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Book Reviews
particular control law (in this case proportional-integralderivative, i.e. PID) and closed-loop identification: the Relay
Auto-tuner (/~str6m and Wittenmark, 1989). In the
identification/tuning phase, it automatically excites the
process in the relevant frequency range. In most cases, there
is no need for operator intervention, and the process
operates in closed-loop, near the setpoint. Following tuning,
identification stops and one has a time-invariant PID
controller. This avoids the need for continuous excitation,
which is usually unacceptable, or other devices whose sole
purpose is to keep an identifier from going astray.t
Enhancements include self-tuning feedforward control, and
automatic gain scheduling, again designed for situations
where one has little prior knowledge of system characteristics. The reliance on the PID algorithm is a potential
drawback, but performance will be acceptable in 80-90% of
process applications.
For more difficult problems, such as the authors' working
example, an alternative to the CRAP controller would be an
infinite-horizon LQG, with a state-space model based on
Laguerre functions (e.g. Dumont et al., 1990). Relayoscillation excitation could provide the data needed to
determine model parameters and/or the filtering strategy.
One might, thus, exploit the strengths of the CRAP
controller without requiring too much effort or skill on the
part of the user.
In summary, Adaptive Optimal Control is a valuable
critique of the current scene in adaptive and non-adaptive
predictive control. It does not attempt to provide
industrially-hardened control algorithms, but the ideas it
contains should inspire those who would reduce theory to
practice.
t The authors note that continuous excitation is "the price
one pays for adaptation".
References
,~str6m, K. J. and B. Wittenmark (1989). Adaptive Control.
Addison-Wesley, Reading, MA.
Clarke, D. W. (1991a). Adaptive Control by K. J. ,~strtim
and B. Wittenmark (book review). Automatica, 27,
207-208.
Clarke, D. W. (1991b). Adaptive generalized predictive
control. In Y. Arkun and W. H. Ray (Eds), Chemical
Process Control--CPC IV. AIChE, New York, pp.
395-417.
Dumont, G. A., C. C. Zervos and G. L. Pageau (1990).
Laguerre-based Adaptive control of pH in an industrial
bleach plant extraction stage. Automatica, 26, 781-787.
Garcia, C. E., D. M. Prett and M. Morari (1989). Model
predictive control: theory and practice--A survey.
Automatica, 25,335-348.
Grimble, M. J., S. de la Salle and D. Ho (1989).
Relationship between internal model control and LQG
controller structures. Automatica, 25, 41-53.
Lambert, E. P. (1987). Process control applications of
long-range prediction. Report OUEL 1715/87, University
of Oxford.
Rouhani, R. and R. Mehra (1982). Model algorithmic
control (MAC); basic theoretical properties. Automatica,
18, 401-414.
Skogestad, S. and M. Morari (1987). Implications of large
RGA elements on control performance. Ind. Eng. Chem.
Res., 26, 2323-2330.
About the reviewer
N. Lawrence Ricker is Professor of Chemical Engineering
at the University of Washington, Seattle. He joined the
model-predictive control (MPC) parade relatively early (in
1981), and has been an active participant in theoretical
developments and applications. He is co-author of the MPC
Toolbox for Matlab. Applications include non-adaptive MPC
of Seattle's sewer network--a MIMO system involving 23
inputs and 44 outputs, which has been awarded the 1992
AMSA Operations Prize.
Modern Signals and Systems*
H. Kwakernaak and R. Sivan
Reviewer: MICHAEL GREEN
Department of Systems Engineering, Australian National
University, Canberra, 0200, Australia.
MODERN SIGNALS AND SYSTEMS is a textbook for undergraduate courses in signal and system theory; it comprises 11
chapters and five appendices in 791 pages. The text provides
a comprehensive treatment of deterministic signals and
system theory from both the time domain and frequency
domain perspective as well as introducing applications in
signal processing, telecommunications and feedback control.
The continuous time and discrete time situations are
presented in an integrated manner, often in two-column
format. The book comes with its own software, called
SIGSYS, for use with a PC; I have not examined the
software and this review is confined to the text itself. Each
chapter concludes with around 20 tutorial exercises and
about half a dozen computer based exercises; instructors
using the text may obtain a solutions manual from the
publisher.
* Modern Signals and Systems, by H, Kwakernaak and R.
Sivan. Prentice Hall, Englewood Cliffs, NJ (1991). $82.00.
ISBN 0-13-809252-4.
The assumed background knowledge is basic algebra and
calculus; the fundamentals of the complex plane; an
introduction to differential equations; basic linear algebra;
the fundamentals of electric circuits and an introductory
physics course. The coverage of material is fairly similar to
other texts on the subject, such as the well-known text
Signals and Systems by Oppenheim, Willsky and Young.
Notable differences are the inclusion of state space system
descriptions and the priority given to time domain analysis.
The pedagogical approach is to introduce concepts in a
general context before moving to the more detailed analysis
of cases of particular interest. A system, for example, is
introduced as a relation between two signal spaces. The
properties of linearity, non-anticipativeness and timeinvariance are defined in this abstract setting. Attention is
then focused on the linear time-invariant case.
This approach requires that priority be given to time
domain analysis, since the frequency domain is relevant only
for linear time-invariant systems; it is the emphasis on time
domain analysis, the inclusion of state space system
descriptions and the unified treatment of continuous and
discrete-time which most clearly herald the modernity of the
text.
The advantages of the approach are generality, completeness and precision; the danger lies in alienating the less
Book Reviews
mathematically sophisticated readers. This is an issue which
any text on a subject so rich in applications and mathematical
heritage must negotiate and the authors are only too well
aware of this: "We hope that teachers and students alike will
appreciate the concise and precise style to which we aspired
without wanting to compromise the intuitive appeal". While
acknowledging that the issue is debatable, in my view the
level of mathematical abstraction and maturity demanded is
arguably beyond the ken of many second year engineering
students.
Chapter 1 is a basic overview of signals, systems and their
application in areas of electrical engineering. Chapter 2
introduces signals and their properties; operations on signals
such as time scaling, sampling and quantization; norms and
normed signal spaces (~p spaces) and finally generalized
signals (delta functions) which are treated in an operational
manner. Chapter 3 focuses on systems. A general definition
is introduced and the properties of linearity, time invariance,
non-anticipativeness and bounded-input-bounded-output
stability are defined. After touching on linearization, the
remainder of the chapter is devoted to linear time-invariant
systems; the central role of the impulse response function is
developed and convolution is shown to characterize all linear
time-invariant systems. The final sections are concerned with
periodic inputs, firstly harmonic inputs and the frequency
response function, then with general periodic inputs and
cyclical convolution. The development is illustrated throughout with first order examples, principally an RC circuit and a
discrete-time exponential smoother.
Chapter 4 is concerned with differential and difference
equations; systems of order greater than one appear here for
the first time. General issues such as non-anticipativeness,
time-invariance and numerical solution are considered. The
linear time-invariant case then dominates and the time
domain solution is developed; considerable space is devoted
to the determination of the impulse response function by
time domain techniques. The final section concerns harmonic
inputs and derives the frequency response function as the
ratio of the polynomials describing the differential/difference
equations.
Chapter 5 introduces the state space description of
systems. The state is introduced by way of examples and is
not rigorously defined; however, a rigorous definition of a
state space system is given. Linearity, non-anticipativeness
and time invariance are discussed in the new environment
and the connection with DEs developed. Conditions for
existence are given and numerical solution techniques
including Euler and Runge-Kutta are described. Linear
systems are considered and the state transition matrix
introduced; matrix exponential notation is used in the
time-invariant case. The stability ideas are reassessed and the
notion of bounded-input-bounded-state stability introduced.
The chapter concludes with a consideration of the frequency
response function of a state space system.
Chapter 6 introduces the notions of bases, orthogonality,
best approximation and the projection theorem. The
application to linear systems begins from the general
perspective; the behaviour of a linear time-invariant system
is completely specified by how it affects the basis signals. The
Fourier series is then introduced as well as some properties
such as convergence and Parseval's Identity. Linear
time-invariant systems with periodic inputs is the concluding
section.
Chapter 7 introduces the Fourier transform. The idea of
problem solving in an indirect manner via a transform and its
inverse is introduced; the Fourier series is revisited and
considered as a transform; the terminology DDFT (discrete
to discrete Fourier transform) and CDFT (continuous to
discrete Fourier transform) is introduced to denote the
Fourier series. Next the Fourier transform proper is
considered and the terminology DCFT (discrete to
continuous Fourier transform) and CCFT (continuous to
continuous Fourier transform) introduced; convergence and
AUTO 29:3-0
801
properties of the Fourier transform are analysed. The
chapter concludes with the frequency domain analysis of
linear time-invariant systems.
Chapter 8 generalizes the Fourier transform to the
z-transform and Laplace transform: analysis of the existence
of the transforms; their relation with the Fourier transform;
the properties of the transforms; the inverse transforms; the
analysis of convolution systems, differential equations and
state space systems via the z-transform and the Laplace
transform.
Chapter 9 considers some applications to signal processing.
The Sampling Theorem is derived and the general
framework of modern signal processing introduced; windowing techniques'of FIR filter design are considered. The
approximation of continuous time filters by discrete time
filters is considered and the chapter concludes with a
discussion of the fast Fourier transform (FFT) and related
computational matters.
Chapter 10 is devoted to telecommunications applications.
The theory of narrow band signals using the complex
envelope is introduced; modulation, demodulation and
multiplexing are considered. The final chapter considers
feedback control; a PI automobile cruise controller is used as
a motivating example; the purpose, properties and pitfalls of
feedback are analysed. Stability is considered: the small gain
and Nyquist theorems are presented. Appendices on
complex numbers, sets and maps; linear spaces, norms and
inner products; generalized signals; Jordan forms and finally
some proofs conclude the book.
The book is of high quality and many will find it a useful
addition to their shelves; graduate level students and others
may find that the precise and unified treatment deepens their
understanding of the subject. Yet, as a teaching text for
engineers, it has a tendency to bury the student in a level of
mathematical analysis perhaps too detailed, too relentless
and too sophisticated. The little biographical snippets which
adorn the text to add life to its pages do little more than
indicate the name and nationality of famous contributors to
the subject; they do not motivate the subject from a
historical or engineering perspective. In the chapters devoted
to applications one finds less application and more theory
than one might like in an engineering text and throughout
the book the tutorial problems, though they are sufficient in
number, are inclined to be rather theoretical.
In conclusion, while the selection of material is in line with
the fundamental role played by signal and system theory in
many branches of engineering, the abstractness and
relentlessness of the mathematical presentation do not
endear the book to me as an undergraduate engineering text
but for mathematics students wishing to take an engineering
perspective on function and operator theory, it is an
excellent text indeed.
About the reviewer
Michael Green was born in Sydney, Australia in 1961. He
received the B.Sc. degree in applied mathematics from the
University of New South Wales, Sydney, Australia, in 1984
and the Ph.D. degree in systems engineering from the
Australian National University in 1987. From 1987 to 1991
he was postdoctoral Research Fellow and subsequently
lecturer in the Department of Electrical Engineering,
Imperial College, London. In 1991 he was appointed Senior
Lecturer in the Engineering Program and Senior Research
Fellow in the Department of Systems Engineering at the
Australian National University, where he is also a member of
the Cooperative Research Center in Robust and Adaptive
Systems. His research interest include multivariable control,
optimal systems, ~'~ control theory and model.reduction.
Dr Green is currently Subject Editor for the International
Journal of Robust and Nonlinear Control, Associate Editor
of Systems and Control Letters, reviewer for many
international journals on control, including Autornatica, and
is a member of IEEE.