Plantwide control – A review and a new designprocedure

TrulsLarsson�andSigurdSkogestad

�Departmentof ChemicalEngineering

NorwegianUniversityof ScienceandTechnology

N–7034TrondheimNorway

April 19,2000

Abstract

Most (if notall) availablecontroltheoriesassumethatacontrolstructureis givenat theoutset.They thereforefail to answersomebasicquestionsthat a control engineerregularly meetsin practice(Foss1973): “Whichvariablesshouldbe controlled,which variablesshouldbe measured,which inputsshouldbe manipulated,andwhich links shouldbemadebetweenthem?”Thesearethequestionsthatplantwidecontroltriesto answer.

Therearetwo mainapproachesto theproblem,a mathematicallyorientedapproach(controlstructuredesign)anda processorientedapproach.Both approachesarereviewedin thepaper. Emphasisis put on theselectionofcontrolledvariables(“outputs”),andit is shown thattheideaof “self-optimizingcontrol” providesa link betweensteady-stateoptimizationandcontrol.

We alsoprovidesomedefinitionsof termsusedwithin theareaof plantwidecontrol.

�PresentlyatABB CorporateReasarch,Norway�Author to whomcorrespondenceshouldbeaddressed.E-mail: skoge@chembio.ntnu.no;phone:+47-7359-4154;fax: +47-

7359-4080

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1 Intr oduction

A chemicalplantmayhave thousandsof measurementsandcontrol loops. By thetermplantwidecon-trol it is not meantthetuningandbehavior of eachof theseloops,but ratherthecontrol philosophyofthe overall plant with emphasison the structural decisions. The structuraldecisionincludethe selec-tion/placementof manipulatorsandmeasurementsaswell asthedecompositionof theoverall probleminto smallersubproblems(thecontrolconfiguration).

In practice, the control systemis usually divided into several layers. Typically, layers includescheduling(weeks),site-wideoptimization(day),localoptimization(hour),supervisory/predictive con-trol (minutes)andregulatorycontrol (seconds);seeFigure 1. Theoptimizationlayer typically recom-

�

Scheduling(weeks)

Site-wideoptimization(day)� � � � � �

Localoptimization(hour)

���� �

�Supervisory

control(minutes)

����� �

�Regulatory

control(seconds)

���� ����� ������ �Control

layer

Figure1: Typical controlhierarchyin achemicalplant.

putesnew setpointsonly oncean hour or so, whereasthe feedbacklayer operatescontinuously. Thelayersarelinkedby thecontrolledvariables,wherebythesetpointsis computedby theupperlayerandimplementedby thelower layer. An importantissueis theselectionof thesevariables.

Of course,we couldimagineusingasingleoptimizingcontrollerwhichstabilizestheprocesswhileat thesametimeperfectlycoordinatesall themanipulatedvariablesbasedondynamicon-lineoptimiza-tion. Therearefundamentalreasonswhy suchasolutionis not thebest,evenwith todaysandtomorrowscomputingpower. Onefundamentalreasonis thecostof modeling,andthefact that feedbackcontrol,without muchneedfor models,is very effective whenperformedlocally. In fact, by cascadingfeed-backloops,it is possibleto control largeplantswith thousandsof variableswithout theneedto developany models.However, thetraditionalsingle-loopcontrolsystemscansometimesberathercomplicated,especiallyif thecascadesareheavily nestedor if thepresenceof constraintsduring operationmake itnecessaryto uselogic switches.Thus,modelbasedcontrol shouldbe usedwhenthe modelingeffort

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givesenoughpay-backin termsof simplicity and/orimprovedperformance,andthis will usuallybeatthehigherlayersin thecontrolhierarchy.

A very important(if not themostimportant)problemin plantwidecontrolis theissueof determiningthecontrol structure:� Which “boxes” shouldwe have andwhatinformationshouldbesendbetweenthem?Notethatthatweareherenot interestedin whatshouldbeinsidetheboxes(whichis thecontrollerdesignor tuning problem). More precisely, control structure design is definedas the structural decisionsinvolvedin controlsystemdesign,includingthefollowing tasks((Foss1973);(Morari 1982);(SkogestadandPostlethwaite1996))

1. Selectionof controlled variables� (“outputs”; variableswith setpoints)2. Selectionof manipulatedvariables� (“inputs”)3. Selectionof measurements� (for controlpurposesincludingstabilization)4. Selectionof control configuration (a structureinterconnectingmeasurements/setpointsandma-

nipulatedvariables,i.e. thestructureof thecontroller � which interconnectsthevariables��� and� (controllerinputs)with thevariables� )5. Selectionof controller type(controllaw specification,e.g.,PID, decoupler, LQG, etc.).

In mostcasesthecontrolstructuredesignis solvedby amixtureof a top-down considerationof controlobjectivesandwhichdegreesof freedomareavailableto meetthese(tasks1 and2), andawith abottom-up designof thecontrolsystem,startingwith thestabilizationof theprocess(tasks3,4and5).

In mostcasestheproblemis solvedwithouttheuseof existingtheoreticaltools. In fact,theindustrialapproachto plantwidecontrol is still very muchalongthelinesdescribedby PageBuckley in his bookfrom 1964. Of course,the control field hasmademany advancesover theseyears,for example, inmethodsfor andapplicationsof on-lineoptimizationandpredictive control. Advanceshave alsobeenmadein controltheoryandin theformulationof toolsfor analyzingthecontrollabilityof aplant.Theselattertoolscanbemosthelpful in screeningalternativecontrolstructures.However, asystematicmethodfor generatingpromisingalternativestructureshasbeenlacking.This is relatedto thefactthatplantwidecontrolproblemitself hasnotbeenwell understoodor evenacknowledgedasimportant.

Thecontrolstructuredesignproblemis difficult to definemathematically, bothbecauseof thesizeoftheproblem,andthe largecostinvolved in makinga preciseproblemdefinition,which would include,for example,a detaileddynamicandsteadystatemodel. An alternative to this is to develop heuristicrulesbasedon experienceandprocessunderstanding.This is what will be referredto asthe processoriented approach.

Therealizationthat thefield of controlstructuredesignis underdevelopedis not new. In the1970’sseveral “critique” articleswherewritten on thegapbetweentheoryandpracticein theareaof processcontrol. The most famousis the one of Foss(1973) who madethe observation that in many areasapplicationwasaheadof theory, andhestatedthat

The centralissueto be resolved by the new theoriesare the determinationof the controlsystemstructure.Whichvariablesshouldbemeasured,which inputsshouldbemanipulatedandwhich links shouldbemadebetweenthetwo sets. ... Thegapis presentindeed,butcontraryto theviews of many, it is thetheoreticianwho mustcloseit.

A similar observationthatapplicationsseemto beaheadof formal theorywasmadeby Findeisenet al.(1980)in theirbookon hierarchicalsystems(p. 10).

Many authorspointout thattheneedfor aplantwideperspective oncontrolis mainlydueto changesin the way plantsaredesigned– with more heatintegration and recycle and lessinventory. Indeed,thesefactorsleadto moreinteractionsandthereforetheneedfor a perspective beyondindividual units.However, wewouldlike to pointout thatevenwithoutany integrationthereis still aneedfor aplantwideperspective asa chemicalplantconsistsof a stringof unitsconnectedin series,andoneunit will actasa disturbanceto thenext, for example,all unitsmusthave thesamethroughputat steady-state.

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Outline

Wewill first discussin moredetailsomeof thetermsusedaboveandprovidesomedefinitions.Wethenpresenta review of someof thework on plantwidecontrol. In section4 we discussthemathematicallyorientedapproach(controlstructuredesign).Then,in section5welook attheprocessorientedapproach.In section6 we considera fairly simpleplant consistingof reactor, separatorandrecycle. In section7 we considerthe most studiedplantwidecontrol problem,namelythe TennesseeEastmanproblemintroducedby DownsandVogel(1993),andwediscusshow variousauthorshaveattemptedto solve theproblem.Finally, in section8 we proposeanew plantwidecontroldesignprocedure.

2 Termsand definitions

We heremake somecommentson thetermsintroducedabove, andalsoattemptto provide somemoreprecisedefinitions,of thesetermsandsomeadditionalones.

Let us first considerthe termsplant andprocess, which in the control communityarealmostsyn-onymousterms. The term plant is somewhat moregeneralthanprocess:A processusually referstothe “processitself” (without any control system)whereasa plant may be any systemto be controlled(including a partially controlledprocess).However, notethat in thechemicalengineeringcommunitythetermplanthasa somewhatdifferentmeaning,namelyasthewhole factorywhich consistsof manyprocessunits;thetermplantwidecontrolis derivedfrom thismeaningof thewordplant.

Let us then discussthe two closely relatedterms layer and level which are usedin hierarchicalcontrol. Following the literature,e.g. Findeisenet al. (1980),thecorrectterm in our context is layer.In a layer the partsact at differenttime scalesandeachlayer hassomefeedbackor informationfromtheprocessandfollows setpointsgivenfrom layersabove. A lower layermaynot know thecriterionofoptimality by which thesetpointhasbeenset. A multi-layersystemcannotbestrictly optimalbecausethe actionsof the higher layersarediscreteandthusunableto follow strictly the optimal continuoustime pattern.(On theotherhand,in a multilevel systemthereis no time scaleseparationandthepartsarecoordinatedsuchthat thereareno performanceloss. Multilevel decompositionmaybeusedin theoptimizationalgorithmbut otherwiseis of no interesthere.)

Control is theadjustmentof availabledegreesof freedom(manipulatedvariables)to assistin achiev-ing acceptableoperationof theplant.Controlsystemdesignmaybedividedinto threemainactivities

1. Controlstructuredesign(structuraldecisions;thetopic of thispaper)

2. Controllerdesign(parametricdecisions)

3. Implementation

The term control structure design, which is commonlyusedin the control community, referstothe structuraldecisionsin thedesignof thecontrol system.It is definedby thefive tasksgiven in theintroduction).Theresultfrom thecontrol structure designis thecontrol structure (alternatively denotedthecontrol strategy or control philosophyof theplant).

The term plantwide control is usedonly in the processcontrol community. One could regardplantwidecontrol as the “processcontrol” versionof control structuredesign,but this is probablyabit too limiting. In fact,RinardandDowns(1992)refer to thecontrolstructuredesignproblemasde-finedabove asthe“strict definitionof plantwidecontrol”, andthey point out thatplantwidecontrolalsoincludeimportantissuessuchastheoperatorinteraction,startup,grade-change,shut-down, fault detec-tion, performancemonitoringanddesignof safetyandinterlocksystems.This is alsoin line with thediscussionby Stephanopoulos(1982).

Maybea betterdistinctionis the following: Plantwidecontrol refersto thestructuralandstrategicdecisionsinvolved in the control systemdesignof a completechemicalplant (factory), and controlstructure designis thesystematic(mathematical)approachfor solvingthisproblem.

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Thecontrol configuration, is definedasthe restrictionsimposedby theoverall controller � by de-composingit into asetof localcontrollers(sub-controllers),units,elements,blocks)with predeterminedlinks andpossiblywith apredetermineddesignsequencewheresub-controllersaredesignedlocally.

Operation involvesthebehavior of thesystemonceit hasbeenbuild, andthisincludesalot morethancontrol. More precisely, thecontrolsystemis designedto aid theoperationof theplant. Operability istheability of theplant(togetherwith its controlsystem)to achieve acceptableoperation(bothstaticallyanddynamically).Operabilityincludesflexibility, switchabilityandcontrollabilityaswell asmany otherissues.

Flexibility refersto the ability to obtain feasiblesteady-stateoperationat a given setof operatingpoints. This is a steady-stateissue,andwe will assumeit to be satisfiedat the operatingpoints weconsider. It is not consideredany furtherin thispaper.

Switchability refersto theability to go from oneoperatingpoint to anotherin anacceptablemannerusuallywith emphasison feasibility. It is not consideredexplicitly in thispaper.

Optimaloperationusuallyrefersto thenominallyoptimalwayof operatingaplantasit would resultby applying steady-stateand/ordynamicoptimizationto a model of the plant (with no uncertainty),attemptingto minimize the costindex � by adjustingthe degreesof freedom.We have hereassumedthat the “quality (goodness)of operation”can be quantifiedin termsof a scalarperformanceindex(objective function) � , whichshouldbeminimized.For example, � canbetheoperatingcosts.

In practice,wecannotobtainoptimaloperationdueto uncertainty. Thedifferencebetweentheactualvalueof theobjective function � andits nominallyoptimalvalueis the loss.

The two main sourcesof uncertaintyare(1) signal uncertainty(includesdisturbances� andmea-surementnoise� ) and(2) modeluncertainty.

Robustmeansinsensitive to uncertainty. Robustoptimaloperation is theoptimalwayof operatingaplant(with uncertaintyconsiderationsincluded).

Integratedoptimizationand control (or optimizing control) refersto a systemwhereoptimizationandits control implementationareintegrated.In theory, it shouldbepossibleto obtainrobust optimaloperationwith sucha system.In practice,oneoftenusesanhierarchical decompositionwith separatelayersfor optimizationand control. In making this split we assumethat for the control systemthegoal of “acceptableoperation”hasbeentranslatedinto “keepingthe controlledvariables( � ) withinspecifiedboundsfrom theirsetpoints( � � )”. Theoptimizationlayersendssetpointvalues( � � ) for selectedcontrolledvariables( � to thecontrol layer. Thesetpointsareupdatedonly periodically. (Thetasks,orpartsof the tasks,in eitherof theselayersmay be performedby humans.)The control layer may befurtherdivided,e.g.into supervisorycontrolandregulatorycontrol. In general,in ahierarchicalsystem,thelower layerswork on ashortertimescale.

In additionto keepingthecontrolledvariablesat their setpoints,thecontrolsystemmust“stabilize”theplant. We have hereput stabilizein quotesbecausewe usetheword in anextendedmeaning,andincludebothmodeswhich aremathematicallyunstableaswell asslow modes(“drift”) thatneedto be“stabilized” from anoperatorpointof view. Usually, stabilizationis donewithin aseparate(lower) layerof thecontrolsystem,oftencalledtheregulatorycontrollayer. Thecontrolledvariablesfor stabilizationaremeasuredoutputvariables,and their setpointsmay be usedas degreesof freedomfor the layersabove.

For eachlayer in a controlsystemwe usethe termscontrolled output( � with setpoint� � ) andma-nipulatedinput ( ). Correspondingly, the term“plant” refersto thesystemto be controlled(with ma-nipulatedvariables andcontrolledvariables� ). The layersareoften structuredhierarchically, suchthat themanipulatedinput for a higherlayer ( "! ) is thesetpointfor a lower layer ( �$#%� ), i.e. �$#%�'&( )! .(Thesecontrolledvariablesneedin generalnot be measuredvariables,andthey may includesomeofthemanipulatedvariables( ).)

Fromthisweseethattheterms“plant”, “controlledoutput” ( � ) and“manipulatedinput” ( ) takesondifferentmeaningdependingon wherewe arein thehierarchy. To avoid confusion,we reserve specialsymbolsfor thevariablesat thetop andbottomof thehierarchy. Thus,asalreadymentioned,thetermprocessis often usedto denotethe uncontrolledplant asseenfrom the bottomof thehierarchy. Here

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themanipulatedvariablesarethephysicalmanipulators(e.g. valve positions),andaredenoted� , i.e. *&+� in the bottom“regulatory” control layer. Correspondingly, at the top of the hierarchy, we usethesymbol � to denotethecontrolledvariablesfor which thesetpointvalues( ��� ) aredeterminedby theoptimizationlayer, i.e. �,&-� in thetop “supervisory”controllayer

(Input-Output)Controllability of aplantis theability to achieveacceptablecontrolperformance,thatis, to keepthecontrolledvariables( � ) within specifiedboundsfrom their setpoints( . ), in spiteof signaluncertainty(disturbances� , noise � ) andmodeluncertainty, usingavailable inputs ( ) andavailablemeasurements.In otherwords,the plant is controllableif thereexists a controllerwhich satisfiesthecontrolobjectives.

This definition of controllability may be appliedto thecontrol systemasa whole,or to partsof it(in thecasethecontrol layer is structured).The termcontrollability generallyassumesthatwe usethebestpossiblemultivariablecontroller, but wemayimposerestrictionsontheclassof allowedcontrollers(e.g.consider“controllability with decentralizedPI control”).

A plantis self-regulating if we with constantinputscankeepthecontrolledvariableswithin accept-ablebounds.(Note that this definitionmay be appliedto any layer in thecontrol system,so theplantmaybea partially controlledprocess).“True” self-regulationis definedasthecasewhereno control isever neededat thelowestlayer(i.e. � is constant).It relieson theprocessto dampenthedisturbancesitself, e.g. by having large buffer tanks. We rarely have “true” self-regulationbecauseit may be verycostly.

Self-optimizingcontrol is whenanacceptablelosscanbeachieved usingconstantsetpointsfor thecontrolledvariables(without theneedto reoptimizewhendisturbancesoccur).“True” self-optimizationis definedas the casewhereno re-optimizationis ever needed(so �/� can be kept constantalways),but this objective is usuallynot satisfied.On theotherhand,we mustrequirethat theprocessis “self-optimizable”within thetimeperiodbetweeneachre-optimization,or elsewecannotuseseparatecontrolandoptimizationlayers.

A processis self-optimizableif thereexists a set of controlledvariables( � ) suchthat if we withkeepconstantsetpointsfor theoptimizedvariables( ��� ), thenwe cankeepthelosswithin anacceptableboundwithin a specifiedtime period.A steady-stateanalysisis usuallysufficient to analyzeif we haveself-optimality. This is basedon theassumptionthattheclosed-looptimeconstantof thecontrolsystemis smallerthanthetimeperiodbetweeneachre-optimization(sothatit settlesto anew steady-state)andthat thevalueof theobjective function( � ) is mostlydeterminedby thesteady-statebehavior (i.e. thereis no “costly” dynamicbehavior e.g.imposedby poorcontrol).

3 General reviewsand bookson plantwide control

Weherepresentsabrief review of someof thepreviousreviews andbooksonplantwidecontrol.Morari (1982)presentedawell-writtenreview onplantwidecontrol,wherehediscusseswhy modern

control techniqueswere not (at that time) in widespreadusein the processindustry. The four mainreasonswerebelievedto be

1. Largescalesystemaspects.

2. Sensitivity (robustness).

3. Fundamentallimitationsto controlquality.

4. Education.

He thenconsideredtwo waysto decomposetheproblem:

1. Multi-layer (vertical),wherethedifferencebetweenthelayersarein thefrequency of adjustmentof theinput.

2. Horizontaldecomposition,wherethesystemis dividedinto noninteractingparts.

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Stephanopoulos(1982)statedthat the synthesisof a control systemfor a chemicalplant is still toa large extent an art. He asked: “Which variablesshouldbemeasuredin orderto monitor completelytheoperationof a plant? Which input shouldbemanipulatedfor effective control? How shouldmea-surementsbe pairedwith themanipulationsto form thecontrol structure,andfinally, what thecontrollaws are?” He notedthat theproblemof plantwidecontrol is “multi-objective” and“thereis a needfora systematicandorganizedapproachwhich will identify all necessarycontrol objectives”. Thearticleis comprehensive, anddiscussesmany of theproblemsin thesynthesisof controlsystemsfor chemicalplants.

RinardandDowns (1992)review muchof the relevant work in the areaof plantwidecontrol, andthey alsoreferto importantpapersthatwehavenot referenced.They concludethereview by statingthat“the problemprobablyneverwill besolvedin thesensethatasetof algorithmswill leadto thecompletedesignof a plantwidecontrol system”. They suggestthatmorework shouldbedoneon the followingitems:(1) A wayof answeringwhetheror not thecontrolsystemwill meetall theobjectives,(2) Sensorselectionandlocation(wherethey indicatethat theoryon partial controlmaybeuseful),(3) Processeswith recycle. They alsowelcomecomputer-aidedtools,bettereducationandgoodnew testproblems.

Thebookby BalchenandMummé (1988)attemptsto combineprocessandcontrolknowledge,andto usethis to designcontrol systemsfor somecommonunit operationsand also considerplantwidecontrol. The book providesmany practicalexamples,but thereis little in termsof analysistools or asystematicframework for plantwidecontrol.

The book “Integratedprocesscontrol andautomation”by Rijnsdorp(1991),containsseveral sub-jectsthatarerelevant here. Part II in thebook is on optimaloperation.He distinguishesbetweentwosituations,sellersmarked(maximizeproduction)andbuyersmarked(produceagivenamountat lowestpossiblecost).He alsohasaprocedurefor designof aoptimizingcontrolsystem.

vandeWal anddeJager(1995)list severalcriteriafor evaluationof controlstructuredesignmethods:generality, applicableto nonlinearcontrolsystems,controller-independent, direct,quantitative,efficient,effective, simpleandtheoreticallywell developed. After reviewing they concludethat sucha methoddoesnotexist.

Thebook by SkogestadandPostlethwaite (1996)hastwo chapterson controllability analysis,andonechapteron controlstructuredesign(Chapter10) wherethey discusstopicsrelatedto partialcontrolandself-optimizingcontrol(althoughthey did notusethatterm).

Theplannedmonographby Ng andStephanopoulos(1998a) dealsalmostexclusively with plantwidecontrol.

Thebook by Luybenet al. (1998)hascollectedmuchof Luybenspracticalideasandsummarizedthemin a clearmanner. Theemphasisis on casestudies.

Therealsoexistsalargebodyof system-theoreticliteraturewithin thefieldof largescalesystems,butmostof it haslittle relevanceto plantwidecontrol.Oneimportantexceptionis thebookby Findeisenetal. (1980)on “Control andcoordinationin hierarchicalsystems”whichprobablydeservesto bestudiedmorecarefullyby theprocesscontrolcommunity.

4 Control Structur eDesign(The mathematicallyorientedap-proach)

In this sectionwe look at themathematicallyorientedapproachto plantwidecontrol.

Structural methods

Therearesomemethodsthatusestructuralinformationabouttheplantasa basisfor control structuredesign.Forarecentreview of thesemethodswereferto theplannedmonographof Ng andStephanopou-los (1998a). Centralconceptsarestructuralstatecontrollability, observability andaccessibility. Based

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on this, setsof inputs and measurementsareclassifiedas viable or non-viable. Although the struc-tural methodsareinteresting,they arenot quantitative andusuallyprovide little informationotherthanconfirminginsightsaboutthestructureof theprocessthatmostengineersalreadyhave.

In thereminderof thissectionwediscussthefivetasksof thecontrolstructuredesignproblem,listedin theintroduction.

4.1 Selectionof controlled variables ( 0 )By “controlledvariables”weherereferto thecontrolledvariables� for which thesetpoints��� aredeter-minedby theoptimizationlayer. Therewill alsobeother(internally)controlledvariableswhich resultfrom thedecompositionof thecontrollerinto blocksor layers(includingcontrolledmeasurementsusedfor stabilization),but thesearerelatedto thecontrolconfigurationselection,which is discussedaspartof task4.

Theissueof selectionof controlledvariables,is probablytheleaststudiedof thetasksin thecontrolstructuredesignproblem. In fact, it seemsfrom our experiencethatmostpeopledo not considerit asan importantissue. Therefore,the decisionhasmostly beenbasedon engineeringinsight andexperi-ence,andthevalidity of theselectionof controlledvariableshasseldombeenquestionedby thecontroltheoretician.

To seethattheselectionof outputis anissue,askthequestion:

Whyarewecontrolling hundredsof temperatures,pressuresandcompositionsin a chemicalplant,whenthere is nospecificationon mostof thesevariables?

After somethought,onerealizesthatthemainreasonfor controllingall thesevariablesis thatoneneedsto specifytheavailabledegreesof freedomin orderto keeptheplantcloseto its optimaloperatingpoint.But thereis a follow-up question:

Whydo weselecta particular set � of controlled variables?(e.g., whyspecify(control) thetopcompositionin a distillation column,which doesnotproducefinal products,ratherthanjust specifyingits reflux?)

Theanswerto thissecondquestionis lessobvious,becauseatfirst it seemslike it doesnot reallymatterwhich variableswe specify (as long asall degreesof freedomareconsumed,becausethe remainingvariablesarethenuniquelydetermined).However, this is trueonly whenthereis no uncertaintycausedby disturbancesandnoise(signaluncertainty)or modeluncertainty. Whenthereis uncertaintythenitdoesmake a differencehow thesolutionis implemented,that is, which variableswe selectto controlattheir setpoints.

(Maarleveld andRijnsdrop1970)),Morari etal. (1980),SkogestadandPostlethwaite(1996)(Chap-ter10.3),Skogestad(2000)andZhengetal. (1999)proposeto basetheselectionof controlledvariablesbasedon consideringthe overall operationalobjective. The overall objective may be formulatedasascalarcostfunction � which shouldbeminimizedsubjectto setof operationalconstraints.(MaarleveldandRijnsdrop1970))foundthatin many casesall thedegreesof freedomareusedto satisfyconstraints,andthecontrolledvariablesshouldthensimply beselectedastheactive constraints.For example,if itis optimal to keepthereactortemperatureat its upperlimit, thenthis shouldbeselectedasa controlledvariable.

The moredifficult caseis if we have unconstraineddegreesof freedom,for example,the optimalheatinputwhenwe bake acake.

Thebasicideaof whatwe herecall self-optimizingcontrol wasformulatedabouttwentyyearsagoby Morari et al. (1980):

“in attemptingto synthesizea feedbackoptimizing control structure,our mainobjective isto translatetheeconomicobjectivesinto processcontrolobjectives.In otherwords,wewantto find a function � of theprocessvariableswhich whenheldconstant,leadsautomaticallyto theoptimaladjustmentsof themanipulatedvariables,andwith it, theoptimaloperating

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conditions. [...] This meansthatby keepingthefunction �213 )4%�65 at thesetpoint��� , throughtheuseof themanipulatedvariables , for variousdisturbances� , it follows uniquelythattheprocessis operatingat theoptimalsteady-state.”

If wereplacetheterm“optimal adjustments”by “acceptableadjustments(in termsof theloss)” thentheabove is a precisedescriptionof whatSkogestad(2000)denotea self-optimizingcontrolstructure.Theonly factorMorari etal. (1980)fail to consideris theeffectof theimplementationerror �"78��� . Morari etal. (1980)proposeto selectthebestsetof controlledvariablesbasedon minimizing theloss(“feedbackoptimizingcontrolcriterion1”). Therelationshipto thework of Shinnaris discussedseparatelylater.

Somewhatsurprisingly, theideasof Morari etal. (1980)receivedvery little attention,at leastduringthefirst 20yearsaftertheirpublication.Onereasonis probablythatthepaperalsodealtwith theissueoffinding theoptimaloperation(andnot only on how to implementit), andanotherreasonis thattheonlyexamplein thepaperhappenedto resultin aoptimalsolutionwhereall degreesof freedomwereusedtosatisfyconstraints.The follow-up paperby Arkun andStephanopoulos(1980)concentratedfurtherontheconstrainedcaseandtrackingof active constraints.

Skogestadand Postlethwaite (1996) (Chapter10.3) presentsan approachfor selectingcontrolledoutputsimilar to thoseof Morari etal. (1980)andtheideaswherefurtherdevelopedin (Skogestad2000)wherethe term self-optimizingcontrol is introduced. Skogestad(2000)stressesthe needto considerthe implementationerror whenevaluatingthe loss. Skogestad(2000)gives four requirementsthat acontrolledvariableshouldmeet:1) Its optimalvalueshouldbeinsensitive to disturbances.2) It shouldbeeasyto measureandcontrolaccurately. 3) Its valueshouldbesensitive to changesin themanipulatedvariables.4) For caseswith two or morecontrolledvariables,theselectedvariablesshouldnotbecloselycorrelated.By scalingof thevariablesproperly, SkogestadandPostlethwaite(1996)shows thattheself-optimizingcontrolstructureis relatedto maximizingtheminimumsingularvalueof thegainmatrix 9 ,where :;�'&@ BAC>D�65FE is small,whereasoneshouldreallyminimizethesteady-statesensitivity of theeconomicloss( G ) to disturbances,i.e. to selectcontrolledvariables( � ) suchthat 1?>@GHAC>@�I5FE is small.

Narraway et al. (1991),Narraway andPerkins(1993)andNarraway andPerkins(1994))stronglystresstheneedto basethe selectionof the control structureon economics,andthey discusstheeffectof disturbanceson theeconomics.However, they do not formulateany rulesor proceduresfor selectingcontrolledvariables.

In astudyof theTenesseeEastmanchallengeproblem,Ricker (1996)notesthatwhenapplyingbothMPCanddecentralizedmethods,oneneedsto makecritical decisionswithoutquantitative justifications.The foremostof theseis the selectionof the controlledvariables,andhe found existing quantititativemethodsfor their selectionto beinadequate.Ricker (1995)statethat thecontrolledvariables“must be

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carefullychosen;arbitraryuseof feedbackcontrolloopsshouldbeavoided”.Finally, Mizoguchiet al. (1995)andMarlin andHrymak(1997)stresstheneedto find a goodway

of implementingtheoptimalsolutionin termshow thecontrol systemshouldrespondto disturbances,“i.e. thekey constraintsto remainactive,variablesto bemaximizedor minimized,priority for adjustingmanipulatedvariables,andsoforth.” They suggestthatanissuefor improvementin today’s real-timeop-timizationsystemsis to selectthecontrolsystemthatyieldsthehighestprofit for arangeof disturbancesthatoccurbetweeneachexecutionof theoptimization.

Therehasalsobeendonesomework on non-squareplants,i.e. with moreoutputsthaninputs,e.g.(Cao1995)and(ChangandYu 1990). Theseworks assumethat the control goal is the keepall theoutputvariablesat given setpoints,andoften the effect of disturbancesis not considered.It may bemoresuitableto definethe cost function � for the operationandreformulatetheseproblemsinto theframework of self-optimizingcontrol.

4.2 Selectionof manipulated variables ( J )By manipulatedvariableswe refer to thephysicaldegreesof freedom,typically thevalve positionsorelectricpower inputs.Actually, selectionof thesevariablesis usuallynot muchof anissueat thestageof control structuredesign,sincethesevariablesusuallyfollow asdirectconsequenceof thedesignoftheprocessitself.

However, theremaybesomepossibilityof addingvalvesor moving them.For example,if weinstallabypasspipelineandavalve, thenwemayusethebypassflow asanextradegreeof freedomfor controlpurposes.

Finally, let usmake it clearthatthepossibilityof not actively usingsomemanipulatedvariables(oronly changingthemrarely),is a decisionthatis includedabove in “selectionof controlledvariables”.

4.3 Selectionof measurements( K )Controllability considerations,including dynamicbehavior, are importantwhenselectingwhich vari-ablesto measure.Thereareoftenmany possiblemeasurementswe canmake,andthenumber, locationandaccuracy of themeasurementis a tradeoff betweencostof measurementsandbenefitsof improvedcontrol.A controllabilityanalysismaybeveryuseful.In mostcasestheselectionof measurementsmustbeconsideredsimultaneouslywith theselectionof thecontrolconfiguration.For example,this appliesto theissueof stabilizationandtheuseof secondarymeasurements.

4.4 Selectionof control configuration

Theissueof controlconfigurationselection,includingmultiloop (decentralized)control,is discussedinHovd andSkogestad(1993)andin sections10.6,10.7and10.8of SkogestadandPostlethwaite(1996),andwe will herediscussmainly issueswhicharenot coveredthere.

Thecontrol configurationis thestructureof thecontroller � that interconnectsthemeasurements,setpoints�/� andmanipulatedvariables� . The controllercanbe structured(decomposed)into blocksbothin anvertical(hierarchical)andhorizontal(decentralizedcontrol)manner.

Why, insteadof finding the truly optimal centralizedcontroller, is the controllerdecomposed?(1)Thefirst reasonis that it may requirelesscomputation.This reasonmayberelevant in somedecisionmakingsystemswherethereis limited capacityfor transmittingandhandlinginformation(like in mostsystemswherehumansareinvolved), but it doesnot hold in todayschemicalplant whereinformationis centralizedandcomputingpower is abundant.Two otherreasonsoftengivenare(2) failuretoleranceand(3) theability of local unitsto actquickly to rejectdisturbances(e.g.Findeisenet al., 1980).Thesereasonsmaybemorerelevant,but, aspointedoutby SkogestadandHovd(1995)thereareprobablyotherevenmorefundamentalreasons.Themostimportantoneis probably(4) to reducethecostinvolved indefiningthecontrolproblemandsettingupthedetaileddynamicmodelwhichis requiredin acentralized

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systemwith no predeterminedlinks. Also, (5) decomposedcontrol systemsaremuchlesssensitive tomodeluncertainty(sincethey oftenusenoexplicit model).In otherwords,by imposingacertaincontrolconfiguration,we areimplicitly providing processinformation,which we with a centralizedcontrollerwould needto supplyexplicitly throughthemodel.

4.4.1 Stabilizing control

Instability requiresthe active useof manipulatedvariables( � ) using feedbackcontrol. Thereexistrelatively few systematictools to assistin selectinga control structurefor stabilizingcontrol. Usually,single-loopcontrollersareusedfor stabilization,andissuesarewhich variablesto measureandwhichmanipulatedvariablesto use. Oneproblemin stabilizationis thatmeasurementnoisemaycauselargevariationsin the input suchthat it saturates.Havre andSkogestad(1996,1998)have shown that thepole vectors may be usedto selectmeasurementsandmanipulatedvariablessuchthat this problemisminimized.

4.4.2 Secondarymeasurements

Extra (secondary)measurementsareoften addedto improve thecontrol. Threealternativesfor useofextra measurementsare:

1. Centralizedcontroller: All the measurementsareusedto computethe optimal input. This con-troller hasimplicitly anestimator(model)hiddeninsideit.

2. Inferential control: Basedon the measurementsa model is usedto provide an estimateof theprimaryoutput(e.g.acontrolledoutput � ). This estimateis sendto aseparatecontroller.

3. Cascadecontrol: Thesecondarymeasurementsarecontrolledlocally andtheir setpointsareusedasdegreesof freedomatsomehigherlayerin thehierarchy.

Notethatbothcentralizedandinferentialcontrolusestheextrameasurementsto estimateparametersin a model,whereasin cascadecontrol they areusedfor additionalfeedback.Thesubjectof estimationandmeasurementsselectionfor estimationis beyondthescopeof this review article;we referto Ljung(1987)for acontrolview andto Martens(1989)for achemometricsapproachto this issue.However, wewould like point out that thecontrolsystemshouldbedesignedfor bestpossiblecontrolof theprimaryvariables( � ), andnot thebestpossibleestimate.A drawbackof theinferentialschemeis thatestimateisusedin feed-forwardmanner.

For cascadecontrol Havre (1998)hasshown how to selectsecondarymeasurementssuchthat theneedfor updatingthe setpointsis small. The issueshereare similar to that of selectingcontrolledvariables( � ) discussedabove. Oneapproachis to minimizesomenormof thetransferfunctionfrom thedisturbanceandcontrol error in thesecondaryvariableto thecontrol error in the primary variable. Asimpler, but lessaccurate,alternative is to maximizetheminimumsingularvaluein thetransferfunctionfrom secondarymeasurementsto theinputusedto controlthesecondarymeasurements.LeeandMorari((Lee andMorari 1991),(Lee et al. 1995)and(Lee et al. 1997))usea morerigorousapproachwheremodeluncertaintyis explicitly consideredandthestructuredsingularvalueis usedasa tool.

4.4.3 Partial control

Most control configurationsarestructuredin a hierarchicalmannerwith fast inner loops,andslowerouterloopsthat adjustthesetpointsfor the inner loops. Control systemdesigngenerallystartsby de-signingthe inner(fast)loops,andthenouterloopsareclosedin a sequentialmanner. Thus,thedesignof an “outer loop” is doneon a partially controlled system.We hereprovide somesimplebut yet veryusefulrelationshipsfor partially controlledsystems.Wedivide theoutputsinto two classes:� �I! – (temporarily)uncontrolledoutput� �$# – (locally) measuredandcontrolledoutput(in theinnerloop)

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We have insertedtheword temporarily above, since �I! is normallya controlledoutputat somehigherlayerin thehierarchy. Wealsosubdivide theavailablemanipulatedvariablesin asimilarmanner:� L# – inputsusedfor controlling �$# (in theinnerloop)� )! – remaininginputs(whichmaybeusedfor controlling �I! )

A block diagramof thepartially controlledsystemresultingfrom closingtheloop involving D# and� # with thelocal controller � # is shown in Figure2.

MM

N ! O !P! O !Q#O #R! O #P#

� SO,T ! O,T #�

�

U #N #

MM

V+ +V+ +V+ +V- +

MW !MW #X

��W #ZY

[ #\\ W #%�

Figure2: Block diagramof apartially controlledplant

SkogestadandPostlethwaite(1996)distinguishbetweenthefollowing four casesof partialcontrol:

Meas./Control Controlobjectiveof �I! ? for �$# ?

I Indirectcontrol No NoII Sequentialcascadecontrol Yes NoIII “True” partialcontrol No YesIV Sequentialdecentralizedcontrol Yes Yes

In all casesthereis a control objective associatedwith � ! anda measurementof � # . For example,for indirectcontrolthereis noseparatecontrolobjective on �$# , thereasonswecontrol �$# is to indirectlyachievegoodcontrolof �I! whicharenotcontrolled.Thefirst two casesareprobablythemostimportantas they are relatedto vertical (hierarchical)structuring. The latter two cases(where �$# hasits owncontrolobjective sothatthesetpoints�$#%� arenotadjustable)givesahorizontalstructuring.

In any case,thelinearmodelfor theplantcanbewritten

�I!]&^9_!P!`1?ab5c )!ed*9f!Q#$1?aC5c D#gd*9 T ! 1?ab5F� (1)�$#h&^9i#R!`1?ab5c )!ed*9j#P#$1?aC5c D#gd*9 T # 1?ab5F� (2)

To derive transferfunctionsfor thepartially controlledsystemwe simply solve (2) with respectto L# (assumingthat 9j#P#$1?aC5 is squareaninvertibleatagivenvalueof a )1 L#k&^9fl !#P# 1?aC5B13�$#m7n9j#R!`1?aC5c "!g7n9 T # 1?ab5F�I5 (3)

Substituting(3) into (1) thenyields(Havre andSkogestad1996a)

�I!o&qp)r@1?aC5c "!edsp T 1?aC5F�jdtp)uv1?aC5c�$# (4)1Theassumptionthat wyx{z|F| existsfor all valuesof } canberelaxedby replacingtheinversewith thepseudo-inverse.

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which is themodelwith D# formally replacedby �$# asanindependentvariable,andp~rD1?aC5/?& 9_!P!`1?ab5e7n9_!Q#9 l !#P# 9j#R!`1?aC5 (5)p T 1?aC5/?& 9 T ! 1?ab5e79f!Q#9fl !#P# 9 T # 1?aC5 (6)p~u61?aC5/?& 9_!Q#9 l !#P# 1?ab5 (7)

Here p T is the partial disturbancegain, p~u is the gain from �$# to �I! , and p~r is the partial inputgainfrom theunusedinputs "! (with �$# constant).If we look morecarefullyat (4) thenwe seethatthematrix p T givestheeffectof disturbanceson theprimaryoutputs�I! , whenthemanipulatedvariables D#areadjustedto keep �$# constant,which is consistentof theoriginal definitionof thepartialdisturbancegaingivenby SkogestadandWolff (1992). Note thatno approximationaboutperfectcontrolhasbeenmadewhenderiving (4). Equation(4) appliesfor any fixed valueof a (on a frequency-by-frequencybasis,ay&*2 ).

Theabove equationsaresimpleyet very useful.Relationshipscontainingpartsof theseexpressionshavebeenderivedby many authors,e.g.seethework of Manousiouthakisetal. (1986)onblockrelativegainsandthework of HäggblomandWaller (1988)on distillationcontrolconfigurations.

Note that this kind of analysiscanbe performedat eachlayersin the control system. At the toplayerwe maysometimesassumethatthecost � is a functionof thevariables� ! (this is theapproachofShinnar(1981)),andwe cantheninterpret �$# asthesetof controlledvariables� . If � is never adjustedthenthis is a specialcaseof indirectcontrol,andif � is adjustedat regular intervals(asis usuallydone)thenthismaybeviewedasaspecialcaseof sequentialcascadecontrol.

5 The ProcessOriented Approach

Weherereview proceduresfor plantwidecontrolthatarebasedonusingprocessinsight,thatis, methodsthatareuniqueto processcontrol.

The first comprehensive discussionon plantwidecontrol wasgiven by PageBuckley in his book“Techniquesof processcontrol” in a chapteron Overall processcontrol (Buckley 1964). Thechapterintroducesthemainissues,andpresentswhatis still in many waystheindustrialapproachto plantwidecontrol. In fact,whenreadingthis chapter, 35 yearslater oneis struckwith the feeling that therehasbeenrelatively little developmentin this area. Someof the termswhich areintroducedanddiscussedin the chapterare materialbalancecontrol (in direction of flow, and in direction oppositeof flow),productionratecontrol,buffer tanksaslow-passfilters, indirectcontrol,andpredictive optimization.Healsodiscussesrecycleandtheneedto purgeimpurities,andhepointsout thatyoucannotatagivenpointin a plantcontrol inventory(level, pressure)andflow independentlysincethey arerelatedthroughthematerialbalance.In summary, he presentsa numberof usefulengineeringinsights,but thereis reallyno overall procedure.As pointedout by Ogunnaike (1995)thebasicprinciplesappliedby the industrydoesnotdeviatefar from Buckley (1964).

Wolff andSkogestad(1994)review previousworkonplantwidecontrolwith emphasisontheprocess-orienteddecompositionapproaches.They suggestthatplantwidecontrolsystemdesignshouldstartwitha “top-down” selectionof controlledandmanipulatedvariables,andproceedwith a “bottom-up”designof thecontrolsystem.At theendof thepapertenheuristicguidelinesfor plantwidecontrolarelisted.

Thereexistsothermoreor lessheuristicsrulesfor processcontrol;e.g.seeHougenandBrockmeier(1969)andSeborg et al. (1995).

5.1 Degreesof fr eedomfor control and optimization

A startingpoint for plantwidecontrol is to establishthe numberof degreesof freedomfor operation;bothdynamically(for control) fY , andatsteady-state(usallyfor optimization)_�F� ). Thesearedefinedas

13

fY Degreesof freedomfor control: Thenumberof variables(temperatures,pressures,levelsetc.) thatmaybesetby thecontrolsystem.

=�c� Degreesof freedomatsteadystate:Thenumberof independentvariableswith asteadystateeffect.Many authorssuggestto useaprocessmodelto find thedegreesof freedom.However thisapproach

will be error prone,it is easyto write too many or too few equations.Fortunately, it is in mostcasesrelatively straightforwardto establishthesenumbersfrom processinsight.

Ponton(1994)proposesarulefor finding =�c� by countingthenumberof streamsandsubtractingthenumberof “extra” phases(i.e. if therearemorethanonephasepresentin theunit). However, it is easyto constructsimpleexampleswheretherule fails. For example,considerasimpleliquid storagetank(0extra phases)with oneinflow andoneoutflow (2 streams).Accordingto therule,we have �c� &q , butwe know _�F�g&

5.2 Production rate

Identifying the major disturbancesis very importantin any control problem,and for processcontrolthe productionrate(throughput)is often the main disturbance.In addition, the locationof wheretheproductionrateis actuallyset(“throughputmanipulator”),usuallydeterminesthecontrolstructureforthe inventorycontrol of the variousunits (Buckley 1964). For a plant runningat maximumcapacity,theproductionrateis setat its bottleneck,which is usuallyinsidetheplant (e.g. causedby maximumcapacityof a heatexchangeror a compressor).Then, downstreamof this location the plant hastoprocesswhatever comesin (givenfeedrate),andupstreamof this locationtheplanthasto producethedesiredquantity(givenproductrate).To avoid any “long loops”, it is preferablyto usetheinputflow forinventorycontrolupstreamthe locationwheretheproductionrateis set,andto usetheoutputflow forinventorycontroldownstreamthis location.

Fromthis it follows thatit is critical to know wherein theplanttheproductionrateis set.In practice,the location may vary dependingon operatingconditions. This may requirereconfiguringof manycontrolloops,but oftensupervisorycontrolsystems,suchasmodelpredictive control,provideasimplerandbettersolution.

5.3 The conceptsof partial control and dominat variables

Shinnar(1981)introducedthefollowing setsof variables�6  (the“primary” or “performance”or “economic”variables)is “the setof processvariablesthatdefinetheproductandprocessspecificationsaswell asprocessconstraints”� T is thesetof dynamicallymeasuredprocessvariables� E T (asubsetof T ) is the“setof processvariablesonwhichwebaseourdynamiccontrolstrategy”�^¡ T is thedynamicinput variables

Thegoal is to maintain 6  within prescribedlimits andto achieve this goal“we choosein mostcasesasmallset E T andtry to keeptheseatafixedsetof valuesby manipulating¡ T ” (later, Arbel etal. (1996)introducedtheterm“partial control” to describethis idea).

Shinnarnotesthattheoverall controlalgorithmcannormallybedecomposedinto adynamiccontrolsystem(whichadjust ¡ T ) andasteady-statecontrolwhichdeterminesthesetpointsof E T aswell asthevaluesof ¡ � (thelatterarethemanipulationswhich canonly bechangedslowly), andthatwe “look fora set E T 4 ¡ T thatcontainsvariablesthathave a maximumcompensatingeffect on 6  ”. If onetranslatesthe wordsandnotation,thenonerealizesthat Shinnar’s ideaof “partial control” is very closeto theideaof “self-optimizingcontrol” presentedin Morari etal. (1980),SkogestadandPostlethwaite(1996),and Skogestad(2000). The differenceis that Shinnarassumesthat thereexist at the outseta set of“primary” variablesv  thatneedto becontrolled,whereasin self-optimizingcontrol thestartingpointis aneconomiccostfunctionthatshouldbeminimized.

Theauthorsprovide someintuitive ideasandexamplesfor selectingdominantvariableswhich maybeusefulin somecases,especiallywhennomodelinformationis available.However, it is notclearhowhelpful theideaof “dominant” variableis, sincethey arenot really definedandno explicit procedureisgiven for identifying them. Indeed,Arbel et al. (1996)write that “the problemsof partial controlhavebeendiscussedin aheuristicway” andthat“considerablyfurtherresearchis neededto fully understandtheproblemsis steady-statecontrolof chemicalplants”.Tyreus(1999b) providessomeadditionalideasonhow to selectdominantvariables,partlybasedontheextensivevariableideaof Georgakis(1986)andthethermodynamicideasof Ydstie,(AlonsoandYdstie1996),but againnoprocedurefor selectingsuchvariablesarepresented.

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5.4 Decompositionof the problem

Thetaskof designinga controlsystemfor completeplantsis a largeanddifficult task.Thereforemostmethodswill try to decomposetheprobleminto manageableparts.Fourcommonwaysof decomposingtheproblemare

1. Decompositionbasedon processunits

2. Decompositionbasedon processstructure

3. Decompositionbasedon controlobjectives(materialbalance,energy balance,quality, etc.)

4. Decompositionbasedon timescale

Thefirst is a horizontal(decentralized)decompositionwhereasthelatter threeprovide hierarchicalde-compositions.Most practicalapproachescontainelementsfrom severalcategories.

Many of themethodsdescribedbelow suggestto performtheoptimizationat theendof theproce-dure,aftercheckingif therearedegreesof freedomleft. However, asdiscussedabove, it is possibletoidentify thesteady-statedegreesof freedominitially andperformanoptimizationto identify controlledvariables( � ’s) that achieve self-optimizingcontrol (a “top-down approach”),andafterwardsto design“bottom-up” a control systemwhich, in additionto satisfyingotherobjectives, is ableto control thesevariablesat their setpoints.This is theapproachwe advocate.

It is alsointerestingto seehow themethodsdiffer in termsof theimportanceassignedto inventory(level) control.Someregardinventorycontrolasthemostimportant(asis probablycorrectwhenviewedpurely from a operationalpoint of view) whereasPonton(1994)statesthat“inventoryshouldnormallyberegardedastheleastimportantof all variablesto beregulated”(which is correctwhenviewedfrom adesignpoint of view). We feel that thereis a needto integratetheviewpointsof thecontrolanddesignpeople.

5.4.1 The unit basedapproach

Theunit-basedapproach,suggestedby Umedaetal. (1978),proposesto

1. Decomposetheplantinto individual unit of operations

2. Generatethebestcontrolstructurefor eachunit

3. Combineall thesestructuresto form acompleteonefor theentireplant.

4. Eliminateconflictsamongtheindividual controlstructuresthroughmutualadjustments.

Thisapproachhasalwaysbeenwidely usedin industry, andhasits mainadvantagethatmany effec-tive control schemeshave beenestablishedover the yearsfor individual units (e.g. Shinskey (1988)).However, with an increasinguseof materialrecycle, heatintegration and the desireto reducebuffervolumesbetweenunits,thisapproachmayresultin toomany conflictsandbecomeimpractical.

As a result,onehasto shift to plantwidemethods,wherea hierarchicaldecompositionis used.Thefirst suchapproachwasBuckley’s (1964)division of the control systeminto materialbalancecontrolandproductquality control,andthreeplantwideapproaches,partly basedon his ideas,aredescribedinthefollowing.

5.4.2 Hierar chical decompositionbasedon processstructure

Thehierarchygivenin Douglas(1988)for processdesignstartsat a cruderepresentationandgetsmoredetailed:

Level 1 Batchvs continuous

Level 2 Input-outputstructure

Level 3 Recyclestructure

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Level 4 Generalstructureof separationsystem

Level 5 Energy interaction

Fisheret al. (1988)proposeto usethis hierarchywhenperformingcontrollability analysis,andPontonandLaing (1993)point out that this hierarchy, (e.g. level 2 to level 5) could alsobe usedfor controlsystemdesign. This framework enablesparalleldevelopmentfor the processandthe control system.Within eachof thelevelsabove any designmethodmight beapplied.

Ng andStephanopoulos(1998b) proposeto useasimilarhierarchyfor controlstructuredesign.ThedifferencebetweenDouglas(1988)andNg andStephanopoulos(1998b)’s hierarchyis that level 1 isreplacedby a preliminaryanalysisandthat levels4 and5 arereplacedby moredetailedstructures.Ateachstepthe objectives identifiedat an earlier stepis translatedto this level andnew objectives areidentified. The focusis on constructionof massandenergy balancecontrol. Themethodis appliedtotheTennesseeEastmancase.

All thesemethodshave in commonthatat eachstep(level), a key point is to checkif thereremainenoughmanipulatedvariablesto meettheconstraintsandto optimizeoperation.Themethodsareeasyto follow andgive a goodprocessunderstanding,andtheconceptof a hierarchicalview is possibletocombinewith almostany designmethod.

5.4.3 Hierar chical decompositionbasedon control objectives

The hierarchybasedon control objectives is sometimescalled the tieredprocedure.This bottom-upprocedurefocuseson thetasksthatthecontrollerhasto perform.Normally onestartsby stabilizingtheplant,whichmainly involvesplacinginventory(massandenergy) controllers.

Priceet al. (1993)build on the ideasthat wasintroducedby Buckley (1964)andthey introduceatieredframework. Theframework is dividedinto four differenttasks:

I Inventoryandproductionratecontrol.

II Productspecificationcontrol

III Equipment& operatingconstraints

IV Economicperformanceenhancement.

Their paperdoesnot discusspointsIII or IV. They performa large number(318) of simulationswithdifferentcontrolstructures,controllers(Por PI), andtuningsonasimpleprocessconsistingof areactor,separatorandrecycle of unreactedreactant.Theconfigurationsarerankedbasedon integratedabsoluteerrorof theproductcompositionfor stepsin thedisturbance.Fromthesesimulationthey proposesomeguidelinesfor selectingthe through-putmanipulatorandinventorycontrols. (1) Preferinternalflowsas through-putmanipulator. (2) the through-putmanipulatorand inventory controlsshouldbe self-consistent(self-consistency is fulfilled whenachangein thethrough-putpropagatesthroughtheprocessby “itself” anddoesnot dependon compositioncontrollers).They apply their ideason theTennesseeEastmanproblem(Priceetal. 1994).

Ricker (1996)commentson thework of Priceet al. (1994)andpointsout thatplantsareoftenrunat full capacity, correspondingto constraintsin oneor severalvariables.If a manipulatedvariableusedfor level control saturates,one loosesa degreeof freedomfor maximumproduction. This shouldbeconsideredwhenchoosinga through-putmanipulator.

Luybenetal. (1997)pointoutthreelimitationsof theapproachof Buckley. First,hedid notexplicitlydiscussenergy management.Second,hedid notlook atrecycles.Third,heplacedemphasisoninventorycontrolbeforequality control.Their plantwidecontroldesignprocedureis listedbelow:

1. Establishcontrolobjectives.

2. Determinethecontroldegreesof freedomby countingthenumberof independentvalves.

3. Establishenergy inventorycontrol,for removing theheatsof reactionsandto preventpropagationof thermaldisturbances.

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4. Setproductionrate. Theproductionratecanonly be increasedby increasingthe reactionrateinthereactor. Onerecommendationis to usetheinput to theseparationsection.

5. Productqualityandsafetycontrol.Herethey recommendtheusual“pair close”-rule.

6. Inventorycontrol. Fix a flow in all liquid recycle loops. They statethatall liquid levelsandgaspressuresshouldbecontrolled.

7. Checkcomponentbalances.(After this point it might beenecessaryto gobackto item 4.)

8. Unit operationscontrol.

9. Useremainingcontroldegreesof freedomto optimizeeconomicsor improve dynamiccontrolla-bility.

They applytheir procedureon severaltestproblems;thevinyl acetatemonomerprocess,theTennesseeEastmanprocess,andtheHDA process.

Step3 comesbeforedeterminingthethroughputmanipulator, sincethereactoris typically theheartof the processandthe methodsfor heatremoval are intrinsically part of the reactordesign. In orderto avoid recycling of disturbancesthey suggestto seta flow-ratein all recyclesloops;this is discussedmorein section6. They suggestin step6 to controlall inventories,but this maynot benecessaryin allcases;e.g. it maybeoptimal to let thepressurefloat (Shinskey 1988). We recommend(seebelow) tocombinesteps1 and9, that is, theselectionof controlledvariables(controlobjectives)in step1 shouldbebasedonoverall planteconomics.

McAvoy (1999) presentsa methodwherethe control objectives are divided into two categories:variablesthat “must” becontrolled,andproductflow andquality. His approachis to identify thesetofinputsthatminimizesvalve movements.This is first solved for the “must” variables,thenfor productrateandquality. Theoptimizationproblemis simplifiedby usinga linearstablesteadystatemodel.Hegivesno guidanceinto how to identify thecontrolledvariables.

5.4.4 Hierar chical decompositionbasedon time scales

Buckley (1964)proposedto designthequality controlsystemashigh-passfilters for disturbancesandto designthemassbalancecontrolsystemaslow passfilters. If theresonancefrequency of thequalitycontrol systemis designedto be an orderof magnitudehigher than the breakfrequency of the massbalancesystemthenthetwo loopswill benon-interacting.

McAvoy andYe(1994)divide theirmethodinto four stages:

1. Designof innercascadeloops.

2. Designof basicdecentralizedloops,exceptthoseassociatedwith qualityandproductionrate.

3. Productionrateandquality controls.

4. Higherlayercontrols.

Thedecompositionin stages1-3is basedonthespeedof theloops.In stage1 theideais to locally reducethe effect of disturbances.In stage2 theregenerallyarea large numberof alternative configurations.Thesemaybescreenedusingsimplecontrollability tools,suchastheRGA. Oneproblemof selectingoutputsbasedonacontrollabilityanalysisis thatonemayendupwith theoutputsthatareeasytocontrol,ratherthantheonesthatareimportantto control. Themethodis appliedto theTennesseeEastmantestproblem.

Douglas(1988),at page414,presentsa hierarchyfor controlsystemdesign,basedon steady-state,normaldynamicresponseandabnormaldynamicoperation.Zhenget al. (1999)continuethis work andplacea greaterattentionon feasibility in faceof constraintsandon robust optimality (self-optimizingcontrol). (ZhengandMahajannam1999)proposeto useminimumsurgecapacityasadynamiccost.

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6 The reactor, separatorand recycleplant

A commonfeatureof most plantsis the presenceof recycle. A simple exampleis distillation, withrecycle (“reflux”) of liquid from thetopof thecolumnandof vaporfrom thebottomof thecolumn.

In this section,we considerthereactorandseparatorprocesswith recycle of unreactedfeedfrom areactor. Thisproblemhaslatelybeenstudiedby many authors,e.g.(Papadourakisetal. 1987),(Wolff etal. 1992),(Priceet al. 1993),(Luyben1994),(LuybenandFloudas1994),(Mizsey andKalmar1996),(Wu andYu 1996),(Hansen1998),(Ng andStephanopoulos1998a). It maybedifficult to follow all thedetailsin thecasestudiespresented,soinsteadweaim in thissectionto gainsomebasicinsightinto theproblem.

In thesimplestcase,let thereactorbeaCSTRwherecomponentA is convertedto aproductandtheamountconvertedis p¢&q£I¤`¥~¦ § �©¨Cª3«iACa¬TheunreactedA is separatedfrom theproductandrecycledbackto the reactor(for simplicity we willhereassumeperfectseparation).To increasetheconversion p onethenhasthreeoptions:

1. Increasethetemperaturein orderto increasethereactionrateconstant£ [sl ! ].2. Increasetheamountof recycle,which indirectly increasesthefractionof A in thereactor, ¤ ¥ [mol

A/mol].

3. Increasethereactorholdup ¦ [mol]. (In a liquid phasesystemthereactorholdupis determinedby thereactorlevel, andin agasphasesystemby thereactorpressure.)

Herewe will assumethatthetemperatureis constant,sotherearetwo optionsleft. Sinceat steady-statewith given productspecificationsthe conversionof A in the reactoris given by the feedrate, itfollows that the two remainingoptionsare dependent,so if we control one variable, then the othervariablewill ”float” andadjustitself.

Two commoncontrolstrategiesarethen

(A) Controlthereactorholdup(andlet therecycle flow float)

(B) Controltherecycle flow (andlet thereactorholdupfloat).

In case(A) onemayencountertheso-called”snowball effect” wheretherecycle goesto infinity. Thisoccursbecauseat infinite recycle flow we have ¤¥®&¯ which givesthehighestpossibleproduction.Ineffect, thesnowball effect occursbecausethereactoris too small to handlethegiven feedrate,so it isreally asteady-statedesignproblem.

Luyben(1992,1994)hasstudiedliquid phasesystemsandhasconcludedthat control strategy (B)(or avariantof it) with oneflow fixedin therecycle loopshouldbeusedto avoid the”snowball effect”.

Wu andYu (1996)alsostudythesnowball effectandproposeto distributethe“load” evenlybetweenthedifferentunits. In effect, they suggestto let thereactorvolumevary and

(C) Controlthereactorcomposition.

However, from aneconomicpointof view oneshouldin mostcasesfor liquid phasesystems(includ-ing theonestudiedhere)keepthereactorlevel at its maximumvalue. This maximizestheconversionper passandresultsin the smallestpossiblerecycle, which generally(unlessbyprodyctsare formed)reducestheoperationalcost.Thus,therecommendationof Luyben(1992,1994)and(Wu andYu 1996),hasasteady-stateeconomicpenaltywhich it seemsthatmostresearchershave sofar neglected.

On the otherhand,for gasphasesystems,thereis usuallyan economicpenaltyfrom compressioncostsinvolved in increasingthe reactorholdup(i.e. the reactorpressure),andstrategy (B) wherewelet theholdup(pressure)float may in fact beeconomicallyoptimal. Indeed,suchschemesareusedinindustry, e.g. in ammoniaplants. For example,for processeswith gasrecycle andpurge,Fisheret al.(1988)recommendsto keepthegasrecycle constantat its maximumvalue.

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Stm

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Figure3: TennesseeEastmanprocessflowsheet

Wolff et al. (1992)studieda similar plant. They includedan inert componentandlooked on theeffectsof recycle on the controllability of the process.Their conclusionis that the purge streamflowshouldbeusedto controlthecompositionof inert. They did notconsiderthereactorholdupasapossiblecontrolledvariable.

All theaboveworkshave in commonthattheauthorsaresearchingfor theright controlledvariablesto keepconstant(recycle flow, reactorvolume,composition,etc.). However, a commonbasisfor com-paringthealternativesseemsto be lacking. In termsof futurework, we proposethatonefirst needstodefineclearlytheobjective function(cost) � for theoperationof thereactorsystem.Only whenthis isgiven,mayonedecidein arigorousmanneronthebestselectionof controlledvariables,for examplebyusingtheideaof “self-optimizing” controlandevaluatingtheloss.

7 TennesseeEastmanProcess

7.1 Intr oduction to the testproblem

Theproblemof DownsandVogel(1993)wasfirst proposedatanAIChE meetingin 1990andhassincebeenstudiedby many authors.Theprocesshasfour feedstreams,oneproductstream,andonepurgestreamto remove inert (B) andbyproduct(F). Thereactionsare

A(g) + C(g)+ D(g) ° G(liq), Product1,A(g) + C(g)+ E(g) ° H(liq), Product2,

A(g) + E(g) ° F(liq), Byproduct,3D(g) ° 2F(liq), Byproduct,

All reactionsareirreversible,exothermicandtemperaturedependentvia theArrheniusexpression.Theprocesshasfivemajorunits;a reactor, aproductcondenser, avapor-liquid separator, a recyclecom-pressoranda productstripper;seeFigure3. Thereare41 measurementsand12 manipulatedvariables.For amoredetaileddescriptionseeDownsandVogel(1993)

Ricker (1995)consideredthesteady-stateoptimaloperationof theplant. In all cases,hefoundthatit is optimal to have maximumreactorpressure,minimumreactorlevel, maximumagitatorspeed,andminimum steamvalve opening. Furthermore,in mostcasesit is optimal to useminimum compressorrecycle valve opening.

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7.2 McAvoy and Yesolution

McAvoy andYe (1994)closeat stage1 innercascadeloopsinvolving eightflows andtwo temperature.Thisreducestheeffectof thedisturbancesassociatedwith theseloops.At stage3 they useasimplemassbalanceof theplant. This givessomeconstraintsfor stage2, for example,thateithertheC-feedor theproductflow mustbeleft for thethird stage.

At stage2 decentralizedloopsareclosed. They startwith the level loopssincethey arethe mostimportantloops.Therearethreelevel loops;reactor, separatorandstripper, andthey considerfour pos-sible level configurations.Threeof theconfigurationswereruledout basedon controllability analysis.Thealternative wheretheE-feedis usedfor reactorlevel controlis analyzedin greaterdetail.They lookat three ±C²6± , eighteen³C²I³ , andfifteen ´$²µ´ systems,wherethe controlledvariablesseemto be ratherrandomlychosen.After ananalysisinvolving RGA, Niederlinskiindex andlinearvalvesaturation,onlyfour alternativesareleft. Thesearefurther screenedon their steady-statebehavior for a rangeof dis-turbances.In additionto levels, productionrateand% G in product(which mustbe controlled),theyproposeto control reactortemperature,reactorpressure,recycle flow rate,compressorpower, concen-trationof B in purge,andconcentrationof E in productflow.

7.3 Lyman, Georgakisand Price’ssolution

Georgakis and coworkers have studiedthe problemin several papers(Lyman and Georgakis 1995),(Priceetal. 1994).They startby identifying theprimarypath,which is from theraw materials,throughthe reactor, condenser, the stripper, andto the productflow. They do not considerthe C-feedsinceitis in excessin the recycle. (Priceet al. 1994) list all candidatesfor through-putmanipulationsalongthe primary path: The feedstreams,flow of coolantto reactorcondenser, theseparatordrum bottomsflows andfinal productflow. Of the feedsonly D is considered.As notedby theauthorsonepossiblethrough-putmanipulatoris missing,theC-feedsinceit wasassumednotto beontheprimarypath.Next,they list the inventoriesthat needto be controlled;pressure,reactorlevel, separatorlevel andstripperlevel. Inventorycontrolsarechosenso to constructa self-consistentpath(which doesnot dependonquality controllers).At this point they have four differentstructures.In theendthey suggestto controlreactortemperature,reactorlevel, recycle flow rate,agitationrate,compositionof A, D andE in reactorfeed,compositionof B (inert) in purgeandcompositionof E in product.Eventhoughthey considertheoperationcostfor thecontrol structure,it cannever becomeeconomicallyoptimalsincevariablesthatshouldbekeptat their constraints(like therecycle valve) areusedin controlloops.

Their procedureis simpleandclearto follow. Theresultis a controlsystemthat is fairly simpletounderstand.

7.4 Ricker’s solution and relatedwork

Ricker andLee (1995)usenonlinearmodelpredictive control (NMPC), andcomparewith the multi-loop (decentralized)strategy of McAvoy andYe (1994)which they find performsadequatelyfor manyscenarios,but they suggestthatcompressorpower shouldnotbecontrolled.For thesesimplercasestheNMPC strategy improvesperformance,but thedifferencemaybetoosmallto justify theNMPCdesigneffort. Ontheotherhand,for themoredifficult cases,thedecentralizedapproachwouldrequiremultipleoverridesto handleall conditions,andnonlinearmodelpredictive controlmaybepreferred.

In anotherstudy, Ricker (1996)considersdecentralizedcontrol andconcludesthat thereis little,if any, advantageto the useof NMPC on this application. He focuseson the selectionof controlledvariables.First,hesuggeststo controlvariableswhichoptimally shouldbeat their constraints.Second,heexcludesvariablesfor which theeconomicoptimalvaluevariesa lot. This is in agreementwith thethe ideaof self-optimizingcontrol. He endsup controllingrecycle valve position(at minimum),steamvalve position(at minimum), reactorlevel (at minimum), reactortemperature,compositionof «qdq¶in reactorfeed,andcompositionof « in the reactorfeed. He notesthat it is importantto determine

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appropriate· setpointvaluesfor the latter threecontrolledvariables.In addition,overridesareinstalled.The productionratemanipulatoris chosenasthe input that mostlikely is going to saturate;namelyacombinationof D andE.

LarssonandSkogestad(2000) follow up the work of Ricker (1995,1996)on selectingcontrolledvariablesbasedon steady-stateeconomics.A degreeof freedomanalysisrevealsthat thereare8 de-greesof freedomat steady-state.In thenominalcase(mode1), 5 constraintsareactive at theoptimum(Ricker 1995),which leaves3 unconstraineddegreesof freedom.They systematicallygo throughmostof thealternative controlledvariables.They find thatgoodself-optimizingpropertiesareachievedwhencontrolling, in additionto theoptimally constrainedvariables,reactortemperature,recycle flowrate(orcompressorwork), andcompositionof A in purge(or in reactorfeed).They alsofind thatthesuggestionRicker (1996)of controllingreactortemperature,A in reactorfeed,andC in reactorfeed,is amongthebetterchoicesfrom a self-optimizingpoint of view. LarssonandSkogestad(2000)concludethat inert(B) compositionshouldnot becontrolled,which is againsttherecommendationsof mostotherauthorsexceptRicker (1996). For thecasethey study, with a givenproductionrate,they alsofind that reactantfeedrates,purgerateor reactorfeedrateshouldnotbeselectedascontrolledvariables.

7.5 Luyben and Tyreus’ solutions

Luybenet al. (1997) look at two casesfor control of through-put;with the productflow or with theA-feed. Herewe only considerthecasewheretheproductflow is thethrough-putmanipulator. In step3 they look at energy inventorycontrol,which in this caseis to controlthereactortemperaturewith thereactorcooling water. In step5 they assignthe strippersteamstreamto control strippertemperature,and thereforealso the productcompositions. Sincethe pressureof the reactormust be kept withinbounds,they usethe largestgasfeed (the feed of C) to control the reactorpressure. Step7 is thecheckof componentbalances,which givesa compositioncontrollerfor inert usingthepurge flow anda compositioncontroller for A usingthe A-feed. After doing somesimulationsthey adda controllerfor control of the condenser, usingthe reactortemperature.Their final schemesetsagitationrateandthe recycle valve at their constraints(which is optimal from an economicpoint of view), andcontrolsreactorpressure,reactorlevel, separatortemperature,strippertemperature,flow andtheratiobetweenEandD feed,compositionof « in purge,andcompositionof ¸ (inert) in purge.

Theresultingcontrolsystemissimple,but therecouldhavebeenabetterjustificationonwhatoutputsto control.

Tyreus(1999a) usesa thermodynamicapproachto solve theproblem.He (correctly)setstheagita-tion on full speedandclosesthesteamandrecycle valves. In addition,hecontrolsreactortemperature,reactorpressure,reactorlevel, A in reactorfeedandB in purgeflow.

7.6 Ng and Stephanopulos’s solution

Ng and Stephanopoulos(1998)start by stabilizing the reactor. Then they proceedto look at the in-put/outputlevel of theplant,wherethecentralpoint is to fulfill materialandenergy balances.At thislevel it shouldhave beenpossibleto saysomethingabouthow the feedsshouldbe adjustedin orderto achieve the right mix of G andH, but they do not. Rather, they look at which feedor exit flowsthat shouldbe usedto maintainmaterialbalancecontrol. At the final level they translatethe controlobjectivesto measurements.Herematerialbalancecontrol is translatedinto inventorycontrollers,likeproductflow to control stripperlevel andbottomflow to control separatorlevel. Thenext objective isthenreactorpressurewherepurgerateis assigned.Finally E feedrateis assignedto control theproductratio,andE is assignedto through-putcontrol.TheA andC feedratesareusedfor controllingcomposi-tion of A andC. In summary, theproposeto controlreactortemperature,reactorlevel, reactorpressure,G in productflow, strippertemperature,C in reactorfeed,A in reactorfeedandB (inert) in purgeflow.

Themethodis somewhatdifficult to follow andthey seemto repeatmany of theargumentsin eachphase.

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7.7 Other work

Theabove review is not complete,andtherearemany authorswho have worked on this problem,e.g.(BanerjeeandArkun 1995),(Wu andYu 1997),(ScaliandCortonesi1995).

7.8 Other testproblems

Thereareseveral other suitabletestproblemfor studyingissuesrelatedto plantwidecontrol. TheseincludetheHDA-plant (Douglas1988),thevinyl acetatemonomerprocess(LuybenandTyreus1998),therecycle plant(Wu andYu 1996)andtheLuybenandLuybenplant(LuybenandLuyben1995).

8 A newplantwide control designprocedure

Basedontheabovereview andasaconclusionto thispaper, weproposeaplantwidedesignprocedureassummarizedin Table1. Theproceduremainly follows themathematicallyorientedapproach,but withsomeelementsfrom theprocessorientedapproach.

We proposeto first performa top-down analysisto selectcontrolledvariables,basedon the ideasof self-optimizingcontrol (step1). For this we needa steadystatemodelandoperationalobjectives(steadystateeconomics).Theresult is oneor more alternative setsfor (primary) controlledvariables( �I!=&¹��5 . The optimal productionratemanipulatorwill usuallyfollow from this analysis,but a moredetailedanalysisof this choiceis recommended(step2). Notethattheselectionof controlledvariablesis alsoimportantalsowhenusingmultivariablecontrol(e.g.MPC) in thelowercontrol layers.

The top-down analysisis followed by a bottom-upassignmentandpossiblydesignof the controlloops. This is donein a sequentialmannerand resultsin a hierarchicalcontrol systemas shown inFigure1. Eachcontrollershouldbeof limited size(usuallywith asfew inputsandoutputsaspossible),andwith emphasisonavoiding “long” loops,thatis, oneshouldpair inputsandoutputswith are“close”to another. Notethatno degreesof freedomarelost aswe closeloops,astheir setpointsaredegreesoffreedomfor thehigherlayers.

Thebottom-updesignstartstheregulatorycontrol layer(step3) wherethemainobjective is faculi-tatemanualoperationwhenthemoreadvancedcontrol layersarenot in use. We proposeto startwithstabilization(step3a)(liquid level control,slowly drifting modes,etc.)whereit is importantto avoid in-putsaturation.Next weconsiderthefastloopsneededfor localdisturbancerejection(step3b). Herewemaymake useof (extra) secondarymeasurements( �$# ). This is the“regulatory” control layer(system).Theobjective for theregulatorylayer is thatmanualoperationof theplant is possibleafter theseloopsareclosed.

We now have asdegreesof freedomthesetpointsof the regulatorylayer ( .# ) plusany unusedma-nipulators( ! ), theseshouldbeusedto controltheprimaryoutputs( � ! &-� ) (step4). This controllayeris herecalledthesupervisorycontrollayer, but othernamesarein use,suchasadvancedcontrolandco-ordinatingcontrol. Therearetwo mainapproacheshere:Useof singleloop (decentralized)controllerswith possiblefeed-forward links (step4a), or useof multivariablecontrol (step4b), e.g. decouplingor modelpredictive control (MPC). Multivariablecontrolwith constrainthandlingmayavoid theneedfor logic to reconfigureloops,andproperlydesignedmultivariablecontrollersgive betterperformance.Theseadvantagesmustbe tradedagainstthecostof obtainingandmaintainingthemodelsusedin themultivariablecontroller.

Themainresultof this will bethecontrolstructure,but control tuningsmayalsobeobtained.Iter-ationmaybeneeded,for exampleonemayneedto go backanconsideralternative controlledvariables(step1) or anotherthroughputmanipulator(step2), if the resultingcontrol problemin step4 is toodifficult. Finally, nonlineardynamicsimulationsshouldbeperformedto validatetheproposedcontrolstructure(step6).

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9 Conclusion

In this paperwe have given a review on plantwidecontrol with emphasison the following tasksthatmake up thecontrolstructuredesignproblem:

1. Selectionof controlled variables( � with setpoints� � ).2. Selectionof manipulatedvariables( � ).3. Selectionof measurements( � )4. Selectionof control configuration

5. Selectionof controller type

For the selectionof controlledvariableswe have seenthat the considerationof steady-stateeco-nomicsis very useful. It appearsthat thesolutionto this taskprovidesthemuchneededlink betweensteady-stateoptimizationandprocesscontrol, andthat the ideaof “self-optimizing control” to reducetheeffect of disturbancesanduncertaintyprovidesa very usefulframework for makingthe right deci-sion.Wethusproposethatthedesignof thecontrolsystemshouldstartwith theoptimization(or at leastidentifying what the control objectivesreally are)andthusproviding candidatesetsfor the controlledvariables.The control problemis thendefined,andonemay proceedto analyze(e.g. usingan input-outputcontrollabilityanalysis,whetherthecontrolobjectivescanbemet).Theactualbottom-updesignof thecontrolsystemis doneafter thecontrolproblemhasbeendefined,includingtheclassificationofall variables(into inputs,disturbances,controlledvariables,etc.).

Mostof theproposedprocessorientedprocedureshaveelementsfrom thiswayof thinking,althoughsomeproceduresfocusmostlyon controlandoperationandseemto skip lightly over thephasewheretheoverall controlproblemis defined.

Several casestudieshave beenproposedandmany have worked on these. However, someof theworksto providelimited generalinsight,andtheirvaluemaythereforebequestioned.A moresystematicapproachandacommongroundof comparisonis suggestedfor futurework.

In summary, the field of plantwidecontrol is still at a relatively early stageof its development.However, theprogressover thelastfew years,bothin termsof casestudiesandtheoreticalwork, showspromisefor the future. Thereis still a needfor a clearerdefinition of the issues,andit is hopedthatthis papermay be useful in this respect.In the longerterm, whereautomaticgenerationandanalysisof alternative structuresmay becomemore routine, the main problemwill probablybe to be able togeneratemodelsin anefficient way, andto provide efficient meansfor their analysis(e.g. usinginput-outputcontrollabilityanalysis).

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