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Computer-controlled systems: Theory and design
746
Book Reviews
We have to consider the product of a sinusoidal signal with a frequency spectrum consisting of two pulse functions, one for a positive frequency value and one for a negative frequency and N equally spaced pulses of which the Fourier transform is easily calculated as the sum of N terms exp(.j~kT). A paragraph in the chapter about digital filters could have been devoted to this subject. In the book the link between the actual real world of the plant to be controlled and the digital world from which this plant is controlled is in all cases such that the loop is closed via the computer. There are cases where the computer via its DAC (digital-analog converter) delivers the desired value. Loops requiring a high bandwidth sometimes, if closed outside the computer, ask very short sampling times. An example of this is the tacholoop in a servo mechanism. On the other hand when the computer delivers the desired value, the accuracy of the reconstruction is more critical due to the fact that the range of the desired value generally is larger than that of the error signal. Then the "'linear slope" prediction/interpolation reconstruction,
suggested as a possibility above, sometimes will become necessary. Another point not mentioned in the book is the necessity of presampling filters for elimination of measurement noise. Frequency components above half of the sampling frequency should be removed. Here again there is a point where the lack of the concept of a stochastic signal in its simplest form is felt. The remarks made in this review do not diminish the appreciation of the reviewer for the book as already expressed in the introduction. The book is indeed very suitable for graduate courses and for self-study for practising engineers. Each chapter starts with an introduction and ends with a summary. Also each chapter contains a number of well-chosen examples and problems and an extensive reference list. A second printing, which hopefully will soon be necessary could possibly include some or all of the points mentioned without making the book too voluminous. There are hardly subjects that could be omitted without reducing the value of the book.
Computer-Controlled Systems: Theory and Design* K a r l J. , ~ s t r 6 m a n d B j 6 r n W i t t e n m a r k
Reciewer: C. RICHARD JOHNSON, JR. School of Electrical Engineering, Cornell University, Ithaca, NY 14853, U.S.A. THE BOOK Computer-Controlled Systems: Theory and Design by AstriSm and Wittenmark is, and will be reviewed here as, a text. It is not a handbook-style reference filled with crucial formulas, tables of comparative examples, and elaborately detailed case studies. Nor is it a mathematical treatise composed about a theoretical structure of broadly generic abstraction. It is instead a text for the current university student of digital control theory and the practising control engineer educated in analog control design but without classroom training in digital control. These two categories of student-readers are advised to examine this text for the same reason: its blend of practical motivation, sound pedagogy and theoretical breadth. The compromises in topic selection and depth of coverage inherent in a text with this style are likely to be the sources of any negative criticisms, primarily by text-seeking teachers. The purpose of this review is to share one teacher's reaction to these choices and their execution. In the preface, the authors comment that the "purpose of this book is to present control theory that is relevant to the analysis and design of computer-controlled systems, with an emphasis on basic concepts and ideas". For this purpose the authors use practical motivation primarily to justify the relevance of theoretical topics to be presented. As such, the practical issues cited determine the topic selection. For example, the second sentence of Chapter 6, entitled "Disturbance Models", states that "without disturbances there is no need for feedback control". Both deterministic and stochastic disturbance models are presented in Chapter 6 due to their proven usefulness in control design. The inclusion of stochastic models for disturbances then requires coverage of the optimal control methods in Chapters 11 and 12 to realize their usefulness. With the emphasis on pedagogical support from sampled-data practice, the motivating applications cited, which .are drawn primarily from process and servo control, are not overloaded with the myriad of details associated with real problems. Instead, their pedagogically pertinent essence is abstracted and * Computer-Controlled Systems: Theory and Design by K. J. Astr6m and B. Wittenmark. Published by Prentice-Hall, Englewood Cliffs, New Jersey (1984), US $44.50.
emphasized. For example, the examples in Chapter 1 are used to demonstrate the need for and uses of computer-control theory. In Chapter 7 they illustrate design philosophies, objectives, and tradeotls. The examples in Appendix A describe physical sources of simple mathematical models, such as the double integrator, which are used repeatedly as academic examples throughout the text. These examples in Chapters 1 and 7 and Appendix A are indicative of the balance the authors seek between practice and theory. The enticement to the reader is that the practicalities of sampled-data control, which the authors do cite, are directly addressable by the theory being presented. Another appealing pedagogical feature of this text is the printing of the intended message of each chapter just below its title. To this reviewer these goals are more succinctly revealing of the scope of the text than the table of contents. The remainder of this review uses these stated goals as a guide in discussing the choices in topic coverage made by the authors. Chapter 1 combines motivation for the need for a theory to describe the use of a digital computer as a feedback compensator of an analog plant with a brief sketch of the history of its development. The reference list at the end of Chapter 1 is indicative of the use of references throughout the text. The authors cite, within a brief commentary, seminal and tutorial sources for the concepts just presented. The reader's ability to divert, when desired, to a more detailed presentation is greatly facilitated. Chapter 2 discusses Shannon's sampling theorem, hold reconstruction, frequency folding due to aliasing, and sample period selection. The chapter closes with the statement that the "'choice of sampling period will be discussed several times later in the book". Though they preceded this statement with a description of the most useful rule-of-thumb for sample rate selection (with relation to the desired closed-loop bandwidth), the authors are foreshadowing the use of a wide range of factors in the application-dependent art of sample rate selection. The subject of sampling and its analysis when included in a control system is examined with more mathematical detail in Chapters 3 and 4. The authors adopt the appealing perspective of viewing the control system from the perspective of the digital controller in Chapter 3 and from the perspective of the analog plant, or the analog output actually being controlled, in Chapter 4. Chapter 3 focuses on the zero-order-hold discrete-time equivalent of a continuous-time state-space plant model.
Book Reviews Transfer functions, z-transforms, the transfer function based zero-order-hold equivalent n ( z ) = (1 - z - ~ ) z { u ( s ) / s } ,
and the transient response effects of discrete-time transfer function poles and zeros are also discussed. Further brief comments on sample rate selection close Chapter 3. One of the tradeoffs made by the authors is that Chapter 3 does not offer an exhaustive development of z-transform theory. The brief tables of z-transform pairs and z-transform properties take up as much space as the text describing the z-transform. Also, the discussion of discrete equivalents, other than the zero-order-hold equivalent, is deferred until Chapter 8. Chapter 4 discusses the periodic character of the continuoustime impulse modulation representation of sampling and the Laplace transform description of the zero-order-hold circuit. Frequency folding is quantified and the fact that a sampled-data system is time-varying is acknowledged. The authors then embark on a rather formal analysis of Laplace transform description of sampled-data systems typical of many sampleddata control texts. The conclusion is always the same: the periodic nature of the sampled-data system inhibits such analysis. In keeping with the authors' ultimate reliance on simulation (as indicated in Chapter 5) for evaluating intersample behavior of sampled-data control systems, this formalism could have been reduced to a reference to an alternate source. This would have allowed a more detailed explanation of the concluding topics in Chapter 3: modified z-transforms and systems with multi-rate sampling. Chapter 5 introduces various discrete-time systems analysis issues: stability tests (Jury's criterion, the Nyquist criterion, robustness to plant parameter variation, and Lyapunov's second method) and state-space realization (controllability, reachability, observability and Kalman's decomposition). The description of frequency domain model inaccuracies robustly tolerated with stability retention in Theorem 5.5 is a welcome, practically insightful addition not typically found in introductory digital control texts. These key bits of theory are described with a concise mixture of motivating examples, definitions and theorems. Missing, in comparison to other introductory digital control texts, is a set of fully detailed numerical examples illustrating these concepts. In fact, this criticism could be raised against the entire text. Although a number of problems that could serve as such illustrations are cited in the problem sets at the end of each chapter, few problems are worked in the text. Any serious student would expect to solve a number of the chapter-end problems to reinforce absorption of the chapter's material. However, the paucity of worked examples and the lack of an answer list to selected problems (or of an adequate number of problems worded such that a known answer is to be demonstrated) inhibits self-study. The double integrator example concluding Chapter 5 is typical of the authors' substitute for tightly focused exercises. The double integrator is used in Section 5.4 to illustrate z-plane root locus, simulated sample-data system response, steady-state response analysis, sample rate selection, and potential oscillations hidden to discrete analysis. Though demonstrative, this example is not as instructive of the computational mechanics as could be. The apparent choice of the authors to suppress the computational details of the application of theory surfaces again in the design Chapters 9-12. Chapter 6 describes polynomial (and piecewise polynomial) and stochastic disturbance models and feedback and prediction methods for their reduction. The mathematics of stochastic processes consume a large portion of this chapter. In the preface the authors admit that this stochastic processes material, and the later chapters (11-14) on optimal control design, identification, and adaptive control that utilize it, are most suited as the core of a graduate course. This material constitutes approximately 30 % of the roughly 400-page text and would likely provide thin support for an advanced theory course. The authors claim that the remaining 70% of the text is suitable for an undergraduate course, which is how this reviewer has used this text. Chapter 7 discusses a number of design issues typically omitted from (or not unified in) introductory undergraduate control texts. These subjects include process and regulator design integration, stability versus maneuverability tradeoffs, operator
747
interaction, manipulated variable selection, and the interrelationship of control objective specification and design procedure selection. Chapter 7 is useful reading for the perspective it provides. Chapter 8 considers the translation to a digital implementation of a satisfactory analog controller. This is the most immediate sampled-data controller design procedure to control engineers with analog design training. The authors present digital approximation techniques (e.g. differencing methods and Tustin's approximation) for direct translation of an analog compensator transfer function, various digitizations of PID controllers, and analog state-feedback digitization given full state measurability. The chapter concludes with a very brief discussion of the conversion of analog frequency response design techniques to discrete-time systems via the w-transform. These developments are brief, possibly due to the authors' opinion (shared by this reviewer) that digital design based on discrete-time modeling of the analog plant is mo re appropriate than digitization of analog controllers. This view is captured by their remark in the introduction to Chapter 8 citing the need for rapid sampling with analog controller digitization relative to "digital-design methods, which allow longer sampling times". The brevity of this chapter also reflects the authors' expectation that the reader has an adequate analog control design background. The most welcome material in this chapter is the discussion of operational aspects of PID controllers commonly lacking in more traditionally academic control texts. One strong justification of a student's exposure to these PID concepts is the current prevalance of PID compensators in process control use. Chapters 9-12 cover digital design procedures. Chapters 9 and 10 cover deterministic pole placement techniques and Chapters 11 and 12 cover optimal stochastic control. The authors have chosen to distribute these techniques based on the type of plant model: state-space (Chapters 9 and 11) or input-output transfer function (Chapters 10 and 12). The design techniques presented are essentially limited to single-input-single-output systems, though the matrix algebra based presentation of state-space techniques is stated generally enough to encompass multi-input, multi-output systems. The subsequent interrelationship of statespace and input-output design methods is quite insightful. Chapter 9 develops the combined observer-controller structure, logical for state-space plant descriptions, for initial nonzero state regulation. The last five pages of this 20-page chapter add a reference input and incorporate integration for trajectory/model following. This reviewer finds the extended focus on regulation versus tracking an unnecessary imbalance, presumably intended to better highlight the initial state uncertainty reduction central to the combined observer-controller. In any event, the combined observer-controller structure nicely supports the choice of the block diagram structure utilized in Chapter 10. Unfortunately, the authors do not exploit this pedagogical support as fully as possible. Chapter 10 does provide welcome pragmatic discussions of compensator causality, pole-zero cancellation admissibility, and high frequency rolloff protection against practical high frequency modeling inaccuracies. At the heart of the input-output based approach in Chapter 10 is the solution of polynomial equations, such as the Diophantine equation. The Diophantine equation also surfaces in the input-output formulation of optimal control as illustrated by equation (12.44). One disappointment is that the Sylvester matrix is never constructed to reveal a matrix inversion solution to the Diophantine equation associated with pole placement design. This reviewer finds the matrix inversion solution to the Diophantine equation as simple and as instructive as the solution to the state-space pole placement problem via, e.g., Ackermann's formula, which is fully developed in Chapter 9 as Theorem 9.1. This matrix inversion formulation could be used to emphasize the near-zero determinant, and the resulting large compensator parameters, arising with plant near-nonminimality. This point is typically incompletely addressed due to focus on the theoretically satisfactory condition of plant minimality, as manifested in Theorem 10.1, with disregard for the influence of the "degree" of this minimality. In Chapter 11 the authors repeat this emphasis on establishing the existence of solutions to key equations, relative to examination of the key features of the numerical procedures for their solution, with their presentation of the Riccati equation
748
Book Reviews
central to state-space-based optimal controllers. Indeed, they remark on p. 260 in Chapter 11 that "in practice it is necessary to have access to interactive programs, which can compute the control law and simulate the systems". It should be noted that the authors use the interactive simulation language S I M N O N , which was developed in their department at the Lurid Institute of Technology, for all of the simulations reported in the text. As we noted earlier, the authors ultimately rely on simulation of sampled-data systems because, as they note in their preface, "there are many detailed questions that are very hard to answer through analysis alone". Given this view, the authors effectively assume that the student will have access to a computer-aided control system design (CACSD) package that will robustly handle the numerical manipulations of design and simulation and, thus, choose not to provide much detail on these numerical procedures. This reviewer agrees that the numerics of control system analysis and design will be increasingly subsumed within sophisticated C A C S D software. The inclusion of this premise in the writing of this text suggests a longer-lasting relevance for this text versus most of its current competitors. However, this reviewer would prefer a more substantial discussion of the key generic features of the machinery of these numerics to insure their welMnformed use by future control engineers. Chapter t0 closes with a description of the connection of the input-output based pole placement procedure to root locus design, lead compensation, t he Smith-predictor, model-following. and the Dahlin Higham algorithm. This clearly demonstrates the central character of pole placement and allows the authors to dispense with more typical separate developments of each of these procedures c o m m o n to industrial practice. Their more traditional separate development tends to lead the novice to view control as a diverse bag of tricks with a well-disguised central theory. The authors have avoided this trap; however, one disappointment is that digital deadbeat control is not more fully elaborated. Its lack of an exact analog counterpart (as noted by the authors on p. 204) suggests more thorough presentation than the brief comments deadbeat design receives (primarily in Chapter 9). The connection to pole placement continues in the optimal control Chapters 11 and 12. T h o u g h much of Chapters 11 and 12 is devoted to statement of the requisite theory, practical issues,
such as achieved gain margin, cost function weighting matrix selection. Kalman filter frequency response shape, non m i n i m u m phase system control, the internal model principle, robustness, intersample behavior, and sample rate selection, are discussed. Chapter 13 describes the structural and parameterization issues in system identification and then focuses on recursive least squares as a solution to the parameter estimation component. Recursive least squares is a computational procedure to which all control engineers should be exposed. The authors undoubtedly agree, because, for this numerical procedure, they even provide a listing of a Pascal program performing the numerically robust U D factorization method of recursive least squares. Chapter 14 on adaptive control is far more superficial, considering the substantial contributions of the authors to this field. Chapter 14 defines adaptive control terminology and concepts, presents an overly simplistic first-order example to show its potential usefulness, and states a general theorem supporting the separability of the tasks of parameter identification and control solution from the current parameter estimates. Even the stated goal of Chapter 14 acknowledges this limited scope. It seems that the usefulness of combining on-line identification and controller reparameterization could have been nicely packaged as a closing section to the preceding chapter on identification. The final chapter discusses implementation, issues including anti-aliasing filters, computational delay, nonlinear actuator counteraction, the operator interface, quantization effects, and microprocessor programming. In summary, this reviewer recommends this text as a readable, practically motivated introduction to sampled-data control. For classroom use, the text is most appropriate for a second undergraduate course following a classical course in analog control. This reviewer has adopted this text for such a course. This adoption reflects this reviewer's opinion that this text is the most suitable for such a second undergraduate course a m o n g the current set of alternative texts. This reviewer has als~ recommended this text to practising control engineers who lack formal training in sampled-data control. The frequent con> mentary on practical issues, moderate theoretical level, and useful references to more detailed sources are appealing to this self-study audience.
Microprocessor-based Process Control* Curtis
Ret~iewer: C. G. P R O U D F O O T
Unilever Research, Bebington, Wirral, Merseyside, L63 3JW, U.K. DIGITAL computers, recently microprocessor based, have been used on-line in the process control field since the mid-1950s. Initially their use was confined to data collection for management information. As hardware and software (and confidence) developed, however, digital computers took on the role of supervisory and sequence control, and have been used for direct digital control in the process industries since the early 1960s. With the development of the mini-computer, and more recently the microprocessor the number of applications of digital controllers has grown. Indeed, most manufacturers of process control hardware now offer a microprocessor-based controller as part of their standard range. The advantages of digital controllers over their analogue counterparts include their flexibility and
* Microprocessor-based Process Control by C. D. Johnson. Published by Prentice-Hall, Englewood Cliffs, New Jersey [19841. US $40.45.
D. J o h n s o n
accuracy. At a non-sophisticated level it is possible to combine many functions in a single digital controller, such as signal limiting, linearization, alarms, engineering units conversion, etc., that would traditionally have required several separate pieces of analogue hardware. It is also possible to easily re-programme such functions, a task that cannot be achieved with analogue circuitry. Controller parameters can also be set accurately over a wide range. At a sophisticated level the advent of the (relatively cheap) microprocessor has made economic the practical development and evaluation of more advanced control techniques than was previously possible. The text under review is aimed, as an introduction to microprocessor-based (digital) process control, at the student who has followed (or is following) a course on assembly language programming for a microprocessor but who has no previous knowledge of control. The book, as outlined below concentrates on describing in detail the hardware and software (programmed instructions) that are necessary to interface a microprocessor to the real world. The control techniques considered are thus limited to sequence control, on/off control and simple PID control, with no discussion on using the power of a microprocessor for more advanced techniques. As no references
Book Reviews
We have to consider the product of a sinusoidal signal with a frequency spectrum consisting of two pulse functions, one for a positive frequency value and one for a negative frequency and N equally spaced pulses of which the Fourier transform is easily calculated as the sum of N terms exp(.j~kT). A paragraph in the chapter about digital filters could have been devoted to this subject. In the book the link between the actual real world of the plant to be controlled and the digital world from which this plant is controlled is in all cases such that the loop is closed via the computer. There are cases where the computer via its DAC (digital-analog converter) delivers the desired value. Loops requiring a high bandwidth sometimes, if closed outside the computer, ask very short sampling times. An example of this is the tacholoop in a servo mechanism. On the other hand when the computer delivers the desired value, the accuracy of the reconstruction is more critical due to the fact that the range of the desired value generally is larger than that of the error signal. Then the "'linear slope" prediction/interpolation reconstruction,
suggested as a possibility above, sometimes will become necessary. Another point not mentioned in the book is the necessity of presampling filters for elimination of measurement noise. Frequency components above half of the sampling frequency should be removed. Here again there is a point where the lack of the concept of a stochastic signal in its simplest form is felt. The remarks made in this review do not diminish the appreciation of the reviewer for the book as already expressed in the introduction. The book is indeed very suitable for graduate courses and for self-study for practising engineers. Each chapter starts with an introduction and ends with a summary. Also each chapter contains a number of well-chosen examples and problems and an extensive reference list. A second printing, which hopefully will soon be necessary could possibly include some or all of the points mentioned without making the book too voluminous. There are hardly subjects that could be omitted without reducing the value of the book.
Computer-Controlled Systems: Theory and Design* K a r l J. , ~ s t r 6 m a n d B j 6 r n W i t t e n m a r k
Reciewer: C. RICHARD JOHNSON, JR. School of Electrical Engineering, Cornell University, Ithaca, NY 14853, U.S.A. THE BOOK Computer-Controlled Systems: Theory and Design by AstriSm and Wittenmark is, and will be reviewed here as, a text. It is not a handbook-style reference filled with crucial formulas, tables of comparative examples, and elaborately detailed case studies. Nor is it a mathematical treatise composed about a theoretical structure of broadly generic abstraction. It is instead a text for the current university student of digital control theory and the practising control engineer educated in analog control design but without classroom training in digital control. These two categories of student-readers are advised to examine this text for the same reason: its blend of practical motivation, sound pedagogy and theoretical breadth. The compromises in topic selection and depth of coverage inherent in a text with this style are likely to be the sources of any negative criticisms, primarily by text-seeking teachers. The purpose of this review is to share one teacher's reaction to these choices and their execution. In the preface, the authors comment that the "purpose of this book is to present control theory that is relevant to the analysis and design of computer-controlled systems, with an emphasis on basic concepts and ideas". For this purpose the authors use practical motivation primarily to justify the relevance of theoretical topics to be presented. As such, the practical issues cited determine the topic selection. For example, the second sentence of Chapter 6, entitled "Disturbance Models", states that "without disturbances there is no need for feedback control". Both deterministic and stochastic disturbance models are presented in Chapter 6 due to their proven usefulness in control design. The inclusion of stochastic models for disturbances then requires coverage of the optimal control methods in Chapters 11 and 12 to realize their usefulness. With the emphasis on pedagogical support from sampled-data practice, the motivating applications cited, which .are drawn primarily from process and servo control, are not overloaded with the myriad of details associated with real problems. Instead, their pedagogically pertinent essence is abstracted and * Computer-Controlled Systems: Theory and Design by K. J. Astr6m and B. Wittenmark. Published by Prentice-Hall, Englewood Cliffs, New Jersey (1984), US $44.50.
emphasized. For example, the examples in Chapter 1 are used to demonstrate the need for and uses of computer-control theory. In Chapter 7 they illustrate design philosophies, objectives, and tradeotls. The examples in Appendix A describe physical sources of simple mathematical models, such as the double integrator, which are used repeatedly as academic examples throughout the text. These examples in Chapters 1 and 7 and Appendix A are indicative of the balance the authors seek between practice and theory. The enticement to the reader is that the practicalities of sampled-data control, which the authors do cite, are directly addressable by the theory being presented. Another appealing pedagogical feature of this text is the printing of the intended message of each chapter just below its title. To this reviewer these goals are more succinctly revealing of the scope of the text than the table of contents. The remainder of this review uses these stated goals as a guide in discussing the choices in topic coverage made by the authors. Chapter 1 combines motivation for the need for a theory to describe the use of a digital computer as a feedback compensator of an analog plant with a brief sketch of the history of its development. The reference list at the end of Chapter 1 is indicative of the use of references throughout the text. The authors cite, within a brief commentary, seminal and tutorial sources for the concepts just presented. The reader's ability to divert, when desired, to a more detailed presentation is greatly facilitated. Chapter 2 discusses Shannon's sampling theorem, hold reconstruction, frequency folding due to aliasing, and sample period selection. The chapter closes with the statement that the "'choice of sampling period will be discussed several times later in the book". Though they preceded this statement with a description of the most useful rule-of-thumb for sample rate selection (with relation to the desired closed-loop bandwidth), the authors are foreshadowing the use of a wide range of factors in the application-dependent art of sample rate selection. The subject of sampling and its analysis when included in a control system is examined with more mathematical detail in Chapters 3 and 4. The authors adopt the appealing perspective of viewing the control system from the perspective of the digital controller in Chapter 3 and from the perspective of the analog plant, or the analog output actually being controlled, in Chapter 4. Chapter 3 focuses on the zero-order-hold discrete-time equivalent of a continuous-time state-space plant model.
Book Reviews Transfer functions, z-transforms, the transfer function based zero-order-hold equivalent n ( z ) = (1 - z - ~ ) z { u ( s ) / s } ,
and the transient response effects of discrete-time transfer function poles and zeros are also discussed. Further brief comments on sample rate selection close Chapter 3. One of the tradeoffs made by the authors is that Chapter 3 does not offer an exhaustive development of z-transform theory. The brief tables of z-transform pairs and z-transform properties take up as much space as the text describing the z-transform. Also, the discussion of discrete equivalents, other than the zero-order-hold equivalent, is deferred until Chapter 8. Chapter 4 discusses the periodic character of the continuoustime impulse modulation representation of sampling and the Laplace transform description of the zero-order-hold circuit. Frequency folding is quantified and the fact that a sampled-data system is time-varying is acknowledged. The authors then embark on a rather formal analysis of Laplace transform description of sampled-data systems typical of many sampleddata control texts. The conclusion is always the same: the periodic nature of the sampled-data system inhibits such analysis. In keeping with the authors' ultimate reliance on simulation (as indicated in Chapter 5) for evaluating intersample behavior of sampled-data control systems, this formalism could have been reduced to a reference to an alternate source. This would have allowed a more detailed explanation of the concluding topics in Chapter 3: modified z-transforms and systems with multi-rate sampling. Chapter 5 introduces various discrete-time systems analysis issues: stability tests (Jury's criterion, the Nyquist criterion, robustness to plant parameter variation, and Lyapunov's second method) and state-space realization (controllability, reachability, observability and Kalman's decomposition). The description of frequency domain model inaccuracies robustly tolerated with stability retention in Theorem 5.5 is a welcome, practically insightful addition not typically found in introductory digital control texts. These key bits of theory are described with a concise mixture of motivating examples, definitions and theorems. Missing, in comparison to other introductory digital control texts, is a set of fully detailed numerical examples illustrating these concepts. In fact, this criticism could be raised against the entire text. Although a number of problems that could serve as such illustrations are cited in the problem sets at the end of each chapter, few problems are worked in the text. Any serious student would expect to solve a number of the chapter-end problems to reinforce absorption of the chapter's material. However, the paucity of worked examples and the lack of an answer list to selected problems (or of an adequate number of problems worded such that a known answer is to be demonstrated) inhibits self-study. The double integrator example concluding Chapter 5 is typical of the authors' substitute for tightly focused exercises. The double integrator is used in Section 5.4 to illustrate z-plane root locus, simulated sample-data system response, steady-state response analysis, sample rate selection, and potential oscillations hidden to discrete analysis. Though demonstrative, this example is not as instructive of the computational mechanics as could be. The apparent choice of the authors to suppress the computational details of the application of theory surfaces again in the design Chapters 9-12. Chapter 6 describes polynomial (and piecewise polynomial) and stochastic disturbance models and feedback and prediction methods for their reduction. The mathematics of stochastic processes consume a large portion of this chapter. In the preface the authors admit that this stochastic processes material, and the later chapters (11-14) on optimal control design, identification, and adaptive control that utilize it, are most suited as the core of a graduate course. This material constitutes approximately 30 % of the roughly 400-page text and would likely provide thin support for an advanced theory course. The authors claim that the remaining 70% of the text is suitable for an undergraduate course, which is how this reviewer has used this text. Chapter 7 discusses a number of design issues typically omitted from (or not unified in) introductory undergraduate control texts. These subjects include process and regulator design integration, stability versus maneuverability tradeoffs, operator
747
interaction, manipulated variable selection, and the interrelationship of control objective specification and design procedure selection. Chapter 7 is useful reading for the perspective it provides. Chapter 8 considers the translation to a digital implementation of a satisfactory analog controller. This is the most immediate sampled-data controller design procedure to control engineers with analog design training. The authors present digital approximation techniques (e.g. differencing methods and Tustin's approximation) for direct translation of an analog compensator transfer function, various digitizations of PID controllers, and analog state-feedback digitization given full state measurability. The chapter concludes with a very brief discussion of the conversion of analog frequency response design techniques to discrete-time systems via the w-transform. These developments are brief, possibly due to the authors' opinion (shared by this reviewer) that digital design based on discrete-time modeling of the analog plant is mo re appropriate than digitization of analog controllers. This view is captured by their remark in the introduction to Chapter 8 citing the need for rapid sampling with analog controller digitization relative to "digital-design methods, which allow longer sampling times". The brevity of this chapter also reflects the authors' expectation that the reader has an adequate analog control design background. The most welcome material in this chapter is the discussion of operational aspects of PID controllers commonly lacking in more traditionally academic control texts. One strong justification of a student's exposure to these PID concepts is the current prevalance of PID compensators in process control use. Chapters 9-12 cover digital design procedures. Chapters 9 and 10 cover deterministic pole placement techniques and Chapters 11 and 12 cover optimal stochastic control. The authors have chosen to distribute these techniques based on the type of plant model: state-space (Chapters 9 and 11) or input-output transfer function (Chapters 10 and 12). The design techniques presented are essentially limited to single-input-single-output systems, though the matrix algebra based presentation of state-space techniques is stated generally enough to encompass multi-input, multi-output systems. The subsequent interrelationship of statespace and input-output design methods is quite insightful. Chapter 9 develops the combined observer-controller structure, logical for state-space plant descriptions, for initial nonzero state regulation. The last five pages of this 20-page chapter add a reference input and incorporate integration for trajectory/model following. This reviewer finds the extended focus on regulation versus tracking an unnecessary imbalance, presumably intended to better highlight the initial state uncertainty reduction central to the combined observer-controller. In any event, the combined observer-controller structure nicely supports the choice of the block diagram structure utilized in Chapter 10. Unfortunately, the authors do not exploit this pedagogical support as fully as possible. Chapter 10 does provide welcome pragmatic discussions of compensator causality, pole-zero cancellation admissibility, and high frequency rolloff protection against practical high frequency modeling inaccuracies. At the heart of the input-output based approach in Chapter 10 is the solution of polynomial equations, such as the Diophantine equation. The Diophantine equation also surfaces in the input-output formulation of optimal control as illustrated by equation (12.44). One disappointment is that the Sylvester matrix is never constructed to reveal a matrix inversion solution to the Diophantine equation associated with pole placement design. This reviewer finds the matrix inversion solution to the Diophantine equation as simple and as instructive as the solution to the state-space pole placement problem via, e.g., Ackermann's formula, which is fully developed in Chapter 9 as Theorem 9.1. This matrix inversion formulation could be used to emphasize the near-zero determinant, and the resulting large compensator parameters, arising with plant near-nonminimality. This point is typically incompletely addressed due to focus on the theoretically satisfactory condition of plant minimality, as manifested in Theorem 10.1, with disregard for the influence of the "degree" of this minimality. In Chapter 11 the authors repeat this emphasis on establishing the existence of solutions to key equations, relative to examination of the key features of the numerical procedures for their solution, with their presentation of the Riccati equation
748
Book Reviews
central to state-space-based optimal controllers. Indeed, they remark on p. 260 in Chapter 11 that "in practice it is necessary to have access to interactive programs, which can compute the control law and simulate the systems". It should be noted that the authors use the interactive simulation language S I M N O N , which was developed in their department at the Lurid Institute of Technology, for all of the simulations reported in the text. As we noted earlier, the authors ultimately rely on simulation of sampled-data systems because, as they note in their preface, "there are many detailed questions that are very hard to answer through analysis alone". Given this view, the authors effectively assume that the student will have access to a computer-aided control system design (CACSD) package that will robustly handle the numerical manipulations of design and simulation and, thus, choose not to provide much detail on these numerical procedures. This reviewer agrees that the numerics of control system analysis and design will be increasingly subsumed within sophisticated C A C S D software. The inclusion of this premise in the writing of this text suggests a longer-lasting relevance for this text versus most of its current competitors. However, this reviewer would prefer a more substantial discussion of the key generic features of the machinery of these numerics to insure their welMnformed use by future control engineers. Chapter t0 closes with a description of the connection of the input-output based pole placement procedure to root locus design, lead compensation, t he Smith-predictor, model-following. and the Dahlin Higham algorithm. This clearly demonstrates the central character of pole placement and allows the authors to dispense with more typical separate developments of each of these procedures c o m m o n to industrial practice. Their more traditional separate development tends to lead the novice to view control as a diverse bag of tricks with a well-disguised central theory. The authors have avoided this trap; however, one disappointment is that digital deadbeat control is not more fully elaborated. Its lack of an exact analog counterpart (as noted by the authors on p. 204) suggests more thorough presentation than the brief comments deadbeat design receives (primarily in Chapter 9). The connection to pole placement continues in the optimal control Chapters 11 and 12. T h o u g h much of Chapters 11 and 12 is devoted to statement of the requisite theory, practical issues,
such as achieved gain margin, cost function weighting matrix selection. Kalman filter frequency response shape, non m i n i m u m phase system control, the internal model principle, robustness, intersample behavior, and sample rate selection, are discussed. Chapter 13 describes the structural and parameterization issues in system identification and then focuses on recursive least squares as a solution to the parameter estimation component. Recursive least squares is a computational procedure to which all control engineers should be exposed. The authors undoubtedly agree, because, for this numerical procedure, they even provide a listing of a Pascal program performing the numerically robust U D factorization method of recursive least squares. Chapter 14 on adaptive control is far more superficial, considering the substantial contributions of the authors to this field. Chapter 14 defines adaptive control terminology and concepts, presents an overly simplistic first-order example to show its potential usefulness, and states a general theorem supporting the separability of the tasks of parameter identification and control solution from the current parameter estimates. Even the stated goal of Chapter 14 acknowledges this limited scope. It seems that the usefulness of combining on-line identification and controller reparameterization could have been nicely packaged as a closing section to the preceding chapter on identification. The final chapter discusses implementation, issues including anti-aliasing filters, computational delay, nonlinear actuator counteraction, the operator interface, quantization effects, and microprocessor programming. In summary, this reviewer recommends this text as a readable, practically motivated introduction to sampled-data control. For classroom use, the text is most appropriate for a second undergraduate course following a classical course in analog control. This reviewer has adopted this text for such a course. This adoption reflects this reviewer's opinion that this text is the most suitable for such a second undergraduate course a m o n g the current set of alternative texts. This reviewer has als~ recommended this text to practising control engineers who lack formal training in sampled-data control. The frequent con> mentary on practical issues, moderate theoretical level, and useful references to more detailed sources are appealing to this self-study audience.
Microprocessor-based Process Control* Curtis
Ret~iewer: C. G. P R O U D F O O T
Unilever Research, Bebington, Wirral, Merseyside, L63 3JW, U.K. DIGITAL computers, recently microprocessor based, have been used on-line in the process control field since the mid-1950s. Initially their use was confined to data collection for management information. As hardware and software (and confidence) developed, however, digital computers took on the role of supervisory and sequence control, and have been used for direct digital control in the process industries since the early 1960s. With the development of the mini-computer, and more recently the microprocessor the number of applications of digital controllers has grown. Indeed, most manufacturers of process control hardware now offer a microprocessor-based controller as part of their standard range. The advantages of digital controllers over their analogue counterparts include their flexibility and
* Microprocessor-based Process Control by C. D. Johnson. Published by Prentice-Hall, Englewood Cliffs, New Jersey [19841. US $40.45.
D. J o h n s o n
accuracy. At a non-sophisticated level it is possible to combine many functions in a single digital controller, such as signal limiting, linearization, alarms, engineering units conversion, etc., that would traditionally have required several separate pieces of analogue hardware. It is also possible to easily re-programme such functions, a task that cannot be achieved with analogue circuitry. Controller parameters can also be set accurately over a wide range. At a sophisticated level the advent of the (relatively cheap) microprocessor has made economic the practical development and evaluation of more advanced control techniques than was previously possible. The text under review is aimed, as an introduction to microprocessor-based (digital) process control, at the student who has followed (or is following) a course on assembly language programming for a microprocessor but who has no previous knowledge of control. The book, as outlined below concentrates on describing in detail the hardware and software (programmed instructions) that are necessary to interface a microprocessor to the real world. The control techniques considered are thus limited to sequence control, on/off control and simple PID control, with no discussion on using the power of a microprocessor for more advanced techniques. As no references