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Introductionne of the best ways of puttingthe new control design0echniques of H optimalcontrol into a perspective is toexamine the historical development ofcontrol system methods over the pastfew decades. The new vocabulary ofcontrol system design of the 1960s

included terms such as state-feedback, the observer, the Kalmanfilter, controllability and linearquadratic [LO)control. These termsand many others were all unleashedby the use of the state-space systemdescription, which provided a usefulclarification of some of the issues insystem analysis.developments on several fronts. ABritish School of control systemdesign pursued multivariable systemgeneralisations of classical frequencydomain methods. Studies of theInverse Nyquist Array (Rosenbrock),the Characteristic Locus method(MacFarlane) and the SequentialReturn Difference method (Mayne)were initiated. Computer-aided designtools were seen as an indispensablerequirement for these methods. Thesame decade saw widespread interestgrow in the self-tuning controllerconcept. This structure, comprisingonline model identification andcontrol design based on the identifiedmodel, was being promoted by suchEuropean practitioners as ktrijm(Sweden) and Peterka(Czechoslovakia),with significantadvances being made by Clarke andCawthrop, and Wellstead.These areas were developing welluntil some (mainly American)researchers began to examine thestability and performance propertiesof a control design if the systemmodel, on which the design wasbased, did not match the actualsystem in certain respects, forexample neglected high-orderdynamics. The major findings wereeffects like loss of closed-loopstability, the very property the designwas supposed to inculcate. Theserather devastating remindersof thefundamentals in control design hadfar-reaching implications. Forexample, the self-tuning concept wasbased on low-order modelidentification and there were simpleexamples to show that neglectinghigh-order dynamics could lead todesigns which could be destabilised.Hence, for the 1980s the key conceptdriving the research offensive wasrobustness and the need to designrobust controllers.1One of the control designtechniques to emerge in this period2.3was the esoterically namedHoptimal control. J ust as in the 1960s

In the 1970s there were

H, robust controldesign-a tutorialrevi ewH robust control design research filled the conference agenda ofthe 1980s. In this article, the importance of these developmentsfor control system design is reviewed and explained.by M. J. Crimble and M.A. JohnsonIndustrial ControlUnitUniversity of Strathclyde

when state-space emerged, theliterature and conferences of the1980s were peppered with a wholelegion of new technical terms relatingto robustness: singular values,additive perturbations, Nevanlinna-Pick algorithms, super-optimal,multiplicative perturbations and theone, two and three Block problems toname just a few. Now that theintellectual dust is beginning to settle,it is an opportune time at thebeginning of the 1990s to reviewsome of the more enduring features ofthe quiet revolution: robustness andH, optimal control.Model uncertainty

wndustry or the aerospaceindustry, the problems facing thecontrol system designer have thesame basic characteristics:Inadequate knowledgeof the systemdynamicsThe days when companies couldinvest in developing highly complexmodels of systems seemstohe fastdisappearing. The more likelysituation is knowledge of lowm-dernominal process dynamics along witha possible guesstimate of high-orderbehaviour. This estimate [oftenintuitive] of the accuracy of basicmodel accuracy is termed modeluncertainty.Differing system operating conditionsMost processes operate for a rangeof system schedules, plant set-ups orin different environmental conditions.Two facets of this problem have to beconsidered, first, the dynamics of the

hatever the industrialsetting, whether the process

COMPUTING & CONTROL ENGINEERING JOURNAL NOVEMBER 1991

system are often schedule or set-updependent.A simple example is amarine vessel whose dynamics[handling behaviour] will depend onvessel speed and loading. Changingdynamics naturally leads to designswhich optimise performance asoperating conditions change. Perhapsthe most common techniques used forsuch problems are adaptive ones:gain-scheduling (open-loopadaptation) or a little moresophisticated, self-tuning control[closed-loop adaptation]. The secondaspect concerns the changingdisturbances to which a system issubjected.To take the marine example,weather and sea-state are examplesof changing marine systemdisturbances. Any control design mustbe stable and perform well forspecified classes of processdisturbances. Already itcan be seenhow the uncertainty n the systemdescription or the processdisturbances is beginning to haveimplications or design. Robust controldesign is the search for controllerswhich can cope with a designerspecified range of process dynamicsor disturbance signals.Model uncertainty, to classes ofvariations in system dynamics, can berepresented using:(i) nominal model:

whereYdS)=Gd~Ms) (1)yds) =nominal system outputGAS) =nominal system transferfunction matrixu(s) =control input

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A G A ( 3P-0a

r---

b u

Fe. 1 Model uncertainty: a)Additive perturbation: b)Mut ip l i ca t i iperturbationand[ii)A model emr, or perturbation,AG[s).Consequently the modelrepresentation is given by

Y[S)=G[slluls)=Gds/+d G~[S)hds)2)where G[S)=GdS)+dGA[S) and themodel uncertainty descriptionAG,[s)is termed an additive perturbation.This is shown in Fig. 1a. There is asecond well-known representation,where the model is:

Yls)=IClsllulsl=lcdsI(r+d GdS ) ) h d S )(3)This time the modeltermed a multiplicative perturbation(see Fig. 1b) since it is quitestraightforward togo from eqn. 3 to:

G[S)=GdS)[/+dG&)) where AGM[S) is

( 4)One more step, rearranging eqn.4 forsingle-input/single-outputsystemsgives

C[S)=GdS)[+A CM[S) )=GdS)+GdS@GM[S)

so that the multiplicative perturbationis motivated as a normalised transferfunction model error, and the additiveperturbation is an absolute transferfunction model error. Clearly,mathematical subtleties are already276

beginning to intrude; however, there isone fact to appreciate. Controlsystems designers have always knownthat their models were inaccurate andoften poor representations of the realsystems. In many cases, the designerhas a good intuition of the extent ornature of the model eror.The robustness work of the 1980stried to explicitly incorporate thatuncertainty knowledge into the designprocess. In the 1970s the testing ofcontrol system robustness went by thename of validationbysimulation; inthe 1990s the control system designenvironment will become far moresophisticated enabling the trade-offsbetween closed-loop requirements(robust stability) and processdisturbance rejection to beoptimised.4 H, design procedureshave the significant advantage thatthe limits of performance in a systemcan be assessed directly. If the peakmagnitude in a certain frequencyresponse cannot be reducedsufficiently with H, design, then it isclear that the basic physical systemmust be reassessed. H, control designis optimised for the worstcaseconditions.Robust control designhe profound issues involved inthe description of uncertaintyT aused a fresh look at the aimsof control design, and in turn a newrefined terminology slowly evolved.A

parallel development through the1980s was the useof computer-aideddesign tools on personal computers.Packages like Matlab, Matrix, andProgramCC exposed the potential ofthese machines as super calculators.The need to use a PC design interfaceimposes its own syntax on problemrepresentation. One result of this wasa careful statement of the many typesof design constraints the controlengineer has to balance and thedevelopment of procedures which giveautomatic satisfactionof the designrequirements. The complicatedengineering calculations of thesolution algorithms could be hiddenand designen could direct theirenergy to design once more. (Theremarks on the PC culture may seemtrite today, but as a measure ofprogress, the recent university memoforbidding the useof laptop PCs in theHonoun examinations is usefulevidence!)Control design objectives remain:closed-loop stability, goodtrackingperformance andgoodattenuation ofdisturbances (arising from processload variations or from sensorsources). However, the addedcomplication comes when theseobjectives have to be realised in thepresence of model uncertainty,sothat the control solution is robust .Control design: a first lookdiscussed is shown in Fig. 2. Thesystem equations may readily beobtained as:output

Control

The detailed configuration to be

y[s)=Glsluls)+d[s) ( 6)

u[s)=Cds)e&) (71ControllernputObservation

eds)=r[s)-z[s) (8 )

zlsl=Y[s)+nlsl (9)and introduce the tracking error as:Tracking emr

From the system eqns. 6-10, theclosed-loop system output, thetracking error and the control signalare given by:

elsl=rlsl-Yls) (101

e[s)=l+G[s)Cds)f 1[r[s)-d[s))+[l+G[s)Cds)fI G[s/Cds)n[s) (12)

The robustness literature, particularlyfor multivariable systems, begins atCOMPUTING & CONTROL ENGINEERING JOURNAL NOVEMBER 1991

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;,d- ---- II uncertainty II II

eqns. 11-13.The compensatorCds)has to be chosensothat the closedloop system has:(i) Robust stability: Namely[l+C[s)Cds)) 1 G[s)CJs) represents aclosed loop system transferfunction which is stable despite thefact that G[s)=G&)+AG[s) has adegree of uncertainty associatedwith it.

various requirements of differentexactitudes must be met. Thetracking error, elsJ , mustbe smallfor low frequencies, the processdisturbance, d[s), must be rejectedin the frequency range of interestand the measurement noise, n[s),must also be attenuated.Satisfactory performance mustalso be attained in the presence ofthe uncertaintyC[s)=Gds)+AG[s).Sensitivity functions and design trade-OffSThe main difficulty with themultivariable problem as expressedthrough eqns. 11-13 is that thealgebraic machinery which needs tobe used tends to obscure some of thefundamentals. Convert the equationsto their single-input/single-output

(ii) Robust performance: This time

lla)

12a)

Fig.2 Control systemconfiguration

The scalar equations have somecommon transfer functions, introducetherefore the sensitivity function:Cds). However, eqn. 18shows thepresence of a principle ofconservation since T[s)andS[s)arenot free and independent transfer

(14) functions available for selection butare tied bv the relation T+S= .

1(1 +g(slcow

S[s)=with nominal value (namelyAg[s)=O]Of:

Conseque;ltly desirable properties of(say]S[s) n a frequency range maylead to undesirable properties n its1(1 +g&)CdSl)

complement, T[s), in that same( 5, frequency range. Control design isthus a matter of finding a satisfactorycompromise behveen severalS&)=

and the complementarysensitivityfunction: conflicting design requirements. Anyformal or automatic method of(16) resolving such design conflicts wouldbe a valuable tool indeed. H, oDtimalg(SJ Co[slT[s)= -S[S]=(1 +g[sICcls))

with value (namelyAg[s)=O) control is one route to formalising andO f solving such design problems.

g0~ s )Co~ s ~ Analysis for robust designTo[S)= -S,[S)= ( 17 ) Consider the case of modeluncertaintv reDresented bv a1 +golslC0[s))

andTds)+Sds)= 1

Introduce a nominal controllerorcompensator,Cds),and multiplyingeqn. 19.this givesg ~ ~ ~ c d S ~ = g d s ) c d s l + g ~ ~ ~ ~ d S ~ g M ~ S )(20)

motivating the prefix ofcomplementary sensitivity for T[s).The use of the sensitivitv functions in

The ful(complexi& oithe control Or4sJ -Ld~l=Us@ g~lsJesign problem can now beamreciated. Itcan be seen that thesensitivity functions Sls) and T[s)govem the characteristics and

DroDerties of the closed-IooD svstem.Hence, in Nyquist curve form, sets = j w and thenthe sensitivity functions eniapblate

performance of reference tracking andthe noise and disturbance rejectionthe stability properties, the LouJ-LduJ=AgM/ju)/ _BM[w)

I L d i dproperties, of the choiceof controller for0%Km (21)

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5. 3 Nyquist geometry for multiplicative uncertainty perturbation

k Lo0w)l- loopfrequency response9.4Nyquist geometry for robust stabil ity result

where ?,(U) is a magnitude bound onthe size of the uncertaintyAg,fiwl atfrequencyw .Alternatively eqn. 21may be writtenIL h J - Uw J 51U w JS M ( ~ ) ( 22)

The geometric interpretation of eqn.22 [see Fig. 3) s of importance sinceLJ jw l andUJwlover a range offrequency are the familiar Nyquistplots from which the classical stabilityresults obtain. In Fig.3, the locusL J j w ) is the open-loop nominalcompensated Nyquist plot, whilstLow) belongs to a set of perturbedbut neighbouring plants.Robust stabilityGiven a model uncertainty,Ag,(s),having a magnitude bound S,(w),such that eqn. 21 holds, it is possible(with some technical assumptions'o)278---

to arrive at a robust stability result.The controllerCJs) is assumed tohave been selected to create a closed-loop stable system for the nominalplant, gJsJ Then for closed-loopstability to hold in the presenceofplant uncertaintyAg,(sl. thegeometry of Fig.4 is used to givethe required condition. Clearly fromFig.4, he family of Nyquist curvesUJw )must not enclose the (- 1 ,0)stability point, or geometrically:{distanceAB)for each frequencyw

1 l+LJjwll>lLJjwllB,(wlforall U

>(radius, circle centre LdjwJJ,Namely

which becomes1x1B,(w]


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The relationship betweenT[s]androbust stability has already beenestablished. Investigate next, therequirement for disturbance rejection.As can be seen from eqn. 1 1 b, thedisturbance, D[sJ.enten the output,Y[s),via the sensitivity transferfunction, S[sJ Hence for a class ofdisturbances, a weighting functionwd[w)can be selected to emphasisethe important intervals of thefrequency spectrum where thesensitivity needs to attenuate thedisturbance, D[sJ Consequently asensitivity minimisation problem maybe posed:

min (sup1S(jw]Wdw)l]controller,C wConsequently, if controllerCOsoptimal and k denotes the optimalcost, then for all values of w,

IsownwD[w~


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H control design: di rectory of termsH, norm This provides a measureof the size of a transfer function and ismeasured by plotting the Bode amplitude diagram and notingthe maximum value of the frequency response.

This refers to the ability of the system to remain stable eventhough the modelusedfor system design is very different fromthe plant model which exists in practice.performance measured, for example, in terms of its trackingaccuracy given that modellingerrors exist when designing thecontroller.

Singular This provides a measure of the size of a matrix and is similar tovalue an eigenvalue but is more numerically reliable.Structured This is similar to the singular value but enables the structure ofsingular value the uncertainty to betaken into accountso that more realistic

Stabilityrobustness

Performance This refers to the ability of the system to maintain a goodrobustness

Hardy spaceParametricuncertaintyUnmodelleddynamics

Unstructureduncertainty

,u synthesis

and hence le& conservative designs canbeachieved.This is the mathematical setting in whichH, optimisation workis posed and is a space of all stable transfer functions.The uncertainty which results in having unknown gains or timeconstants in transfer functions which are otherwise well defined.Part of the system transfer function or state space model whichis discarded or unknown when basing a design on the nominal,usually low-order. plant model.Often an unrealistic representationof uncertainty since itallowsfor the presence of modelling errors in all the elements of asystem transfer function matrix, whereas in practice onlycertain modellingerrors can result which have a well definedstructure.This is a design method which uses repeated terations of anH,design algorithm and invokes the structured singular value totest whether the design is robust.

error-weighting term select asuitable weighting function to giveadequate performance robustness,disturbance rejection robustnessand tracking performance.5 Introduce the control or controlsensitivity weighting term,increasing ts gain until adequatemeasures of stability robustnessand measurement noise rejectionhave been achieved. This normallyinvolves tailoring the high-frequency characteristics of thecontrollers whilst the previous stepconcentrated on low-frequencybehaviour.6 Once the frequency domain trade-offs between sensitivity and controlsensitivity costing have been madea simulationof the transientresponse characteristics should beinspected to ensure performance isadequate.7 If steady-state error is too large,the gain can be increased bypenalising the sensitivity or errorterm at low frequency using itsweighting function.8 If the bandwidth of the controller istoo wide greater roll-off can beintroduced at an earlier point byusing a lead term on the controlsensitivity function or by

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introducing a measurement noisemodel which has high gain in thisfrequency range.Advantages and disadvantagesof H robust designAdvantages

First rigorous mathematical methodof dealing with systems havinguncertainty in the model definition.Some engineering problems requirefrequency responses to be limitedand this is a naturalH, normminimisation problem.Design procedures may beformalised and computer toolsinvoked0 Frequency domain intuition may beemployed in the design procedures.Taken together with the structuredsingular value analysis method thetechnique provides a designprocedure with certifiable results.DisadvantagesController designs are more

sensitive than LQG systemsregarding the choice of costweightings. Physically unrealisticcontrollers can result unless carefulchoices of cost weights are used.0 The theory underpinningH, designis more abstract and complicated

than that for the usual LOG orleast-squares problems.Controllers tend to be of higherorder than LOG designs sincedynamic weighting functions arenormally imperative n H, designsand these add to the orderofthecontroller.0 Poor robustness properties canresult unless care is taken in the

selectionof the cost weightings; i.e.robustness is not automatic butmust be earned.Commercially availableHdesign software

here are a number ofcommercially available softwareT uites which have H, features orsub-packages. Such packages include:1 The Matlab Robust ToolboxThis has the older H, calculationmethods pioneered by researcherssuch as Safonov together with thelatest two Riccati equation methodsintroduced by Doyle, Glover,Khargonegar and Francis.' For furtherdetails contact: The Mathworks Inc.,Natick, MA 01760,USA: Tel: (508)653 14 14;Fax: (508) 653 2997.2 ProgramCCThis package has H, calculations forboth state space and frequencydomain (transfer unction) methods.For further details contact: SvstemsTechnology Inc., California 90250-7083,USA; Tel: (2 131 679 2287;Fax: (2 13) 644 3887.3 Matrix,This package is based on the sameroutines used by Matlab but is muchmore extensive having sophisticatedsimulation as well as design tools. Forfurther details contact: IntegratedSystems Inc., California 95054, USA;Tel: (408)980 1500;Fax: (408)9800400.4 Robust Control PackageFor the users of Ctrl-C, a new andcomprehensive robustness analysisand control design package has beenreleased. For further details contact:SystemsControlTechnology Inc.,California 94303, USA; Tel: (4 15) 4942233; Fax: (4 15) 496 6595.5 University SoftwareMany of the university researchworkers have developed their ownresearch software. Some softwaresuites have been commercialised andsome are simply ad hoccomputational tools. The state-spaceoriented research groups includethose at Imperial College, UK (D. . N.Limebeer), University of Cambridge,UK [K. Glover), University of Leicester,UK (I.Postlethwaite), CALTECH, USA(J . C. Doyle), University of California,Los Angeles, USA (M.G. Safonov) and

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Osaka University, apan [ H. imura).Researchers who have pursued thepolynomial systems or frequency-domain methods include those ofTwente University, The Netherlands(H. Kwakernaak) and StrathclydeUniversity, UK [M. J . Grimble).Applications where H, robustdesign is appropriate

n the opening years of the 1970s,Peterka [1970), and Astrom andI Wittenmark (1973) created asignificant interest in the concepts ofself-tuning. The commercialisation ofthese and related techniques in off-the-shelf industrial form took about12 years and second-generationproducts a further six years.Hoptimal control theory is now tenyears old and sufficient of the crucialintellectual ssues have been resolvedfor the technique to merit the transferto industrial practice. The types ofapplication which might benefit fromH design have the followingcharacteristics:1 Industrial applications where adetailed high-order model of theprocess exists but traditionally alow-order controller has beencalculated based on anapproximate low-order model. Theerror between the two models canbe used inH design to guide theselection of the most robustsolution. The trend in Americanflight control system design studiesis to use this approach.2 Systems where safety is ofparamount importance and whereguaranteed stability margins mustbe ensured, as for example, innuclear power station controlproblems. Such problems wereraised recently byG. Stein in his

Plenary Lecture on UnstableSystems at the 1st EuropeanControl Conference [July, 1991 ,Grenoble, France.3 Systems where the disturbancemodels change and an adaptivesolution is too complicated. Acommon philosophy is to widen theoperational envelope and validityofixed controllers and decrease thecomplexity of gain schedules usingH robust controllers. There isacademic evidence for the successof this H, approach, but anindustrial mplementation s notknown.4 For systems where the plant modelis poor,H design procedures canprovide simpler commissioningtechniques provided that the formof the system models anduncertainties s known. Forexample, there is a very interestingreport from researchers n Taiwan 1dealing with the successful

microprocessor implementation ofH, controllers or permanent-magnet AC servo motor drives. ThepolynomialH controller yieldedbetter performance than Hzmethods and the experiments wereseen as a first step towards a newdesign framework for advanced ACservo-drives, using very simplifiedmodel information.Adaptive versus robust control:which to choose?

ew algorithms are now beingdeveloped which combine thebest features of robust andadaptive strategies. However, thesealgorithms will not be considered forthe following comparison:H robust1 A fixed controller simple toimplement and not subject tovariation in use.2 Easy to commission and withtuning options which have welldefined predictable results.3 May involve considerable designengineering effort before thesystem gets to plant but will requireless commissioning time.4 Since the controllen are fixed andas simple as any other digitalcontroller they should be easy toimplement and with readilyassessed performance.5 Engineers may be intimidated bythe background mathematics eventhough this need not be understoodto implement the designs.6 Design engineers need not knowthe theory but only how to use thedesign algorithms effectively.

frequency unmodelled dynamics.7 Can readily cope with high-

computing power to implementthan for a robust controller.To combine the cautious,H self-tuning controllerconservative features of H, designwith the responsive action of a self-tuner, the first H self-tuningcontroller was proposed in 1986atStrathclyde University. Patent

protection has been sought for thiscontroller in the UK, several Europeancountries, Japan and the USA, by theUKs British Technology Group;Contact: Roger Clark, Tel: 071-4036666; Fax: 071-403 7586. In theUSA the patent application has beenallowed and the formal notice ofGrant of a Patent is expected soon.The muttivariableH, robustcontrol problem

Multivariable gain and phasemargins can be related to sensitivityfunction minimisation using the Hnorm. Such concepts are helpful forengineers experienced in the use ofgain and phase margins in scalarsystems.methods,6 which for some time havebeen used with LQC multivariablecontrollers, have now been tailoredfor usewith H, designs.multivariable systems are undulyconservative and this resulted in theintroduction of the structuredsingular value which leads to lessconservative or higher performanceH, multivariable designs.

0 The selection of H, cost functionweights for multivariable systemshas not been studied intensively butit is likelv that similar rules to those

0 Loop transfer recovery design

0 Uncertainty descriptions for

Self-tuningand adaptivecontrol1 A self-tuning and self-

commissioning controller is anappealing concept to processengineers wishing to relegateresponsibility to the device.2 The unreliability of early academicself-tuners is well known.3 Design office engineering time neednot be large but plant testing maybe necessary with experiencedengineers tuning the self-tuningalgorithm.4 Some problems may involve suchlarge gain or time-constantvariations that an adaptivecontroller becomes imperative.5 Although a robust controller mightoperate effectively over a wideoperating envelope itmay havevery poor performance due to theuse of low gains. An adaptivecontroller should be capable ofmaintaining high performance asthe system changes.6 The online control and protectionsoftware will require much more

0

used foiscalar systems can be usedfor the choice of multivariableweightings. For example,introducing an integrator on thesensitivity costing automaticallyintroduces integral action into thecontroller, whether itbe scalar ormultivariable.Both LQG andH designapproaches are true multivariabledesign procedures n that noattempt s made to try to reducethe design problem to the choice ofa scalar measure of systemperformance. To some extent manyof the other multivariable designprocedures do in fact try to reducethe problem to a scalar design. Forexample, inverse Nyquist arrayessentially diagonalises the system,characteristic loci enable theeigenvalue loci to be treated asNyquist loci and sequential returndifference builds up the controllerby single loops. NeitherH, nor LOGneeds these devices to obtain aformal controller design procedure.

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Concluding remarksH, robust design is particularlyappropriate in, for example, flightcontrol systems and gas-turbineengine designs. In such systems it isworthwhile to invest in long anddetailed design studies usingsophisticated software to obtainvery high performance and veryrobust and reliable systems.Training courses and formaliseddesign procedures are to bedevelopedso that the bestadvantage can be taken of new H,design software. The subject is lessmysterious now and some of theterminology should be enteringbasic undergraduate courses in thecoming years.Where the overhead on design timeis unacceptable, and a measure ofself design is of value, self-tuningcontrollers will be important. Inmany process-control applications tis easier to determine modelsthrough plant testing than bymodelling procedures. Adaptivesystems in this case haveadvantages.The recent state space H, designprocedures7 will be particularly

appropriate for larger systems, andthe lower-order polynomial basedmethods8.9 will be particularlyvaluable when adaptive featuresmust be added.

References1 DOYLE, J .C.: Guaranteed margins forLQC regulators E Trans.,1978,2 ZAMES, C.: Feedback, optimalsensitivity, and plant uncertainty viamultiolicative seminorms IFACAC-23, (41, PP.756-757

Congkss VIII, Kyoto, J apan,1981,DD.74-783ZAMES. C . and FRANCIS, B.A.: A newapproach to classical frequencymethods: Feedback and minimaxsensitivity, CDC Conference 1981, SanDiego, California, USA4 POSTLETHWAITE,I.,YOUNG, S. D.0..CU, D. W., and HOPE, J .: H, controlsystems design: A critical assessmentbasedon industrial applications, IFAC10th World Congresson Auto Control,Munich, 1987.8, pp.328-3335 CLOVER, K.. LIMEBEER, D. . N..DOYLE, J . C., KASENALLY, E. M.,andSAFONOV, M. C.: A characterizationof all solutions to the four blockgeneral distance problem, SlAM J.ControlOpt., 1991,29, (21,pp.283-324

6ATHANS, M.: A tutorial on the LQiLTRmethod, American Contr. Conf. 1981,Seattle, WA. USAKHARCONECAR,P,and FRANCIS,7 DOYLE, J . C., CLOVER, K.,B.A.: State-space solutions tostandard H, and H, control problems,~~.831-847l Trans.,1989,AC-34, (8).8 GAKERNAAK, H.: Minimaxfrequency domain performance androbustness optimisation of linearfeedback systems, fEEE Trans., 1985.robustness and the relationshio to LQAC-30, ( IO] . Pp.994-10049 CRIMBLE, M. .: Optimal H,design problems, Int. J . Contrbl. 1986.43 , (21, pp.351-372I O MORARI, M., and ZAFIRIOU, E.:

1 1 L1U.T.-H., and LIU. C.-H.:Robust process control (Prentice-Hall,Inc., 1989, SBN0-13-78956-0)Implementation of AC servocontrollers employing frequencydomain optimisation techniques, /ETrans., 1990.37, (41, pp.275-282

0 IEE: 1991Prof. Mike Crimble and Dr. Mike ohnsonare with the Industrial Control Unit,University of Strathclyde, Marland House,50 George Street, GlasgowC IQE , UK.Prof. Crimble is an IEE Fellow

CONTRACTS &ORDERSLichfield basedECS Ltd. has securedan order for f 300000worth of newbusiness from the BonasMachineCompany Ltd.for a fully networkedcomplete CAD/CAM solution basedon ECSs Concerto CAD and Aries 3Ddesign software.Bonas, based in the Team ValleyTrading Estate in Gateshead,manufactures weaving machines andJ acquards for the textile industry, andhas embarked on a programme ofexpansion to include a new R&Dfacility and a major factory extension.A networkedCADsystem is seen asintegral to reducing productdevelopment lead times; improvingright first time design performance,and providing an engineering controlto enable BS5750 Part 1 registration.The installation will consistof 1 1workstations running Concerto, acomprehensive set of 2D drawingfacilities for producing manufacturingdrawings. The Concerto drawingmanagement system will alsointerface with the companysVAXmainframe network for futuredevelopments of the informationtechnology system.a powerful set of tools for creatingand analysing 3D models ofcomponents and assemblies. Its282

Another workstation will run Aries,,dvanced solid modeller gives fastresponse, and colour shading offersvisualisation and interpretation of thedesign. Further modules includedprovide parametric design facilities,finite-element analysis andmechanisms analysis.The total system will also provideengineering change control and billsof material links to the companysmainframe.Both Concerto and Aries willoperate on the companys CompaqPC hardware, and the integratednetwork, designed and supplied bythe Connectivity Division of ECS, willallow the addition of desktoppublishing and PCB design.* * *CRiD Comput er Systems Ltd. hasannounced a f450000 order fromApplied Materi als Inc., one of theworlds leading ndependentproducers of wafer fabricationsystems for the worldwidesemiconductor industry. The order isfor 100 GRiDCASE 1550sx laptopcomputers with CD-ROM drive, whichwill be used by Applied Materialsservice engineers throughout Europeto replace paper-based operationsand improve the efficiency and accuracy of the companys data-retrieval system.provide Applied Materials serviceengineers with up to 600 Mbytes ofportable CD-ROM storage. This willallow them to store technicalinformation about individual machineson compact discs, eliminating theneed for cumbersome manuals andsimplifying technical reference dataupdates. Engineen will be able totransmit and receive data fromcustomers sites, ensuring a fast on-site service to customers.The 1SSOsx, based on a 20MHz16-bit 80386sx processor, s the firstportable PC designed for usen ofgraphical applications such asWindows. Itfeatures an inbuiltlsopoint mouse to allow users to makefull use of mouse-operated softwarewhile in the field.Options include RAM of 2,4 or 8Mbytes, VGA, EGA and CGA graphicsmodes, and hard-disc storage of 60or120 Mbytes. A three-slot expansionchassis transforms the 1550sx into apowerful 386sx-based desktopcomputer, while retaining tsportability for use in the field, and anoptional Ethernet cartridge offerssupport for a range of networksincluding Novell, DECnet and ARCnet.The GRiDCASE 1550sx laptops willCOMPUTING & CONTROL ENGINEERING J OURNAL NOVEMBER 1991-

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