electromagnetic Suspension: Dynamics and Control (IEE/Peter Peregrinus, 1987). His current research interests are multivariable systems, fault tolerant control, and algorithms for high-speed precision visually-guided robots.
Optimal Control: Linear Quadratic Methods* Brian D. O. Anderson and John B. Moore
Reviewer: VLADIM[R K U ~ E R A Institute of Information Theory and Automation, Czechoslovak Academy of Sciences, P.O.B. 18, 18208 Prague, Czechoslovakia.
* Optimal Control: Linear Quadratic Methods by B. D. O. Anderson and J. B. Moore. Prentice-Hall, Englewood Cliffs, NJ (1990). ISBN-0-13-638560-5.
OPTIMAL CONTROL is a branch of modern control theory that provides analytical designs of systems that are supposed to be the best possible ones within a particular class. Linear optimal control is a special sort of optimal control that restricts attention to linear systems and linear control laws. This constraint is justified: many engineering systems are linear and linear optimal controls have readily computable solutions, are simple to implement and will frequently
Book Reviews suffice. Furthermore, the linear results may often be applied to nonlinear systems as well. Linear optimal controls are achieved by working with quadratic performance indices. Such methods are termed linear-quadratic (LQ) methods and there is a vast body of literature on this subject. One of the recent additions is Optimal Control: Linear Quadratic Methods by Brian D. O. Anderson and John B. Moore. It is a major revision of their earlier work, Linear Optimal Control, published by Prentice-Hall in 1971. In revising the original text, the authors omitted material on relay control systems, dual-mode controllers, and so-called specific optimal regulator problems; added material on second variation theory, frequency shaping, loop recovery, and controller reduction; included new Appendices and changed the title to focus on LQ methods, as opposed to H~ and L 1 methods now being developed. The aim of the book is to construct bridges that are required for the student and practising control engineer between the familiar classical control methods and those of modern control theory. It attempts to do so by consistently adopting the viewpoint that many modern control results have interpretation in terms of classical control notions; many modern control results do have practical engineering significance, as distinct from applied mathematical significance; classical design insights and modern control tools are synergistic in achieving practical designs. The text is intended for the first or later year graduate student. The background assumed of the reader is an elementary control course and an elementary introduction to linear algebra and linear systems. Exposure to a prior or concurrent course in optimal control is not assumed. The book contains three major parts. Part One introduces and outlines the basic theory of the optimal regulator. Chapter 1 is introductory. Chapter 2 sets up the problem by translating into mathematical terms the physical requirements on a regulator. The derivation of the optimal control law is via the Hamilton-Jacobi equation which is introduced using the Principle of Optimality. The infinite-time interval problem is studied in Chapter 3, which includes the stability properties of the optimal regulators. Chapter 4 considers tracking problems by building on the regulator theory. Part Two outlines the engineering properties of the optimal regulator. Degree of stability, gain and phase margins, tolerance of time-delay and effect of nonlinearities are studied in Chapter 5. Also frequency domain formulas are derived to deduce sensitivity and robustness properties. In Chapter 6, the relationship between quadratic index weight selection and closed-loop properties is studied with
1069
emphasis on the asymptotic properties as the control cost weight approaches infinity or zero. Part Three considers state estimation and linear-quadraticGaussian (LQG) design. Chapter 7 deals with state estimation, including the case when measurements are noisy, by exploiting to some extent the theory of Parts One and Two. Chapter 8 deals with control law synthesis when the states of the system to be controlled are not available. When the system is precisely known, then in the LQG case, certainty equivalence is the optimal approach, resulting in the separation of state estimation and state feedback. Otherwise, there can be poor robustness properties, unless loop transmission recovery and frequency shaping techniques are adopted, as shown in Chapter 8 and 9. Controller reduction methods are studied in Chapter 10. Finally, in Chapter 11, some practical aspects concerning implementation of controllers via digital computers are studied. The Appendices summarize results in matrix theory, linear system theory, the Minimum Principle, stability theory and Riccati equations relevant to the material in the book. Author Index and Subject Index are included for the reader's convenience. There are dozens of problems to be found at the end of the sections, which extend and complete the theoretical material. The solutions are available in a separate "Solutions Manual", There are also open-ended problems which require computer studies. In summary, the book is an up-to-date revision of the earlier successful text. It explores linear optimal control theory as seen from the engineering viewpoint. It is extremely well written, with chapter outlines, step-by-step explanations, main point summaries of each section and numerous illustrative and practical examples. The overall appearance is also very good, resulting in a pleasant reading and easy orientation in the text. The book will be appreciated by both the student and the teacher, and will be a valuable acquisition for everybody's library.
About the reviewer Vladimir Ku~era is Director of the Institute of Information Theory and Automation in Prague, Czechoslovakia. He graduated from Czech Technical University, Prague with degrees in electrical engineering and automatic control. He contributed to the theory of Riccati equations, to the design of deadbeat controllers, and pioneered the use of polynomial equations in linear control systems. He is a member of the IFAC Council, a senior member of the IEEE, and serves on the editorial boards of a number of journals.
System Identification* Torsten
S6derstr6m
Reviewer: H. G. NATKE Universit~it Hannover, CurtRisch Institut fiir Dynamik, Schali- und MeBtechnik, Appelstr. 9A, 3000 Hannover, Germany. SYSTEM IOErCn~CATIOr~(SI) is an important field, not only in engineering. It can be called test and computer aided modelling and also experimental analysis. These terms provide an impression of the interdisciplinary character of SI. It combines testing (excitation and measurement) and analysis, deterministic and stochastic processes and systems. Analysis here means the theoretical handling of the system as well as the analysis of the system itself. Applications are manifold; they begin with economic problems, include
* System Identification by Torsten S6derstr6m and Petre Stoica. Prentice Hall, Englewood Cliffs NJ (1989). $75.95. AUTO 28:5-N
and Petre
Stoica
biological tasks, and do not end with engineering problems. The book to be reviewed gives an introduction to the subject. This contains mention of some problems and some definitions, and seems to be adequate to the purpose. Next to the Introduction, the Introductory Examples inform the reader of the contents of the remaining chapters. Here concepts are introduced like system, process, model structure, ID methods and the experimental condition. "System" is defined as a mathematical description of the process and not as the object under test. Among these concepts the reviewer finds no reference to model definition or any statements on the model building process dependent on the aim, etc. and model structure (parametrization) is a part of this. Apart from this criticism both introductory chapters are an excellent contribution towards motivating the reader and taking him close to the problems arising in SI.