CorrespondenceMULTIVARIABLE POLE-ASSIGNMENTSELF-TUNING REGULATORS

In paper 1126D [IEE Proc. D, Control Theory & Appl., 1981,128, (1), pp. 9—18], Prager and Wellstead suggested a multi-variable pole-assignment self-tuning regulator. This correspon-dence points out that the computational effort involved intheir algorithm can be greatly reduced by an alternativemethod for computing the control input.

In the paper, Prager and Wellstead suggested two methodsfor computing the input ut given by eqn. 3:

One method was to multiply both sides of eqn. 3 by det(/ + F(z~l)) and so obtain eqn. 11:

{det (/ + F(z-» ))}/«, = C(z-1){adj(/ + F{Z-'))}yt

The other method was to find polynomial matrices F(z~x)and G (z'1) such that

Giz-^il + Fiz-1))'1 =(I + F(z-l)TlG(z-1)

Thus the input ut could be computed from eqn. 18:

(A)

ut = -

Both methods are time consuming. By introducing an instru-mental variable yt, we can easily compute ut from

= yt (B)

and

ut = G(z~l)yt

The choice of the initial values of yt does not influence thelimit property of the algorithm provided that yt converges;convergence ensures the stability of the system.

It is obvious that the method proposed here can easily berealised on a microcomputer, as can the complete algorithm,modified by replacing the original procedures for computingthe control input with that given here.

23rd November 1981

Department of Radio EngineeringChina University of Science & TechnologyHefei, Anhwei, China

GONG WEI-BO

The correspondent proposes a neat way of avoiding the onlinesolution of a pseudocommutativity relation by invoking anintermediate variable yt defined thus:

(z-l))yt = yt

The idea is a clever one, but is problematic for the followingreasons:

(a) In general, the unknown initial conditions in filteringeqn. B will propagate through into the control signal ut viathe equation

ut = G(z~l)yt

and could affect the self tuning of the closed-loop process.(b) There is no guarantee that the polynomial matrix

I + F(z~l) will be inverse stable. In fact, the raison d'etreof pole assignment is to avoid inversion of nonminimum-phase open-loop dynamics, and as a result these noninvertiblemodes of Biz'1) influence the zeros of/ + F(z~l). It followstherefore that (/ + F{z~x))~x may be unstable so that theintermedidate variable yt given by

yt = Fiz-^pyt (D)

would diverge, and the correspondent's proposal would fail.In summary, one cannot say generally whether the proposal

will work or not, owing possible divergence of yt. Otherwise,it is an interesting comment and is certainly worth tryingbecause of the computations it saves. However, a practicalimplementation would need 'boundedness checks' on yt sothat one could flip back to the direct solution for F{z~l)

dGC"1)

25th January 1982

Control Systems CentreUniversity of Manchester

Institute of Science & TechnologyPO Box 88Manchester M60 IQPEngland

P.E. WELLSTEADD.L. PRAGER

DTC116D

Book reviewsSystems modelling and optimizationP. Nash (Ed.)Peter Peregrinus, 1981, 201 pp., £14.25ISBN: 0-9060-48-63-X

Although this volume arose out of a Science Research Councilvacation school for research students in control engineering,held at Cambridge in 1980, and appears in an IEE seriesdevoted to that subject, it is in fact concerned with a per-ipheral area, around the blurred borderline with operationalresearch and management science. The title is actually some-what misleading, since the majority of the articles, based onlectures given at the school, are primarily concerned withoptimisation, either in theory or practice, rather than withmodelling. There is, moreover, a striking contrast in the typesof treatment accorded to these two topics. The first fivechapters are concerned with optimisation theory, and thepresentation here is quantitative and precise; I found thearticles by L.H. Campbell on linear programming particularly

clear and lucid. Also, in later sections dealing with applications,the optimisation aspects are again treated quantitatively, withnumbers, formulas and equations. On the other hand, whenmodelling is under discussion, the style changes, becomingalmost entirely qualitative. Only in the chapter by M.B.Zarrop on macroeconomics is there a substantially math-ematical presentation and even here the treatment is generalrather than specific; in other articles, it is largely verbal,although illustrated by diagrams. These remarks, however,are not intended as a criticism of the authors involved. Indeed,much of the material is both informative and thought pro-voking; notably, the final chapter, by J.M. Macieowski onmodel evaluation, is worthy of deep study. My intention issimply to comment on the phenomenon and speculate as toits possible significance. Even for the supposedly well under-stood physical systems with which control engineers havetraditionally been concerned, model building is fraught withdifficulties, and it is hardly surprising that the problems should

142 IEE PROC, Vol. 129, Pt. D, No. 4, JULY 1982

become much more acute when one attempts to deal withsystems which, like most of those encountered in this book,involve human behaviour as an essential component. It maybe that only a qualitative analysis is appropriate, or evenpossible, in this context.

Nevertheless, the book succeeds in illustrating how thequantitative methods of optimisation theory can be usefullyapplied even in such areas. A welcome feature, also, is theinterdependence established between many of the chapters,despite their varied authorship, so that, for example, thefinal article draws on those preceding it for much of its illustra-tive material. Knowing from personal experience the difficultiesof achieving coherence in a multi-authored work of this kind,I feel that the Editor deserves congratulation.

P.A. COOK

Elements of computer process control with advanced controlapplicationsP.B. Deshpande and R.H. AshInstrument Society of America, 1981, 382 pp., £21.35ISBN: 87664-449-3

From the title, one would be expecting this book to give areasonably well balanced review of all aspects of computercontrol in the process industries. However, a very brief scanthrough the book reveals a heavy bias towards mathematicalanalysis and less emphasis on the hardware and softwareaspects of computer control.

To be more specific, the opening chapter gives a briefreview of classical control; to appreciate this and subsequentchapters, a good working knowledge of Laplace transformsis essential. Chapter 2 covers hardware and software, whilethe following ten chapters cover what is best described assampled-data control theory; the final five chapters comingin part II, devoted to 'advanced control concepts'.

The essentials of the hardware and software are coveredin chapter 2, and much of the 'jargon' is introduced; un-fortunately, it is crammed into a mere 36 pages althoughthe book has some 380 pages. There is insufficient treatmentof the software organisation associated with online computercontrol systems, and the whole chapter lacks depth. I wouldhave expected at least half of the book to have been devotedto the hardware and software aspects.

The section of the book covering sampled-data theoryand system analysis can be found in a number of other texts(which are referenced). However, it does give a more practicalviewpoint than is found in most other texts. Throughout itrefers to 'PID control', the mainstay algorithm of the processindustries, together with guidelines on selection of samplingrates, a discussion on digital filtering and dead-time algorithms,including the Smith predictor.

Part II examines process modelling and identification,together with a discussion of feedforward and cascade control.This section gives a good review of these standard techniquesas applied in the process industries. However, it has not beenwritten with particular reference to computer control andcould equally well apply to conventional analogue control.

This book would give the reader unfamiliar with computercontrol concepts in the process industries a good appreciationof the factors involved. It would be suitable for final yearstudents, and the industrial user wishing to delve further intothe theory. However, it cannot be considered a completetext on computer control in the process industries becauseof its scant treatment of the hardware and software aspects.

D. ROBINSON

Modelling of dynamical systems Vol. 1H. Nicholson (Ed.)Peter Peregrinus, 1980, 227 pp., £24.25ISBN: 0-906048-38-9This book is the first of two volumes on the subject ofmathematical modelling of dynamical systems. The systemsconcerned arise from a wide range of research interests, butthey all have one common attribute: that of being modelled interms of sets of ordinary or partial differential equations.

The mathematical modelling of systems requires consider-able understanding of the processes involved; hence it may atfirst be thought by the reader that a book on the subjectwould be difficult to read and understand. This possibilityappears to have been recognised by the contributors to thisvolume, for each chapter carries its own introduction to theunderlying principles in the modelling methods presented.

There are seven chapters in the book. The first chapter givesan introduction to the principles of model building in general,covering such aspects as material and energy balances, lumped-parameter modelling analogues, distributed systems, processtime and transport delays, linearisation techniques and systemidentification. The treatment is necessarily short, but manyreferences are given for further reading.

The next five chapters are devoted to the modelling ofvarious engineering systems, and the last chapter is concernedwith biological system modelling. The categories covered inthe contributions on engineering systems represent a very goodcross-section of the types of modelling problem one couldcome across in engineering. Chapter two concerns the modellingof chemical process plant, and the application to severalchemical engineering unit operations is concerned. The maincharacteristic evident in this type of model is the distributednature of the systems concerned. This leads to considerationof the use of linearisation to yield suitable transfer functions,and incidentally, to check the 'goodness' of plant design.

The third chapter, modelling of refrigeration and air-conditioning systems, gives the reader an introduction to theproblems of modelling two-phase flow dynamics applied toevaporators and condensers in refrigeration plant. The secondpart of the chapter covers the modelling of a complete air-conditioning system followed by discussion of the problemsof modelling the air conditioning of buildings.

Chapter four concerns the modelling of the spatial kineticsof neutron flux and power density in a somewhat idealisednuclear reactor. This is a distributed-parameter system thatdiffers from the chemical plant systems discussed earlier, inseveral important respects:

(a) More than one space dimension is considered.(b) The assumption of an axis of symmetry allows use of

polar co-ordinates for a cylindrical representation of thereactor.

(c) More than one type of symmetry can be considered.These complications ensure that the modelling of nuclearreactors in this way is very different from other distributedsystems.

A very important area of mathematical modelling is coveredin the fifth chapter, namely the treatment of the dynamics ofcontrolled flight. A glossary of terms is given to try to coverthe lengthy terminology involved, and the reader is takenthrough the stages of applying the traditional two-partmodelling process to various examples of aerospace systems.By contrast, the sixth chapter deals with marine systems.Although there is similarity with the previous chapter, con-cerning a rigid body moving through a fluid, the effect ofnonlinearities has to be taken much more into account if goodmodelling results are to be obtained. There is also some dis-cussion of the problems to be faced in using system identifi-cation techniques.

IEEPROC, Vol. 129, Pt. D, No. 4, JULY 1982 143