MIT Symposium 2040 Visions of Process Systems Engineering

George’s Impact

Manfred Morari Electrical & Systems Engineering University of Pennsylvania

June 1, 2017 George’s Formative Years

1965 1974 1977 MIT Symposium 2040 Visions of Process Systems Engineering

George’s Impact

Manfred Morari Electrical & Systems Engineering University of Pennsylvania

June 1, 2017 Outline • My Time with George at U of MN • Past Attempts to Predict the Future • Predicting the Future Outline • My Time with George at U of MN • Past Attempts to Predict the Future • Predicting the Future My advisors at the U of Minnesota 1975-77

George Stephanopoulos

Rutherford “Gus” Aris 1929-2005 Accompanying Note ~ 1995 Technology: Digital Control Computer IBM 1800 (introduced 1964)

[wikipedia] Computer Control ~1968 Standard Oil of California

Courtesy: Chevron Advanced Process Control Textbooks with Origins at U of Minnesota

1969 1981 Critique of (Process) Control JOURNAL CRITIQUE Critique of Chemical Process Control Theory 1973 JOURNAL CRITIQUE A. S. FOSS Critique of Chemical Process Control Theory Department of Chemical Engineering University of California, Berkeley, California 94720

A. S. FOSS 84 When it is stated, as it has been inDepartment more than of Chemicalone instance, EngineeringIEEE TRANSACTIONSare complex enough ON to AUTOMATIC tax one’s ability CONTROL, to un- VOL. AC-20, NO. 1, FEBRUARY 1975 1976 recent publication, that thereUniversity is a wide of California, gap between Berkeley, the Californiatangle 94720 the relationships even at steady conditions (Shah theory of process control and its application, one is left and Stillman, 1970). ‘The inert level in the synthesis loop with the unmistakable impression that those who conceive may be regulated by manipulation of the purge rate, but When it is stated, as it has been in morethe than theory one are in some sense leagues ahead of those who since the purge constitutes a large fraction ok the reformer would use it. Thatinstance, the contraryare complex is the enough case is to the tax thesis one’s ability to un- recent publication, that there is a wide gap between the tangle the relationships even at steady conditionsfuel flow,(Shah one finds that such an adjustment influences Perspectivesof this essay. Indeed, the theory of chemical process the temperature and methane content of the reformer theory of process control and its application, one is left and Stillman, 1970). ‘The inert level in the synthesis loop control has some rugged terrain to traverse before it process effluent stream. Steam production in the waste with the unmistakable impression that those who conceive may be regulated by manipulation of the purge rate, but meets the needs of those who would apply it. heat boilers is thus upset and so too are the compressors the theory are in some sense leagues ahead of those who since the purge constitutes a large fraction ok the reformer would use it. That the contrary is the case is the thesis fuel flow, one finds that such anDesign adjustmentdriven Conceptsinfluences by that steam. for The compressorsProcess are also Control upset by the change in recycle rate in the synthesis loop. The of1976 this essay. Indeed, the theory of chemicalPROBLEMS process OF CHEMICALthe temperature PROCESS and CONTROL methane content of the reformer control has some rugged terrain to traverse before it process effluent stream. Steam production in resultantthe waste flow changes influence temperature rises in the 84 The needsIEEE TRANSACTIONS are intimately ON AUTOMATIC related CONTROL, to the VOL. problems, AC-20, NO. and1, FEBRUARY synthesis 1975 reactor, leading perhaps to higher temperatures meets the needs of those who would apply it. heat boilers is thus upset and so too are the compressorsA. Kestenbaum,’ R. Shinnar,*l and F. E. Thau2 Design Conceptsthe problems,for asProcessdriven usual, bywear that a steam. sometimes TheControl effective compressors camou- are also at upsetwhich by the side reactions that produce ether and flage. Superficiallythe thechange pioblem in recycleof chemical rate inprocesy the synthesiscon- methaneloop. The contribute significantly to the total heat libera- PROBLEMS OF CHEMICAL PROCESS CONTROL trol appears to involve the regulation of complex, often tion andDepadments to reduction of Chemical in methanol Engineering production. and Electrical Further, Engineering, The City College of The City University of New York, Perspectives resultant flow changes influence temperature rises inNew the York. New York 10031 The needs are intimately related to the problems,poorly understoodand synthesis physicochemical reactor, leading processes perhaps in theto higherface temperaturesthe upsets in the reformer lead to concentration distur- the problems, as usual, wear a sometimes effectiveSuperiorityof many camou- unknown at whichand uncharacterized the side reactions disturbances. ofthat produce TheTransfer bances ether andin the synthesis loop makeupFunction gas, which also Over flage. Superficially the pioblemA. Kestenbaum,’of chemical procesyword regulationcon- R. Shinnar,*lmethane has several contribute interpretations and significantly F. E. when Thau2 to appliedthe total heatdisturbs libera- the methanol production rate. trol appears to involve the regulation of complex,to industrial often processes,tion and butto reductionit usually in implies methanol the desireproduction. NowFurther, add to these static interactions the influence of a 1975 to hold constant certain states or perhaps a time-average 20-minute thermal lag in the reformer, the composition poorly understood physicochemical processes in the face the upsets in the reformer lead to concentration Six distur- criteria are offered for the evaluation of the performance of process controllers. Classical techniques for of the states. Disturbances may consist of slow drifts such and thermal lags in the carbon dioxide absorber-stripper of many unknownSuperiority andState-Variable uncharacterizedDepadments disturbances. of of ChemicalTransfer The Engineeringbances in Functionthe and synthesis ElectricalMethods loop Engineering, makeupOver gas, which Thethe City also design inCollege of PID ofLinear controllersThe City University and modern ofTime-Invariant control New York,theoretic techniques for controller design are reviewed. It is word regulation has several interpretations whenas thoseapplied originating disturbs in thediurnal methanol temperature production changes, rate. of system, the treacherous feed-effluent heat exchange in a New York. Newmonadnocks York 10031 illustrated by the explosive vaporization of synthesisshown reactor that modernthat can optimal exhibit wrong-waycontrol algorithms (nonmini- often do not lead to useful controller designs. They are useful to industrial processes, but it usually implies the desire Now add to these static interactions the influenceonly of asa tools in heuristic design methods. Their main problem is sensitivity to the nature of the process transfer to State-Variablehold constant certain states or perhaps Methods a time-averagea slug of water in 20-minutein theLinear feed thermalto a crude Time-Invariant lag still, in theor ofreformer, persistent the compositionmum phase) temperature effects, and the long-lived com- of the states. Disturbances may consist of slow randomdrifts such upsets suchand thermalas the step-like lags in fluctuationthe carbon in dioxide pressure absorber-stripper positionfunction transient and inthe the lack synthesis of conservative loop. Even design were methods.the The problems faced in developing better algorithms are Feedback Systemoutlined. Design as those originating in diurnalFeedback temperature changes,in utility System of headers. system, Sometimes the Design treacherous disturbances feed-effluent result from heat a exchangeprocess in well a understood, the dynamic cause-effect rela- monadnocks illustrated by the explosive vaporizationpurposeful of changesynthesis in the reactorlevel of thatoperation, can exhibit but with wrong-way the tionships(nonmini- would be difficult to untangle. a slug of water in the feed to a crude still, or ofexception persistent of batchmum operations,phase) temperature these changes effects, are and infre- the long-livedBut com-such processes are not completely understood. The ISAAC M. HOROWITZ, FELLOW, IEEE, AND URI SHAKED random upsets such as the step-like fluctuation quent.in pressure In additionposition toISAAC transientthe continuous in M.the regulationsynthesisHOROWITZ, loop.tasks, Even coke were FELLOW, level the on the IEEE, reformer AND catalyst URI is likely SHAKED unknown, in utility headers. SometimesSix disturbances criteria result arethere from offeredare a the tasksprocess for of start-upthewell understood,evaluation and shut-down. the dynamicof In1. theIntroductionall ofcause-effect performancedifferent rela- from furnace of process to furnace, andcontrollers. drifting; the firing Classical It is trivial techniques in the sense thatfor classical frequency response these activities, there is the dominating necessity for safe distribution of the burners in the reformer changes in an methods lead to satisfactory designs. Interestingly enough, purposefulAbstm-The change objectives in the and level achievements of operation, of state-variable but with methods the in tionships would be difficult to untangle.In recent years there has been a growing literature on the the design ofoperation PID controllersin thehis eventwork ofon andmalfunction controllability modern or failiueand control observability. of any theoreticundefinedState way techniques with fuel flow for changes; controller and the carbondesign are reviewed. It is exceptionlinear time-invariant of batch feedback operations, system synthesis these are changes examined. are It is infre-argued But such processes are not completely understood. The a considerable part of our optimal control literature deals part of the processvariables or control are the system. natural formulationapplications for these problems.dioxide of optimal separation control efficiency techniques is a poorly in theunderstood process func- quent.that the In philosophy addition and objectivesto the shown associatedcontinuous with that eigenvalne regulation modern realization tasks, by optimalcoke level control on the reformer algorithms catalyst isoften likely unknown,do not lead to useful controller designs.with examples They ofare this usefultype (Lim, 1970; Lueck, 1968; Cegla, But there isHowever, much beneath since thenthe surface.there has One been findsindustries an enormousthat (Bryson,tion litera- of changing 1967; Cegla, flows 1969;and Denn,absorbent 1972; concentrations. Doug- therestate arefeedba&, the withtasks or withoutof start-upAbstm-The observers,only and areas highlyshut-down. tools naiveobjectives and inIn incomplete heuristicall of and different achievements design from furnacemethods. of state-variable to furnace, Their and drifting;main methods problemthe infiring is sensitivity to the nature of1969; the Koppel, process 1968; transfer Kalman, 1960). thesein the activities, practical -ontext there of iscontrol the dominatingsystems. Furthermore, necessity eventhe the forprocesses objec-safe ture possessdistribution on linear dynamic oftime-invariant the components burners feedback in andthe lass, reformer thatsystem 1972;in design changes Gould,Uncertainties using in 1969;an his inLim, other work1970; processes Lapidus, on are, controllability1967;for example, Lueck, the and observability.State operationtives undertaken in the have eventnot reallylinear of malfunctionfunction time-invariantbeen attained or andby failiuethe the state-variablethefeedback designof lackany of systemthecontrolofundefined state-variable conservative systems synthesis way attentionformalism. with arefuel must design examined. Thisflow be paperchanges; 1968).given methods. reviews It to However,and is the arguedcourse the topics carbonThe it and is generally rateproblems of the felt solid that facedreactions these in methods cementdeveloping havekilns, the betterWe started algorithms our own research are with the same type of prob- parttedmiques of the which process have beenor control developed. system. The extremely importantthis factorscharacteristic. of whichdioxide Inhave one separationreceived view the efficiencydynamica great deal characteristicsis a ofpoorly attention understood byreactions state- func- and variables their dependence are on thethe hydrodynamics natural informulation lem for the reason for that these a well problems. understood example is the sensor noise and loop that theare philosophy obscured by andstate-variable objectives associated with eigenvalnenot realizationmade the expected by impact on the industrial practice of But there is much bandwidths beneathoutlined. the surface. Onethe are finds seen that to affectspacetion methods:adverselyof changing eigenvaluethe flowscontrollability realizationand absorbent byof thestate concentrations. feedback,multiphase hydrocracking reactors, and the dependence best test for any algorithm. If the algorithm fails to produce formnlalion andhave been ignoredin the state-variable literature.process Theowing to lagging of process states to correctiveprocess control,of conversion a problem However, on whichthe flow was regime since the subject in fluidthen ofbed panel reactors.there has been an enormous litera- thebasic processes fundamental possess problemstate dynamicof feedba&, componentsin the facewith of significantand or thatwithout plant in observers observers,Uncertainties for states arein otherhighlywhich mayprocesses naive not are,andbe sensed, forincomplete example, and de- the reasonable process performance we can thoroughly analyze sensitivity commands. In another view the dynamic characteristicsdiscussions Andat severalit is well recent recognized AIChE that meetings no amount (National of detailed thep%rameter design uncertaintyof control has systems hardlyreceived attentionany mustattention. be Instead,given theto couplingcourse and theory rate (Sectionof the solid II), reactionssensitivity in theory cement (Section kilns, the the example system and hopefully understand why. in the practical -ontextare welcomed of control as fortunate systems. endowments Furthermore, that lend even Science a degree the Foundation studyobjec- will Workshop, everture replace on 1973; all linear uncertainties Foss, 1973). time-invariant with certainties. feedback system design using thisliteratme characteristic. bas concentrated In one primarily view onthe differential dynamic sensitivity characteristics functions III),reactions and controllabilityand their dependence and observability on the hydrodynamics(Section V). in We are fully aware that the interesting problems are far areand seen even thoseto affectresults areadverselytives so highly undertaken obscuredthe controllability in the state-variable haveof stabilitynot of forma-really the to Whileprocessesmultiphase thesebeen andproblems hydrocracking attainedthat sometimesare by reactors,very canthe interesting beOftenandstate-variable ex- the from the dependenceRather, hypothesisthe it is forthe is theraised state-variable control that system the lackdesigner of formalism. applica-to recognize This paper reviews the topics processtion as toowing lead to toincorrect lagging conclusions. of process states toploited corrective for usefulmathematicalof conversionpurposes. viewpoint, And on the because it flowis regimearguedthe dynamicstions in here fluid is that due bed somethe to reactors. thesignificant of lack of uncertainties sophistication and ofto theconceive practitioner controls that more complex and that optimal control has been applied to 1.In Introductioncontrast, the importanttedmiques practical considerations which and have constraints been have developed. The extremely important factorsIt functionis trivial of effectively in nonetheless.the sense that classical frequency response commands. In another view the dynamic characteristicsof a process arethemAnd directly areit notis influenced wellsignificant recognized by from its design, thethat feedback andno the amountcon-might control beof engine- thedetailed result which of the normalhave receivedtime lag between thea greatmultiple-input, deal of multiple-outputattention byproblems. state- We will show, arekn welcomedclearly revealed as fortunate and considered endowments in the -fer thatfunction lendtrol formulation. a systemdegree designerstudy finds will thatever his replace sphere all of uncertaintiesresponsibility with certainties.While it is the presence of coupling among many however, that our approach and conclusions also apply to Differentid sensitivity resultssensor are simplenoiseand andtransparent. loop For bandwidthssingle ering viewpoint. are obscured In others, theby state-variabletheconception state-variablemethods formalism of modern lead control to system satisfactory design techniques designs. in Interestingly enough, of stabilityIn recent to processes years and thatthere sometimes has been canencompasses be ex-a growing processRather, design itliterature is foras the well. control Indeed, on system them aorj designer con- tovariables recognize that space is primarily methods: responsible foreigenvalue the near in- those realization cases. by state feedback, input-utput systems, thereformnlalion exists an exact design and techniquehave tributions for achievingbeen to ignored effectivegreatlyobscures in control thethe problem, systemstate-variable whereas performancemuch the more literature. oftenacademic a considerablescrutable communityThe complexity and part oftheir dynamic industrialof ourprocesses, application.optimal the nature control of literature deals ploitedquantitative for sensitivityuseful purposes.speeircations And in the becauseface of signircant the dynamics parameter the significant uncertainties and to conceive controls that of applicationsa process are directly of influenced optimal by its design,controlderive the con- fromtechniques perceptivetransparentfunction effectivelyand resultsin clever the arenonetheless. obtained modifications process bySome oftransfer the are function lessthe generouscoupling observers andas well claim often that playsfor the aproblems statessignificant dealt which role. By may An important not featurebe sensed, of a good controland de-system design al- uncertainty, which is optimumbasicin fundamentalan important practical problem sense. This of methods.sensitivity A review in isthe given face (Section of IV)significant of transferwith plant func- examples of this type (Lim, 1970;gorithm Lueck, is that 1968; it provides Cegla, the practicing engineer with a trolindustriesproblem system is mu&designer more difficult(Bryson,finds andthat bashis not sphere1967; been completelyof responsibilityCegla,process solved itself. for1969; While Denn, it is the1972; presence Doug- of withcoupling in the among academicnature many and world by design are toothe farcoupling removed among from most reality variables But perceptiontion methodsis difficult for to satisfying acquire systemin this response field be- specifications in chemical processescoupling is nonlinear: theory temperature-reaction (Section II), sensitivity theory (Section encompassesmultivariablesystems, processbut it p%rameter designhas atas least well. beenuncertainty Indeed, realistidy m aorattackedj has con- by hardlyvariablesreceived thatany is primarilyattention. responsibleto lead Instead, for to1969; theuseful nearthe Koppel, results. in- One 1968; of the authors Kalman, (R.S.) 1960). has been framework within which to cast his problem and provides a tributionslass,some transfer 1972;to functioneffective methods.Gould, control system 1969; performance Lim,cause 1970; oftenthe dynamic overLapidus,scrutable abehavior range complexity of ofplant1967; chemical parameterof dynamicLueck, processes uncertainty. processes, is not Thistherate, natureis thefeed of enthalpy-vapor/liquid split, temperature- systematic design procedure which can be applied to a larg- Finally, the conceptsliteratme of controllability bas and concentratedobservability much primarily on differential sensitivityinvolved functions in industry forIII), many yearsand and controllability has often tried to and observability(Section derive from perceptive and clever modificationssimple. soof Therethe arecentralthe many coupling basic variables problem as wellwhose in feedback often dynamic plays system behavior a significant design toWeequilibrium which role. started By conversion, our ownboilup research rate-overhead withconcentra- the er numbersame typeof similar of prob-problems. If, however,V). an algorithm 1968).emphasized in However,the state-variable literature it is are generally examined. It isis arguedof feltconsequence. that thatstate-variable theseThe behavior methodsmethods ofhave anymade onehaveessentially variableapply someis no tion, ofsignifi- these and optimalon and controlon. Such techniques effects often with needrather direct process itself. and even those results are so highlynature obscuredand by design in thethe coupling state-variable among most forma- variables gives unsatisfactory results, we have to understand why, theirBut importanceperception in thisis problemdifficult class to has acquire been greatly in thisexaggerated.influenced field be- On by manycantin chemicalcontributions. others through processes the isinnumerable nonlinear:limited physi- temperature-reaction lemsuccessattention; for and the reluctantly indeed,While reason the has stabilitythese comethat problemsofto a theexothermic well conclusion understood chemical are very example interesting is thefrom the notthe one madehand, transfer the functiontion expected asmethods to canlead be nsedimpactto toincorrect checkcal and foron their chemical conclusions.the rate, industrial interactions feed enthalpy-vapor/liquid found practice in these ofprocesses. split, temperature-reactors may be assured only through consideration of and put proper safeguards into the design algorithm. causeexistence. the Ondynamic the other behavior hand, nothing of is chemicallost when they processes are ignored, is if notthe The following fairly standard state-variablethat in the system present de- state of the art it is quite difficult to simple. There are many variables whose dynamicThe behavior interactions equilibrium in a modern conversion, methanol boilup process, rate-overhead for best theconcentra- testnonlinear for mathematicaldependence any algorithm. of the chemical viewpoint, If the reaction algorithm rateit is Hence, argued infails section to 2produce here below wethat state some our interpretation of of the processsynthesis problem control, is lreated asIn one contrast, awitfi problem parameter the uncertainty important which by transfer was practicalscription the is considerations subjectused. with the of bracketed panel and apply constraintssubscripts optimal giving have control the theory to an industrial problem. It is is functionof consequence. methods. The behavior of any one variable is numbertion, andof rowson and columnson. Such of effectsthe matrix. oftenreasonable The need system direct themprocess are performance not significant we fromcanprincipal thoroughly the desirablefeedback analyzecharacteristics control thatengine- should be achieved influenced by many otherskn throughclearly the revealed innumerable and physi- considered attention; in indeed,the -fer the stabilityfunction notof exothermic that formulation. the techniques chemical are not useful. In fact, they often discussions at several recentAlChE AIChE Journalstates (Vol. meetings are 19,denoted No. by2) x, (National the plant input control vector by March, 1973 Page 209 by a process controller. In section 3 we describe and com- cal and chemical interactionsI. INTRODUCTION found in these processes. reactors may be assured only throughcontribute considerationthe significantly example of to system our understanding and hopefully of the prob- understand why. Differentid resultsu. simpleand transparent. For single ering viewpoint. In others,pare the various state-variable design methods for formalism the classic PID controller TheScience interactions Foundation in a modern methanolWorkshop,sensitivity process, 1973;for the Foss,areand nonlinear the system1973). dependence output by y, of with the lem.the chemical relations It is reactionrather thatrate they are often not in a state where TAT€-VARIABLEinput-utput formalism was systems, introduced therein feed- exists an exact design techniquetheir for application achievingWe areis straightforward fullygreatly awareobscures enough that theto the allowproblem, interesting their whereas in terms problemsmuch of theirmore achieving are far these goals. In section 4 we de- backOften control the theory hypothesis primarily in the study is raisedof nonlinear that the lack of applica- scribe some approaches to the design of process controllers AlChES Journal (Vol. 19, No. 2) = A (nn)XMarch, + B(nm)u(ml)use 1973 in a reasonablePage(14 209 amount of time without extensive study system stability byLyapunov’s quantitativemethod sensitivity andin optimalspeeircations in the face of signircant parametermore complex and that optimal control has been applied to tions is due to the lack of sophistication of the practitionerand research, and wheretransparent straightforward applicationresults mightareobtained using frequency-domain by transfer andfunction time-domain optimization control theory. Kalmanuncertainty, used state-variable which formalism is optimum for in an importantY(pl)= C(pn)X practical multiple-input,This(1b) multiple-output problems.procedures. We Section will 5 show,contains an evaluation of three com- and might be the result of the normal time lag between theeven leadsense. to serious troubles.methods. A review is given (Section IV) of transfer func- mu& bas peting process controller designs for a simplified problem. Manuscript received Septemberproblem 18, 1973;is revised Julymore 26, 1974. difficult Paper and not been completelyWe solvedthereforehowever, forneed thatto rethink our our approach approach to theand prob- conclusions also apply to conceptionrecommended by S. J. Kahne,of modern Chairman of the control IEEE S-CS Urban system and giving design the “plant” techniques matrix of transfer in lem,functions and this paper is intendedtion methods to be a first startfor insatisfying this di- Our system conclusions response are summarized specifications in section 6. Social Systems Committee.multivariable This work was supportedsystems, in but part it by the has at least been realistidy attackedthose bycases. theNational academic Science Foundation community under Grant GK-33485 and A-1 at thetheir Un- industrial application.rection. We will try to present a critical review of the appli- iversity of Colorado, andsome in part bytransfer the European function Office of Aerospace methods. Y(pI)= P(pm)U(ml) over a range of plant parameter2. Design Criteriauncertainty. for Process This Control is the Research (AFSC) under Grant AFOSR 73-2549 at the Weizmann Insti- cation of modernAn important control theory feature techniques of to aprocess good con- control system design al- Sometute. are lessFinally, generous the andconcepts claim of thatcontrollability the problems and observability dealt much central basic problem in feedbackBefore discussing system in designdetail the toadvantages which or disadvan- I. M. Horowitz is with theDepartment of Applied Mathematics, P(s)= C(sI-A)-’B trol, and,gorithmso although is thethat paper it providescontains considerable the practicing engineer with a withWeizmann in Institute the of Science,academicemphasized Rehovot, Israel, worldin andthe the state-variable areDepartment too of far removedliterature are from examined. reality amountsIt is argued of heretofore that unpublished work of our own, it is tages of specific controllers, let us restate the aims and Electrical Engineering, University of Colorado, Boulder, Colo. 80302. state-variable methodshave goalsmade of essentially process control and theno specifications signifi- that such a U. Shaked was with the Department of Applied Mathematics, Weiz- = CAdj(s1-A)B/det(sl-A) notN(s)/d(s) a regularframework research (2b) paper, within but rather which a special to cast type ofhis re- problem and provides a tomann lead Institute ofto Science, usefultheir Rehovot, importanceresults. Israel. He is now One within thethis of Engineer- problemthe authors class has(R.S.) been has greatly been exaggerated. On controller must fulfill. We will list them first without any ing Department Control Group, Cambridge University, Cambridge, En- view. systematic cantdesign contributions. procedure which can be applied to a larg- involvedgland. in theindustry one hand, for transfer many functionyears whereand methods Y, hasU, R denote oftencan thebe triedrespectivensed to to vectors check We doof transforms.fornot intendtheir to cover the whole spectrum of process intention of ranking them. Again, we are referring here to a existence. On the other hand, nothing is lost when they arecontrol, ignored, erbut number ifwe thechoose toof The concentratesimilar following onproblems. a rather fairly simple If, standard however,simple continuous state-variable an algorithm feedback controller, system as de- discussed in the apply some of these optimal control techniques with rather optimal control literature (Horowitz, 1963; Hougen, 1964; synthesis problem lreated one witfi parameter uncertaintyand almost bygives transfer trivial unsatisfactory problem: the design results,of analog controllers we have to understand why, limited success and reluctantlyis hasas come to the conclusionfor single-input single-outputscription systems, is and used. specially with over- the Ziegler,bracketed 1942; Cohen, subscripts 1952), which giving may bethe part of a more and put proper safeguards into thecomplex design system algorithm. but which can be designed separately. that in the functionpresent methods. state of the art it is quite difficult todamped systems. An examplenumber of such of a system rows is andthe trans- columns of the matrix. The system fer functionHence, in section 2 below we state our interpretationIt is important to rememberof the that in process control we apply optimal control theory to an industrial problem. It is states are denoted by x, theseldom plant totally input rely on control such controllers, vector and by that they nor- I. INTRODUCTION principal desirable characteristics thatmally should are part be of aachieved more complex scheme which is managed not that the techniques are not useful. In fact, they often u. and the system output(1.1) by y, with the relations by a process controller. In section 3 weby describean operator who and achieves com- the desired control of the total contribute significantlyTAT€-VARIABLE to our understanding formalism wasof the introduced prob- in feed- process by adjusting the set-points of individual control- lem. It is rather that they are often not in a state where pare various design methods for the classiclers. Interestingly, PID controller contrary to quality control in mass pro- Sback control theory primarily in the study of Departmentnonlinearin terms of Chemical of their Engineering. achieving these goals.duction In section by machine 4 wetools, de- there has been little systematic their application is straightforward enough to allow their Department of Electrical Engineering. = A research(nn)X + on B(nm)u(ml) the way an operator should(14 or does control a use in a reasonablesystem amountstability of by timeLyapunov’s withoutmethod extensive studyandin optimalscribe some approaches to the design of process controllers 2 Ind. Eng.using Chem., frequency-domainProcess Des. Dev., Vol. 15,No. 1,and 1976 time-domain optimization and research,control and where theory. straightforward Kalman used application state-variable might formalism for Y(pl)= C(pn)X (1b) even lead to serious troubles. procedures. Section 5 contains an evaluation of three com- We thereforeManuscript need to received rethink September our approach 18, 1973; to revised the prob- July 26, 1974.peting Paper process controller designs for a simplified problem. recommended by S. J. Kahne, Chairman of the IEEE S-CS UrbanOur andconclusions giving are the summarized “plant” matrix in section of transfer 6. functions lem, and thisSocial paper Systems is intended Committee. to be This a first work start was insupported this di- in part by the rection. We Nationalwill try toScience present Foundation a critical under review Grant of GK-33485the appli- A-1 at the Un- iversity of Colorado, and in part by the European Office of Aerospace2. Design CriteriaY(pI)= for P(pm)U(ml) Process Control cation of modernResearch control (AFSC) theory under Granttechniques AFOSR to 73-2549 process at thecon- Weizmann Insti- trol, and, tute.although the paper contains considerable Before discussing in detail the advantages or disadvan- amounts of heretoforeI. M. Horowitz unpublished is with the workDepartment of our ofown, Applied it is Mathematics,tages of specificP(s)= controllers, C(sI-A)-’B let us restate the aims and Weizmann Institute of Science, Rehovot, Israel, and the Department of not a regular research paper, but rather a special type of re- goals of process control and the specifications that such a Electrical Engineering, University of Colorado, Boulder, Colo. 80302.controller must fulfill. We will list them first without any view. U. Shaked was with the Department of Applied Mathematics, Weiz- = CAdj(s1-A)B/det(sl-A) N(s)/d(s) (2b) We do notmann intend Institute to cover of Science, the whole Rehovot, spectrum Israel. He of is processnow with the Engineer-intention of ranking them. Again, we are referring here to a ing Department Control Group, Cambridge University, Cambridge,simple En- continuous feedback controller, as discussed in the control, butgland. we choose to concentrate on a rather simple where Y,U, R denote the respective vectors of transforms. and almost trivial problem: the design of analog controllers optimal control literature (Horowitz, 1963; Hougen, 1964; for single-input single-output systems, and specially over- Ziegler, 1942; Cohen, 1952), which may be part of a more damped systems. An example of such a system is the trans- complex system but which can be designed separately. fer function It is important to remember that in process control we seldom totally rely on such controllers, and that they nor- mally are part of a more complex scheme which is managed (1.1) by an operator who achieves the desired control of the total process by adjusting the set-points of individual control- lers. Interestingly, contrary to quality control in mass pro- Department of Chemical Engineering. duction by machine tools, there has been little systematic Department of Electrical Engineering. research on the way an operator should or does control a

2 Ind. Eng. Chem., Process Des. Dev., Vol. 15,No. 1, 1976 Theory-Practice Gap

Main theme of CPC I in 1976

Explosive development of theory had taken place

• Industry did not understand theory • Academia had no clue about real controller design

Exceptions: Åström, Gilles, Balchen,… George’s Research Theme in the 1970s

“The research community is studying the wrong problems” Importance of Timing and a Good Start

If you are to do important work then you must work on the right problem at the right time and in the right way. Without any one of the three, you may do good work but you will almost certainly miss real greatness. An important aspect of any problem is that you have a good attack, a good starting place, some reasonable idea of how to begin.

A Stroke of Genius: Striving for Greatness in All You Do R. W. Hamming October 1993 Socratic Method: Learning by Debate

Success is a journey, not a destination. The doing is often more important than the outcome.

Arthur Ashe Major Themes of George’s Research Program in the 1970s

“The research community is studying the wrong problem”

• Architectures – Control Structure – Decomposition for optimization • Design for Control Solubilization and Microemukions, Vol. 2, Plenum, New Schulman, J. H., W. Stroeckenius, and L. M. Prince, “Mech- York ( 1976). anism of Formation and Structure of Microemulsions by Ruckenstein, E. and J. C. Chi, “Stability of Microemulsions,” Electron Microscopy,” J. Phys. Chem., 63, 1677 (1959). J. Chem. SOC. Faraduy Trans. II, 71, I690 (1975). Schulman, J. H. and J . B. Montagne, “Formation of Microemul- Ruckenstein, E., “Stability Phase Equilibria, and Interfacial sions by Amino Alkyl Alcohols,” Ann. New York Acad. Sci., Free Energy in Microemulaions,” pp. 755ff in K. L. Mittal 92,366 ( 1961). ( ed. ), Micellization, Solubilization and Microemulsions, Vol. Scriven, L. E., “Equilibrium Bicontinuous Structures,” Nature, 2, Plenum, New York ( 1976). 263,123 (1976). Ruckenstein, E., “The Origin of Thermodynamic Stability of Talmon, Y. and S. Prager, “Statistical Mechanics of Micro- Microemulsions,” Chem. Phys. Letters, 57, 517 (1978). emulsions,” Nature, 267, 333 ( 1977). Ruckenstein, E., “On the Thermodynamic Stability of Micro- Talmon, Y. and S. Prager, “Statistical Thermodynamics of emulsions,” J. Cdl. Interface Sci., 66, 369 (1978). Phase Equilibria in Microemulsions,” J. Chem. Phys., 69, Saito, H. and K. Shinoda, “The Stability of w/o Type Emul- 2984 ( 1978 ), sions as a Function of Temperature and of the Hydrophilic Winsor, ‘P. A.,’ “Hydrotropy, Solubilization, and Related Emul- Chain Length of the Emulsifier,” J. Coil. Interfoce Sci., 32, sification Processes,” Trans. Faraday SOC., 44, 376 ( 1918 ). 647 ( 1970). Salter, S. J., “The Influence of the Type and Amount of Al- cohol on Surfactant-Oil-Brine Phase Behavior and Proper- ties,” Soc. Petrol. Eng., Preprint 6843, Annual Meeting, Manuscript receieed April 11, 1979; reoision received July 26, and Denver ( 1977). uccepted August 30, 1979.

Studies in the Synthesis of Control

Solubilization and Microemukions, Vol. 2, Plenum, New Schulman, J. H., W. Stroeckenius, and L. M. Prince, “Mech- Structures for ChemicalYork ( 1976). Processes anism of Formation and Structure of Microemulsions by Ruckenstein, E. and J. C. Chi, “Stability of Microemulsions,” Electron Microscopy,” J. Phys. Chem., 63, 1677 (1959). J. Chem. SOC. Faraduy Trans. II, 71, I690 (1975). Schulman, J. H. and J . B. Montagne, “Formation of Microemul- Part I: Formulation of the Problem.Ruckenstein, E., Process “Stability Phase Equilibria, and Interfacial sions by Amino Alkyl Alcohols,” Ann. New York Acad. Sci., Free Energy in Microemulaions,” pp. 755ff in K. L. Mittal 92,366 ( 1961). Decomposition and the Classification( ed. ), Micellization, of Solubilizationthe Control and Microemulsions, Vol. Scriven, L. E., “Equilibrium Bicontinuous Structures,” Nature, 2, Plenum, New York ( 1976). 263,123 (1976). Tasks. Analysis of the OptimizingRuckenstein, E.,Control “The Origin Structures. of Thermodynamic Stability of Talmon, Y. and S. Prager, “Statistical Mechanics of Micro- Solubilization and Microemukions,Microemulsions,” Vol. 2, Plenum, Chem. Phys.New Letters, 57, 517 (1978). emulsions,” Nature, 267, 333 ( 1977). Ruckenstein, E., “On the ThermodynamicSchulman, Stability J. H., of W.Micro- Stroeckenius, and L. M. Prince, “Mech- York ( 1976). anism of FormationMANFRED and StructureTalmon, MORARI Y.of andMicroemulsions S. Prager, by “Statistical Thermodynamics of emulsions,” J. Cdl. Interface Sci., 66, 369 (1978). Phase Equilibria in Microemulsions,” J. Chem. Phys., 69, Part I of this seriesRuckenstein, presents E. a andunified J. C.formulation Chi, “Stability of the ofproblem Microemulsions,” of synthesiz- Electron Microscopy,”YAMAN J. Phys. Chem., ARKUN 63, 1677 (1959). J. Chem. SOC. Faraduy Trans.Saito, II, 71, H. I690and K.(1975). Shinoda, “The Stability of w/o Type Emul- 2984 ( 1978 ), ing control structures for chemical processes. Thesions formulation as a Function is rigorous of Temperature and free Schulman, and of GEORGEthe J. H. Hydrophilic and STEPHANOPOULOSJ . B. Montagne, “Formation of Microemul- Ruckenstein, E., “Stability Phase Equilibria, and Interfacial sions by Amino Alkyl Alcohols,”Winsor, Ann. ‘P. NewA.,’ “Hydrotropy, York Acad. Sci.,Solubilization, and Related Emul- of engineering heuristics, providing the frameworkChain Length for generalizations of the Emulsifier,” and J. Coil. InterfoceDepartment Sci., 32,of Chemical sification Engineering Processes,” Trans. Faraday SOC., 44, 376 ( 1918 ). further analytical developmentsFree Energy in on Microemulaions,”this important problem. pp. 755ff in K. L. Mittal 92,366 ( 1961). ( ed. ), Micellization, Solubilization647 (and 1970). Microemulsions, Vol. and Materials Science Decomposition is the underlying, guiding principle,Salter, leading“The to Influence the classifica- of the TypeScriven, and L. Amount E., “Equilibrium of Al- Bicontinuous Structures,” Nature, 2, Plenum, New York ( 1976). S. J., University of Minnesota tion of the control objectives (regulation, optimization) and the partitioning of the 263,123 (1976). Ruckenstein, E., “The Origin of coholThermodynamic on Surfactant-Oil-Brine Stability of Phase Behavior and Proper-Minneapolis, Minn. 55455 process for the practical implementation of the ties,”control Soc. structures. Petrol. Eng.,Within Preprint the Talmon,6843, AnnualY. and Meeting,S. Prager, “Statistical Mechanics of Micro- Microemulsions,” Chem. Phys. Letters, 57, 517 (1978). emulsions,” Nature, 267, 333 (Manuscript 1977). receieed April 11, 1979; reoision received July 26, and framework of hierarchicalRuckenstein, E., control “On theand Thermodynamic multi-levelDenver ( 1977). optimization Stability of Micro-theory, uccepted August 30, 1979. mathematical measures have been developed to guide the decomposition of the Talmon, Y. and S. Prager, “Statistical Thermodynamics of emulsions,” J. Cdl. Interface Sci., 66, 369 (1978). Phase Equilibria in Microemulsions,” J. Chem. Phys., 69, control tasks and the partitioning of the process. Consequently, the extent and-the Saito, H. and K. Shinoda, “The Stability of w/o Type Emul- 2984 ( 1978 ), purpose of the regulatorysions as and a Function optimizing of controlTemperature objectives and offor the a given Hydrophilic plant are Winsor, ‘P. A.,’ “Hydrotropy, Solubilization, and Related Emul- well defined, and alternative control structures can be generated for the de- Chain Length of the Emulsifier,” J. Coil. Interfoce Sci., 32, sification Processes,” Trans. Faraday SOC., 44, 376 ( 1918 ). signer’s analysis and647 screening. ( 1970). In addition, inSalter, this firstS. J., part “The we Influence examine oftheStudies the features Type andof various Amount optimizingin of Al- the Synthesis of Control control strategies (feedforward,cohol on Surfactant-Oil-Brine feedback; centralized, Phase Behavior decentralized) and Proper- and de- velop methods for ties,”their Soc.generation Petrol. and Eng., selective Preprint screening. 6843, Annual Application Meeting, of all Manuscript receieed April 11, 1979; reoision received July 26, and these principlesDecomposition is illustratedDenver ( 1977). on an integrated chemical plant that offers enough uccepted August 30, 1979. variety and complexity to allow conclusions aboutStructures a real-life situation. for Chemical Processes

Part I: FormulationSCOPE of the Problem. Process During the last ten years, numerous works haveDecomposition dealt with control and as a simple the extension Classification of unit operations of control. the These Control the design of controlStudies systems to regulate in specific the unit opera- Synthesis interconnections decrease of the numberControl of degrees of freedom, tions (e.g., distillation), to bring a system (e.g., Tasks.a reactor) back Analysis and great of care the must Optimizing be taken not to over- Control or under-specify Structures. the to the desired operating point in some optimal fashion, to cmtrol objectives in a process. guarantee optimal profiles in nonhomogeneous reactors, etc. All available control theories assume that measured and The interactions Structuresbetween different pieces of equipment for in Chemicala manipulated variables haveProcesses been selected, thus not answering MANFRED MORARI chemical plant are complex, and do not allow us to regardPart I plantof this seriesone presents of the basic a unified questions formulation an engineer of the is problem facing when of synthesiz- designing YAMAN ARKUN ing control structuresa forplant. chemical Rules processes. of thumb Theand formulationexperience isguide rigorous the designer’sand free GEORGE STEPHANOPOULOS All correspondence \huuldPart be addressedI: Formulation to M. Morari, Department of of Chemicalthe Problem.choice of measured Process and manipulated variables. Naturally, Engineering, University of Wixonsin, Madison, Wscconsin, 5.3706of engineering heuristics, providing the framework for generalizations and Department of Chemical Engineering Present address for Arkun: Department of Chemical Engineering,further Hensselaer analytical developmentswithout a systematic on this importantprocedure, problem. there is no guarantee that all Polytechnic Institute, Troy,Decomposition New York, 12181 and the Classificationthe feasible alternatives of the are Control explored, and even less that the and Materials Science Decomposition is the underlying, guiding principle, leading to the classifica- University of Minnesota OOO 1- I-X0-3238-O220-$01.45. best possible structure is chosen. The lack of sound techniques IS4 Tasks. Analysis oftion the of the Optimizing control objectives (regulation, Control optimization) Structures. and the partitioning of the Minneapolis, Minn. 55455 RThe American Institute of Chemical Engineers, 1980. process for the practicalfor solving implementation those problems of the has control been criticized structures. frequently, Within the and framework of hierarchical control and multi-level optimization theory, Page 220 March, 1980 mathematical measures have been developed AlChEto guide Journal the decomposition (Vol. 26, MANFREDofNo. the 2) MORARI Part I of this series presentscontrol a unified tasks formulation and the partitioning of the problem of the of process. synthesiz- Consequently, the extent and-theYAMAN ARKUN ing control structures for chemicalpurpose processes. of the Theregulatory formulation and optimizing is rigorous control and free objectives forGEORGE a given plant STEPHANOPOULOS are well defined, and alternative control structures can be generated for the de- found the framework of the multilayer-multiechelon concept to of engineering heuristics, providing the framework for generalizations and Department of Chemical Engineering be very meaningful, convenient, and having the potential for further analytical developmentssigner’s on this analysis important and screening.problem. and JCOORDINATORMaterials Science min @(x, m, d) addition,I in this first part we examine the features of various optimizing I, further development. Let us elaborate further on this, and on Decomposition is the underlying,In guiding principle, leading to the classifica- University of Minnesota control strategies (feedforward, feedback; centralized, decentralized) and de- how it affects the synthesis of control structures. tion of the control objectives (regulation, optimization) and the partitioning of the Minneapolis, Minn. 55455 m (PI') (5) process for the practical implementationvelop methods of thefor1 controltheir generation structures.t‘ and Within selective the screening. Application of all these principles is illustrated on an integrated chemical plant that offers enough s.t. Ax, m, d) = 0 Multiloyer Decomposition framework of hierarchical control and multi-levelADAPTATION optimization theory, mathematical measures have beenvariety developed and complexity to guide to the allow decomposition conclusions ofabout the a real-life situation. where During chemical plant operation, the basic goal is to optimize control tasks and the partitioning of the process. Consequently, the extent and-the an economic measure of the operation (e.g. minimize operating purpose of the regulatory and optimizing control1 objectives for a given plant are f'= [g", g;"] with g"' = [gYT, gg'] and gi < 0. cost, maximize profit), while at the same time satisfying certain wellDISTURBANCES defined, and alternatived control structures can be generated for the de- SCOPE ~ OPTIMIZATION equality or inequality constraints (quality and production spec- signer’s analysis and screening. During the last ten years, numerous works have dealtCONTROL with SYSTEMcontrol I as a simple extension of unit operations control. These ifications, environmental regulations, safety etc.). This optimi- In addition, in this first partthe wedesign examine of control the features systems of to various tregulate optimizing specific unit opera- interconnections decrease the number of degrees of freedom, Wealso omitted the subscript and superscript of dl for simplicity zation must be achieved in the presence of external disturbances control strategies (feedforward,tions feedback; (e.g., distillation), centralized, to bring decentralized) a system (e.g., and a de- reactor) back and great care must be taken not to over- or under-specify the because we will be dealing with non-stationary disturbances which enter the plant. Thus, we formulate the optiqization velop methods for their generationto the desiredand selective operating screening. point inApplication some optimal of all fashion, to cmtrol objectives in a process. these principles is illustrated on an integrated chemical plant that offers enough only. For the decomposition, we assume the function of the problem to reflect these attitudes during the operatio; of a guarantee optimalREGULATION profiles in nonhomogeneous reactors,SUBSYSTEM etc. I All available controlSUBSYSTEM theories 2 assume that measured and variety and complexity to allow conclusions about a real-life situation. SUBSYSTEM 5 chemical process The interactions between different pieces of equipment in a manipulated variables have been selected, thus not answering overall plant to be the sum ofthe operatingcosts ofall processing chemical plant are complex, and do not allow us to regard plant one of the basic questions an engineer is facing when designing units, that is, a plant. Rules of thumb and experience guide the designer’s G UI All correspondence \huuld be addressedSCOPE to M. Morari, Department of Chemical choice of measured and manipulated- - - - -variables. - - - Naturally, 5 m Engineering, University of Wixonsin, Madison, Wscconsin, 5.3706 PROCESS without a systematic procedure, there is no guarantee that all During the last ten years, numerousPresent address works for have Arkun: dealt Department with of Chemicalcontrol Engineering, as a simple Hensselaer extension of unit operations control. These @ = @i(xi, m,, ui,d) (6) subject to Polytechnic Institute, Troy, New York, 12181 Figurethe feasible2. Multiechelon alternatives decomposition are explored, andof theeven control less that tasks. the x the design of control systems to regulate specific unit opera- interconnections decrease the number of degrees of freedom, i=l c best possible structure is chosen. The lack of sound techniques f = g’ m, state equations (2) tions (e.g.,Figure distillation), 1. Multiloyer to bring decompositionOOO a 1-system IS4 I-X0-3238-O220-$0 (e.g., of the a control reactor)1.45. tosks. back and great care must be taken not to over- or under-specify the (x, 4 RThe American Institute of Chemical Engineers, 1980. for solving those problems has been criticized frequently, and x(0) = xo to the desired operating point in some optimal fashion, to cmtrol objectives in a process. We have s processing units in the plant, and the subscript i STWrn, I I g”(x, m, 5 0 feasibility constraints (3) guarantee optimal profiles in nonhomogeneous- reactors, etc. All available control theories assume that measured and denotes the states (xi), manipulated variables (mi)and distur- d) Page 220 March, 1980 manipulated variables have been selected, thus not answeringAlChE Journal (Vol. 26, No. 2) y = h(x, m, 6) outputs from the process. (4) The interactions between differentg”(x, m,pieces d,) of5 equipment0 in a \\ I I I bances (di)associated with processing unit Further, the set of chemical plant are complex, and do not allow us to regard plant one of the basic questionsI an engineer is facing when designing\\ i. Y = h(x, m, 4) a plant. Rules of thumb and experience guide the designer’s constraints is assumed to be decomposable All correspondence- \huuld be addressed to M. Morari, Department of Chemical where x E Rn is the vector of state (dependent) variables choice of measured and manipulated variables. Naturally, Engineering,where d1 University = E{dl(T,)}; of Wixonsin, dl(0) Madison, = dlo Wscconsin,and the5.3706 time period, To, is s m E R‘ is the vector of manipulated (independent) vari- Present address for Arkun: Department of Chemical Engineering, Hensselaer without a systematic procedure, there is no guarantee that all fi(xi, mi, ut, di) = O for i 1, 2, . . ., (7) Polytechniclarge enough Institute, forTroy, the New predictionYork, 12181 to be approximately constantthe feasible alternatives?rLm8:;o:m::emd are explored, and even less that1 the~ j;03:R;;;l;r Synrheris- ables , Shift Converter and the plant dynamics to be negligible. The optimum solution best possible structure is chosen. The lack of sound techniques ionr ~ ui d E Rm is the vector of external disturbances OOO 1- IS4 I-X0-3238-O220-$01.45. The inputs result from the interconnections of unit i with the RTheof the American problem Institute (Pl) of Chemical is Engineers, 1980. for solving those problems has been criticized frequently, and ___ y, E R‘ is the vector of process outputs. - other units of the processing system and x* = x(m*, dl) I @ is the operating cost (performance function) of the Page 220 March, 1980 AlChEit Journal (Vol. 26, No. 2) P process. Y* = y(m*, Prvreor R" I ~i = (Iijyi = QiY (8) Plant control is required because of external disturbances d. 4) x I j=l Their stochastic nature makes solving the resulting nonlinear 2) Regulatory Control: stochastic control problem (1)an impossible task. If we partition where Qi is the incidence matrix describing the interconnection the disturbance vector in the following fashion (which can always Minimize ./$ {(y - y*)W,(y - y*) + Figure 3. One possible decomposition of an ammonia plant. be done by an appropriate change of the coordinate system), a m (m- m*)Wz(m- m*)}dt ofuniti with the other units. (PI') reflects the extreme situation manageable degree of complexity can be reached of completely centralized data acquisition and decision making s.t. Figure 2). This multiechelon decomposition is also a natural (control action). On the other hand d, eRmlsuch that lim E{dJ = d, # 0, d,(O) = d,o 1-m element arising from the structure of a chemical process. F & E RmZ such that lim E{& = d, = 0, &(O) = 40 Decomposing the process under steady state assumptions is t-r Min @ = Min Q(xi, mi, ui, d;) (P2) necessary for the following reasons: xi=l where 1. Developing an optimizing control strategy for an inte- m ml dT= idf, 4. grated plant often goes contrary to the designer's or the s.t. (7), (8) operator's intuition, which is to think in terms of groups of This partition into a stationary (d2) and a nonstationary (d,) where W1andWz are positive definite and symmetric weighting represents complete decentralization down to the basic operat- units with a common functional goal. Further, different disturbance component is discussed in more detail in Part 111. matrices. A natural definition would be ing unit. (PI') suffers from too much complexity, while in (P2) The disturbance model underlying dl has its poles on the aggregates of operating units will have different functional a2cp the extensive coordination between the subunits may unde- imaginary axis, while the poles of the model ford, lie strictly in goals. be the left half plane. This strict partition into d,, d, is rarely u=u* sirable. The multiechelon decomposition criteria to be de- m=-m* m=m* 2. Solution of the on-line optimization problem every time an possible from experimental observations alone. A suitable d=d 1 d=dl veloped later supply quantitative means for judging the attrac- important disturbance enters the system can be over- criterion is to assume the poles of the disturbance model, which tiveness of the different decompositions. are several times slower than the time constant of the system, to Note that 0 to t, To,i.e. the time horizon for regulation is whelming; decomposition facilitates its solution. be effectively zero. The partition defines implicitly two-time significantly shorter than for optimization. 3. Synthesis of- the regulatory control structure is also sim- The previous discussion indicates that the “multilayer struc- scales, the basis of the “temporal hierarchy” (Findeisen 1976) in plified, since it is concentrated within a group of units the control activities on a chemical plant. The disturbance com- ture” is a natural element of the control activities in a chemical CLASSIFYING DISTURBANCES AND DECOMPOSING THE ponents d, are “fast” varying. They are irrelevant for the long plant and leads to a vertical decomposition of the control tasks. (subgroup. echelon) with a common functional goal. CONTROL TASK: term optimization of the process, because their predicted value The first (lower) layer takes care of the regulation and allows the As an example, consider an ammonia plant (Figure 3),where is essentially zero after a short time. Regulatory control is used process to be considered at pseudo steady state. The second one possible process decomposition for optimization is dernon- Formalizing the discussion in the last section we can state for to suppress their influence. (higher) layer is responsible for determining the optimal set stratcd. Note that each subgroup of units has a very well spec- Disturbance Classifiation 1 : (a) the nonstationary "slowly vary- On the other hand, d, contains persistent and/or periodic points under the influence of changing disturbances. For a ing" disturbances d, are candidates for optimizing control ac- general system, more layers can be realized (Figure l),but they ified and well understood operational objective. Thus, the oper- disturbances which have to be included in the long term optimi- tion, and (b)only regulatory action will bc taken to deal with the zation. Without much error, we can neglect the time averaging will not be discussed here. ational goal of the first subgroup (the primary and secondary of the objecive function (1) and reformulate it in mathematical reformer and the shift converter) is to provide the hydrogen remaining disturbances dz. terms employing a pseudo steady state assumption. Not all the slow disturbances will affect seriously the optimum Multiechelon Decomposition necessary for the ammonia synthesis. The goal of the second economic performance of the process. It is therefore impcrtant 1) Optimizing Control: subgroup is to prepare the reaction feed of nitrogen and hydro- The second type of decomposition is done horizontally, de- to realize which disturbances are of economic interest and to act veloping multiple echelons for control action in the chemical gen at the desired stoichiometry, by removing the undesired process. The plant is divided into interacting groups of process- components. The third subgroup is to achieve the desired con- appropriately. Here, we establish a measure to classify the m ing units, for which the optimization is carried out separately. version of the Hz and N2 to ammonia. disturbances from an economic point of view and thus establish subject to These are coordinated from time to time by a coordinator (see The decomposition of the process should be made in such a the optimization requirements for the control structure. Since way that an involved coordination among the subgroups is not the external disturbancesd,,i = 1, . . . s are considered constant AlChE Journal (Vol. 26, No. 2) March, 1980 Page 223 required every time a disturbance enters the system. Qther- in a particular optimization step, we can regard them as ad- wise, it loses its attractive features. This, along with our desire to ditional constraints on the process, i.e. di = d:, i = 1, , . . s. If develop processing groups with functional uniformity, consti- we let A, be the Lagrange multipliers associated with the inter- tute the two basic design guidelines in decomposing the process connections (8) and rj the multipliers associated with the con- for the optimizing control structure. straints d, = d: then the sub-Lagrangian associated with unit i is Bcfbre we proceed with the mathematical formulation of the defined as multiechelon decomposition, let us simplify the notation of (P1). Some of the inequality constraints, g", will be active at thc li = Qi(xi, mi, ui, d,) - ATui + ~A~Qiiyi- .rrTddi (9) optimum. Since all our considerations will be of a local nature, I we hypothesize that the set of active inequality constraints does The stationarity condition at the optimum, with respect to the not change with changing disturbances. Then, we can combine disturbance di, yields the steady-state transformation equations (i.e. g' = 0) and the active inequality constraints into one vectorfand upon substitu- tion for we obtain

Page 224 March, 1980 AlChE Journal (Vol. 26, No. 2) George Arguing about Decomposition George’sJOURNAL OF Dissertation OPTIMIZATION THEORY ANDwith APPLICATIONS: Art Westerberg Vol. t5, No. 3, 1975

JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS: Vol. t5, No. 3, 1975

The Use of Hestenes' Method of Multipliers to Resolve Dual Gaps in EngineeringThe Use System of Hestenes' Optimization Method 1 of

G. STEPHANOPOULOSMultipliers 2 AND to A. ResolveW. WESTERBERG Dual 3 Gaps in Engineering System Optimization 1 Communicated by R. Jackson G. STEPHANOPOULOS 2 AND A. W. WESTERBERG3

Abstract. For nonconvexCommunicated problems, the saddleby R. Jacksonpoint equivalence • Lagrangianof the Lagrangiandecomposition approach need not hold. The nonexistence of • a saddle point causes the generation of a dual gap at the solution Methodpoint, andtoAbstract. resolvethe Lagrangian Forthe nonconvexapproach dual gap thenproblems, failsdestroying tothe give saddle the point thesolution equivalence separability of separableto the original ofsystems the problem. Lagrangian Unfortunately, approach dualneed gapsnot arehold. a fairly The commonnonexistence of phenomenona saddle for engineeringpoint causes system the generation design problems. of a dual gap at the solution Methodspoint, which and the are Lagrangian available toapproach resolve thethen dual fails gapsto give destroy the solution the separabilityto the original of separable problem. systems. Unfortunately, The present dual gaps work are employs a fairly common the methodphenomenon of multipliers for engineeringby Hestenes system to resolve design the problems. dual gaps of engineering systemMethods design which problems; are available it then to develops resolve anthe algorithmic dual gaps destroy procedurethe which separability preserves of theseparable separability systems. characteristics The present ofwork the employs system. Thethe theoreticalmethod of multipliersfoundations by of Hestenes the proposed to resolve algorithm the dualare gaps of developed,engineering and examples system are designprovided problems; to clarify it thenthe approach develops antaken. algorithmic procedure which preserves the separability characteristics of the Key Words.system. Decomposition The theoretical methods, foundations duality of theory,the proposed engineering algorithm are design, methoddeveloped, of multipliers,and examples nonconvex are provided programming, to clarify the approachmathe- taken. matical programming. Key Words. Decomposition methods, duality theory, engineering design, method of multipliers, nonconvex programming, mathe- I, Introduction matical programming. The Lagrangian approach, representing a dual method, has often been proposedI, Introduction for solving optimization problems. In many engineering design problems, the system to be optimized comprises several fairly conlplex subsystemsThe Lagrangian or units approach,which are representingconnected togethera dual method,by sets hasof often 1 This workbeen was supportedproposed by for NSF solving Grant No.optimization GK-18633. problems. In many engineering 2 Graduate designStudent, problems, Department the of system Chemical to Engineering,be optimized University comprises of Florida,several fairly Gainesville,conlplex Florida. subsystems or units which are connected together by sets of a Associate Professor, Department of Chemical Engineering, University of Florida, Gainesvitle,1 This Florida. work was supported by NSF Grant No. GK-18633. 2 Graduate Student, Department of Chemical Engineering, University of Florida, Gainesville, Florida. 285 © 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of tMs publication maya Associate be reproduced, Professor, stored inDepartment a retrieval system, of Chemicalor transmitted, Engineering, in any form or University by arty means, of Florida, eleetronle, mechanical,Gainesvitle, photocopying, Florida. microfilming, recording, or otherwise, without written permission of the publisher. 285 © 1975 Plenum Publishing Corporation, 227 West 17th Street, New York, N.Y. 10011. No part of tMs publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by arty means, eleetronle, mechanical, photocopying, microfilming, recording, or otherwise, without written permission of the publisher. Literature from the 1970s Decomposition and Optimization

Current revival because

• Suitable hardware has become available • Problems have become too large, e.g. machine learning Edgar, 1’. F., “Status of Design Methods for Multivariable Control” in Maarleveld, A,, and J. E. Hijnsdorp, “Constraint Control on Distillation Chemical Process Control, AIChE Symp. Ser. 159, 72 (1976). Columns,” Proc. 4th IFAC Congress, Warsaw (1969) (also iiuto- Findeisen, W., “Lectures on Hierarchical Control Systems,”Center for matica, 6, 61 (1970)). Control Sciences, U. of Minnesota, Minneapolis (1976). Masso, A. H., and D. F. Rudd, “The Synthesis of System Design, 11. Findeisen, W., F. N. Bailey, M. Brdys, K. Malinowski, P. Tatjewski, Heuristic Structuring,” AIChE J., 15, 10 (1969). and A. Wozniak, Control and Cuordination in Hierurchical Systems, Mesarovic, M., D. Macko, and Y. Takahara, Theory of Hierarchical Intern. Inst. for Applied Systems Anal., Laxenburg, Austria (1979). Multiletjel Sgstems, Academic Press, (1970a). Foss, A. S., “Critique of Chemical Process Control,”AIChEJ., 19, 209, Mesarovic, M., “Multilevel Systems and Concepts in Process Control,” (1973). IEEE Proc., 58, 111 (1970b). Foss, A. S., and M. M. Denn, (eds.),ChemicalProcessControl, AIChE Mordri, M., “Studies in the thesis of Control Structures for Chemi- Symp. Ser. 159, 72 (1976). cal Processes,” Ph. D. th Univ. Minnesota (1977). based on the concepts of controllability and observability.Friedman, But P., extendedand K. L. Pinder, for “Optimizationthe design ofaSiniulation of the regulatory Model of structures.Motard. R. L., Within H. M. Lee, R. W. Barkley. D. M. Ingels, CHESS, they go far beyond the general textbook definitions, which aCheinicalare Plant,”lnd.the above Eng. framework, Chenz. Proc. Des.we Deo.,develop 11, 512 an (1972). algorithmic Chem. procedure Eng. Simulation to System System’s Guide, Technical Publ. Co., demonstrated to be too weak in certain cases and too strongGaines, in L. D., and J. L. Gaddy, “Univ. of Missouri-RollaPROPS Users Houston (1968). Guidc,” Rolla,generate MO (1974). alternative control structures for a givenRudd, D.steady-state F., “The Synthesis of Systems Design I. Elementary Decom- others. Gaines, L. D.,chemical and J. L,. Gaddy, process “Process design. Optimization We by demonstrateFlowsheet position the synthesisTheory,” AIChE J., 15, 343 (1968). The process decomposition developed in Part I for the syn-Simulation,” strategies Ind. Eng. Chem. in a Proc. series Des. of Deo., examples. 15, 206 (1976). Schoeffler, J. D., and L. S. Lasdon, “Decentralized Plant Control,” thesis of decentralized optimizing control structures canGovind, be R., and 6. J. Powers, “Control System Synthesis Strategi Proc. 19th Ann. ISA Conference, lS(III), 3.3-3-64, (1964). AIChE 82nd National Meeting, Atlantic City NJ, (1976). Tinnis, V., “An Optimum Production Control System,” ISA Trans., Johns, W. R., “Asscssing the Effect of Uuccrtainty on the Probable 13(1), 70 (1974). Performance of Chemical Processra,” Symp. on Uncertain Systems, Umeda, T., T. Kuriyama, and A. Ichikawa, “A Logical Structure for Cambridge, July (1973). Process Control System Synthesis,” Proc. IFAC Congress, Helsinki, CONCLUSIONSKestcvbauni, AND A,, R.SIGNIFICANCE Shinnar, and H. E. Thau, “Design Concepts for (1978). Process Control,” Ind. Eng. Chcm., Proc. Dcs. Dee., 15, 2 (1976). Westerherg, A. W., “Decomposition Methods for Solving Steady State Lasdon, L. W.,Optimizution Theory for Large Systems, Macmillan, Process Design Prohlems” in Decomposition of Large-Scale Prob- Ncw York, (1970). lems, D. M. Hiinmelblau (Ed.), North Holland Publishing Co., A method for synthesizing control structures is presented.Lee, W., and V.heuristic W.Wwkinan, criteria Jr,. “Advanced can enter Control at any Practice stage in the of the synthesis(1973). proce- Chemical Industry,” AIChE J., 22, 27 (1976). Wismer, D. A. (Ed.), Optimization Methods for Large-Scale Systems, Systems are represented as structured matrices and the dure, and thus, the method should be suitableMcGraw for industrial Hill, New York, (1971). Lefkowitz, I., “Multilevc~lApproach Edgar, Applied 1’. F., “Status to Control of Design System Methods Dr- for Multivariable Control” in Maarleveld, A,, and J. E. Hijnsdorp, “Constraint Control on Distillation method uses extended versions of the conditions for structuralsign,” ASMEapplications. Truns., J. Basic Eng.,Second,Chemical 392 (June, Processthe 1966).usefulness Control, AIChE and Symp. implication Ser. 159, 72 of(1976). the Columns,” Proc. 4th IFAC Congress, Warsaw (1969) (also iiuto- controllability and observability as feasibility criteria. Mainly,Lrfkowitz, I., “Systcins ControlFindeisen, of Chemical W., and “Lectures Related on Process Hierarchical Sys- Control Systems,”Center for matica, 6, 61 (1970)). tems” Proc.properties, 6th IFAC Congress, controllability Boston, 38.2 (1975).and observability, have been only Control Sciences, U. of Minnesota, Minneapolis (1976). Masso, A. H., and D. F. Rudd, “The Synthesis of System Design, 11. feedback control structures are addressed, and feedfonvardLottkin, M., and R. Rcimage, “Scaling and error analysis for matrix incompletelyFindeisen, covered W., and F. N.understood Bailey, M. Brdys, in theK. Malinowski, Monrracriptchemical receibed P. engi-Tatjewski, Februury 6, 1979:Heuristic rwi,sion rrreirrd Structuring,” August 26, AIChE und UCL J.,epted 15, 10 (1969). compensation is developed as a logical extension. Numerousinversion hy pnrtitioning.” Ann Math. Stutist., 24, 428 (1953). August 27, 1879. neering literature.and A. Wozniak,Here aControl unified and Cuordinationrepresentation in Hierurchical is given, Systems, Mesarovic, M., D. Macko, and Y. Takahara, Theory of Hierarchical examples show the various characteristics of the synthesis Edgar, 1’. F., “StatusIntern. of Design Inst. for Methods Applied for Systems Multivariable Anal., Laxenburg, Control” in AustriaMaarleveld, (1979). A,, andMultiletjel J. E. Hijnsdorp, Sgstems, “Constraint Academic ControlPress, (1970a). on Distillation Columns,” Proc. 4th IFAC Congress, Warsaw (1969) (also iiuto- method. A hypothetical plant (Williams and Otto 1960) demon- explainingChemical ProcesstheFoss, physical Control, A. S., “Critique AIChEmeaning ofSymp. Chemical of Ser. those Process 159, concepts.72 Control,”AIChEJ., (1976). 19, 209, Mesarovic, M., “Multilevel Systems and Concepts in Process Control,” Findeisen,The results W., “Lectures are(1973). by onno Hierarchical means final, Control but Systems,”Center they are a first for stepmatica, to 6, 61 (1970)).IEEE Proc., 58, 111 (1970b). strates the applicability of the method. Control Sciences,Foss, U.A. S.,of Minnesota,and M. M. Denn,Minneapolis (eds.),ChemicalProcessControl, (1976). Masso, AIChE A. H., andMordri, D. F. M., Rudd, “Studies “The in Synthesis the thesis of System of Control Design, Structures 11. for Chemi- The significance of the paper is twofold: First, it presents a bridgeFindeisen, the W., discontinuity F.Symp. N. Bailey, Ser. 159,M. betweenBrdys, 72 (1976). K. Malinowski, the employed P. Tatjewski, completely Heuristic Structuring,”cal Processes,” AIChE Ph. J., D. 15, th 10 (1969).Univ. Minnesota (1977). Part II: Structuraland A. Wozniak, Aspects Control and Cuordination and the in Hierurchical Synthesis Systems, ofMesarovic, M., D. Macko, and Y. Takahara, Theory of Hierarchical theory-based method for developing alternative control heuristic structuringFriedman, P., procedures and K. L. Pinder, and “Optimization the available ofaSiniulation sophisti- Model of Motard. R. L., H. M. Lee, R. W. Barkley. D. M. Ingels, CHESS, Intern. Inst. foraCheinical Applied Systems Plant,”lnd. Anal., Eng. Laxenburg, Chenz. Proc. Austria Des. (1979). Deo., 11, 512Multiletjel (1972). Sgstems,Chem. Academic Eng. Simulation Press, (1970a). System System’s Guide, Technical Publ. Co., structures-excluding the possibility of singularities, overspec-Alternative catedFoss, A.Feasible detailed S., “CritiqueGaines, design of L.ChemicalControl D., techniquesand ProcessJ. L. Gaddy,Schemes Control,”AIChEJ., for “Univ. multivariable of Missouri-RollaPROPS 19, 209, controlMesarovic, Users M., “MultilevelHouston (1968). Systems and Concepts in Process Control,” ifications and undetectable local instabilities. Engineering loops.(1973). Guidc,” Rolla, MO (1974). IEEE Proc., Rudd,58, 111 D. (1970b). F., “The Synthesis of Systems Design I. Elementary Decom- Foss, A. S., andGaines, M. M. Denn, L. D., (eds.), and J.ChemicalProcessControl, Gaddy, “Process Optimization AIChE by FlowsheetMordri, M., “Studiesposition in the Theory,” thesis AIChE of Control J., 15, Structures 343 (1968). for Chemi- L,. MANFREDUniv. Minnesota MORARI (1977). Symp. Ser. 159,Simulation,” 72 (1976). Ind. Eng. Chem. Proc. Des. Deo., 15, 206 (1976).cal Processes,” Schoeffler, Ph. D. th J. D., and L. S. Lasdon, “Decentralized Plant Control,” Motard. R. L., H. M. Lee, R. W. Barkley. D. M. Ingels, CHESS, The classificationFriedman, of control P., andGovind, K.objectives L. R.,Pinder, and and “Optimization6. externalJ. Powers, disturbances “Control ofaSiniulation System in Model a Synthesis chemical of Strategi GEORGEProc. 19th STEPHANOPOULOS Ann. ISA Conference,and lS(III), 3.3-3-64, (1964). plant determinesaCheinical the extent Plant,”lnd. ofAIChE the optimizing 82nd Eng. NationalChenz. and Proc. Meeting, regulatorv Des. Deo., Atlantic control 11, City 512 structures(1972).NJ, (1976). Chem. Eng. SimulationTinnis, V., System “An Optimum System’s Guide, Production Technical Control Publ. System,” Co., ISA Trans., Houston (1968). (see Part I). InGaines, this article L. D., we andJohns, discuss J. L. W. Gaddy, theR., “Asscssingstructural “Univ. of Missouri-RollaPROPSthe design Effect of ofalternative Uuccrtainty Users regula- on the Probable 13(1), 70 (1974). Guidc,” Rolla, MO (1974). Rudd, D. F., “TheDepartment Synthesis of of ChemicalSystems Design Engineering I. Elementary Decom- tory control schemes to satisfyPerformance the posed of objective.Chemical Processra,” Within the Symp. framework on Uncertain of Systems, Umeda, T., T. Kuriyama, and A. Ichikawa, “A Logical Structure for Gaines, L. D., and J. L,. Gaddy, “Process Optimization by Flowsheet position Theory,” AIChE J.,and 15, Materials 343 (1968). Science hierarchical control, criteria areCambridge, developed July for (1973). the further decomposition of the Process Control System Synthesis,” Proc. IFAC Congress, Helsinki, Simulation,”Kestcvbauni, Ind. Eng. Chem. A,, R.Proc. Shinnar, Des. Deo., and H. 15, E. 206 Thau, (1976). “Design ConceptsSchoeffler, for J. D.,(1978). and L. S.University Lasdon, “Decentralized of Minnesota Plant Control,” process subsystems,Govind, reducing R., and 6. the J. Powers,combinatorial “Control problem System Synthesis while not Strategi eliminating Proc. 19th Ann.Westerherg, ISA Conference,Minneapolis, A. W., “Decomposition lS(III), Minn. 3.3-3-64, 55455 Methods (1964). for Solving Steady State feasible control structures. WeProcess use structural Control,” models Ind. Eng. to Chcm.,describe Proc. the Dcs.interactions Dee., 15, 2 (1976). AIChE 82nd Lasdon,National L. Meeting, W.,Optimizution Atlantic City Theory NJ, (1976).for Large Systems, Macmillan,Tinnis, V., “An OptimumProcess Design Production Prohlems” Control in System,”Decomposition ISA Trans., of Large-Scale Prob- In Part I we presented the general philosophy for theamong syn- the unitsmodelJohns, of a W.plantas R.,simple and “AsscssingNcw the as York,physicochemical possible,the (1970). Effect of isUuccrtainty phenomenato use on criteria occurringthe Probable of instructural the 13(1), 70 (1974).lems, D. M. Hiinmelblau (Ed.), North Holland Publishing Co., Umeda, T., T. Kuriyama, and A. Ichikawa, “A Logical Structure for various units. ThePerformance relevance Lee,of Chemicalcontrollability W., and Processra,” V. andWwkinan, observability Symp. Jr,.on Uncertain “Advanced in the Systems, synthesis Control Practice of in the (1973). thesis of control structures for chemical processes. The steps are controllability and observabilityW. (Lin 1976). These properties,Process Control System Synthesis,” Proc. IFAC Congress, Helsinki, control structuresCambridge, is discussed, JulyChemical and (1973). modified Industry,” versions AIChE are J., used22, 27 to (1976). develop all the Wismer, D. A. (Ed.), Optimization Methods for Large-Scale Systems, summarized in Figure 5 of Part'I. Specification of the controlalternative feasiblehowever,Kestcvbauni, regulatory are A,,Lefkowitz, neither R. structuresShinnar, I.,necessary “Multilevc~land in H. an E. noralgorithmicThau,Approach sufficient “Design Applied fashion. Concepts for to a Control Variouscontrol for System sys-(1978). Dr- McGraw Hill, New York, (1971). Westerherg, A. W., “Decomposition Methods for Solving Steady State objectives is the first step, and dictates that the control taskexamples be illustratetemProcess to the work developedControl,” in practice.sign,” Ind. concepts ASME Eng. Extended Truns.,Chcm., and strategies, J.Proc. Basic concepts Dcs. Eng., including Dee., 392 of 15, (June,output the2 (1976). applica- 1966). structural Process Design Prohlems” in Decomposition of Large-Scale Prob- Lasdon, L. W.,Lrfkowitz,Optimizution I., “Systcins Theory for Control Large of Systems, Chemical Macmillan, and Related Process Sys- composed of a regulatory part and an optimizing part. Classifica-tion of the overallcontrollability synthesis method and observability to an integrated have chemical been plant.formulated to rem-lems, D. M. Hiinmelblau (Ed.), North Holland Publishing Co., Ncw York, (1970).tems” Proc. 6th IFAC Congress, Boston, 38.2 (1975). (1973). tion of the expected disturbances determines the extent of each edyLee, these W., and deficiencies V.Lottkin, W.Wwkinan, M., and Jr,. R. “AdvancedRcimage, “Scaling Control Practiceand error in analysisthe for matrix Wismer, D. A. (Ed.),Monrracript Optimization receibed Februury Methods 6, for 1979: Large-Scale rwi,sion rrreirrd Systems, August 26, und UCLepted of these control parts. Chemical Industry,”inversion AIChE hy pnrtitioning.”J., 22, 27 (1976). Ann Math. Stutist., 24, 428 (1953). August 27, 1879. Lefkowitz, I., “Multilevc~lApproach Applied to ControlSCOPE System Dr- McGraw Hill, New York, (1971). Part I concentrated further on optimizing controllers after sign,” ASME Truns., Basic Eng., 392 (June, 1966). In Part I, theMODELING control tasks ASPECTS were J.divided into those of the 2. Formulation of mathematical criteria to be satisfied by developing the proper decomposition of the process. The im- Lrfkowitz, I., “Systcins Control of Chemical and Related Process Sys- regulatory and oftems” the optimizing Proc. 6th IFAC type. Congress, The first Boston, can always 38.2 (1975).be every feasible control structure. plicit assumption made at that point is that the regulatoryexpressed con- in the formMost of results functions of ofthe operating current variables, systems which theory are based on linear Lottkin, M., and R. Rcimage, “Scaling and error analysis for3. matrixDevelopment Monrracript of guidelines receibed Februury for decomposing 6, 1979: rwi,sion the rrreirrd overall August 26, und UCLepted trollers would he designed for each subsystem develooedhave from to be keptor atlinearizedinversion desired hylevels pnrtitioning.” system through models Annthe use Math. manipulated Stutist., 24, 428 (1953). August 27, 1879. the decomposition, but no guidelines were established onvariables. how TheControl same is possiblePart for the II: second, StructuresStructural if certain condi- Aspects problem and into manageable the Synthesis subproblems. of to develop these regulatory structures. It is this question thattions we derived in Part I are satisfied.Alternative Thei structure = A(t)x Feasible of + the B(t)u feed- Control4. Algorithmic Schemes (1)procedure to develop alternative control back controllers used for that purpose is developed here on a structures. mainly address here. sound theoretical basis, The fnllowing problemsy are= C(t)x addressed: (2) The approach adopted in this work is based on the structural Regulatory control structures for a chemical process are 1.de- Development of a suitable type of system representation MANFRED MORARI signed to keep certain processing variables at desired set points.(model), requiring(xPart E A",a minimal II: u EStructural R",amount y Eof A'information. and Aspects A@), B(t), and C(t)characteristics theare compatible Synthesis describing (a)of the interactions among the units The classification of control objectivesof aand chemical external process disturbances and (b) in the a chemical logical dependence GEORGE(of the STEPHANOPOULOSand These set points might be the results of product quality spec- matrices). Consequently, the linearized descriptionBoolean type) of a among non- the variables used to model the dynarnic linearAlternative systemplant will determines beFeasible accurate the in extentControl an infinitesimal of the optimizing Schemes region and aroundregulatorv control structures ifications, safety considerations, environmental regulations etc. (see Part I). In this article we discuss thebehavior structural of the design various of alternative units. Thus, regula- detailed dynamic model-Department of Chemical Engineering or from feedback optimizing structures. These objectives should the point of linearizationtory control schemes only. A to compromise satisfy the posed lingwould atobjective. an be early to use Withinstage a is theavoided. framework The mathematical of feasibility criteria for the generated alternative control structuresMANFRED are MORARIand Materials Science be satisfied almost continuously, and indicate the set of mea- linear model whichhierarchical is approximately control, criteria valid are developedin a finite forregion the further ofthe decomposition of the University of Minnesota GEORGE STEPHANOPOULOSand surements that should be made in the process. In case these stateThe space. classification Mostprocess ofthe ofsubsystems, control elements objectives reducing in the and the matricesil, external combinatorial disturbances B andC problem in will a chemicalwhile not eliminating Minneapolis, Minn. 55455 feasible control structures. We use structural models to describe the interactions measurements cannot be made for various reasons-becausePage of232 varyplantMarch,- from determines 1980one linearization the extent of thepoint optimizing to another, and regulatorv but some control of the structures AlChE Journal (Vol. 26, No. 2) (see Part I). Inamong this article the units we ofdiscuss a plant the and structural the physicochemical design of alternative phenomena regula- occurring in theDepartment of Chemical Engineering undesirable large time lags or low reliability, we select sec- elementstory control will schemesvarious always units. to be satisfy Thezero. relevancethe This posed suggests of objective. controllability a structural Within and the observability repre- framework in ofthe synthesis of sentation of the system, where A, B and C consist of elements and Materials Science ondary measurements in conjunction with an estimation scheme hierarchical control,control structurescriteria are is developed discussed, forand the modified further versions decomposition are used of to the develop all the University of Minnesota (Part 111). whichprocess are subsystems, generallyalternative reducing nonzero feasible the and regulatorycombinatorial others whichstructures problem are in alwayswhile an algorithmicnot zero. eliminating fashion. Various Minneapolis, Minn. 55455 As a first step we have to determine what variables have to be Thefeasible model control ofexamples astructures. double illustrate Weeffect use the evaporatorstructural developed models concepts (DEE) to describe and (Figure strategies, the 1) interactions is including the applica- among the unitstion of of a theplant overall and the synthesis physicochemical method to phenomena an integrated occurring chemical in theplant. measured and controlled to guarantee smooth plant operation. various units. The relevance of controllability and observability02 in the synthesis of elements could be zero as a special case and then the rank would Before the actual control algorithms can be designed, the alter- control structures is discussed, and modified versions are used to develop all the be 1. native sets of manipulated variables which can be used in a alternative feasible regulatory structures in an algorithmic fashion. VariousSCOPE We define a node i to be nonacessible from a nodej if there is feedback arrangement must be developed. examples illustrate the developed concepts and strategies, including the applica- no possibility of reaching node i starting from nodej and going to tion of the overallIn Part synthesis I, the method control to tasks an integratedwere divided chemical into those plant. of the 2. Formulation of mathematical2 criteria to be satisfied by node i only in the direction of the arrows along a path in the Whenever we approach a design problem, establishing suita- regulatory and of the optimizing type. The first can always be every feasible control structure. 3 graph. ble process models offers great difficulties. The underlying expressed in the form of functions of operating variables, which Govind and Powers (1976) used a steady-state cause and effect philosophy is to make initial decisions based on a crude model, have to be kept at desired levels through the use manipulated 3. Development of guidelines for decomposing the overall graph as their basic modeling for the synthesis of control struc- SCOPE problem into manageable subproblems. and refine the model appropriately after each design step. The variables. The same is possible for the second, if certain condi- tures and accessibility, as one of the feasibility criteria that a control structure should satisfy. We show this later to be in- use of a simple model at the start is adopted here. The most In Part I, thetions control derived tasks in Part were I are divided satisfied. into Thethose structure of the of the2. feed- Formulation 4. Algorithmicof mathematical procedure criteria toto developbe satisfied alternative by control regulatory andback of thecontrollers optimizing used type. for thatThe firstpurpose can alwaysis developed be hereevery on feasible a structures. control structure. sufficient, i.e., additional modeling is needed and further feasi- primitive model for control purposes is one which displays the expressed in thesound form theoretical of functions basis, of operating The fnllowing variables, problems which are addressed: Y bility criteria should be imposed. structural dependencies of the variables only, showing if the have to be kept 1.at desiredDevelopment levels throughof a suitable the usetype manipulated of system representation 3. Development The of approach guidelines adopted for decomposing in this work isthe based overall on the structural time derivative of one variable depends on another or not. For variables. The(model), same is requiringpossible for a theminimal second, amount if certain of information. condi- problem into characteristicsmanageable subproblems. describing (a) the interactions among the units tions derived in Part I are satisfied. The structure of the feed- of a chemical process and (b) the logical dependence (of the FEASIBILITY ANALYSIS OF CONTROL STRUCTURES initial structural considerations, this turns out to be sufficient. 4. AlgorithmicBoolean procedure type) among to develop the variables alternative used to control model' the dynarnic back controllers used for that purpose is developed here on a structures. rrApart from the available engineering rules of thumb, we We found that the most efficient way to determine feasible w-2behavior of the various units. Thus, detailed dynamic model- sound theoretical basis, The fnllowing problems are addressed: u would like to establish rigorous mathematical critieria to decide sets of measured and manipulated variables, and to keep the 1. DevelopmentFigure of 1.a suitableThe double type effect of system evaporator. representation The approachling adopted at anFigure early in this2. stage The work digraph is isavoided. based for the on The double the mathematicalstructural effect evaporotor. feasibility characteristicscriteria describing for the(a) thegenerated interactions alternative among controlthe units structures are the feasibility of a suggested control structure. Every regulatory (model), requiring a minimal amount of information. control structure should achieve the following two objectives: (i) of a chemicalused process as an and illustrative (b) the logicalexample dependence at this point. (of theDeveloping the March, 1980 PageBoolean 233 type) among the variables used to model the dynarnic Be it a regulation or a servo problem, the goal is to bring several AlChE Journal (Vol. 26, No. 2) Page 232 March,- 1980 structural linearized equationsAlChE is quite Journal straightforward, (Vol. 26, andNo. is2) outputs of the system from an undesired state to the desired one behavior of thegiven various units. Thus, detailed dynamic model- by Newell and Fisher (1972). in some tolerable fashion, under the influence of disturbances ling at an earlyWi stage =fi(Cl,hl;F,BJ is avoided. The mathematical feasibility criteria for the generated alternative control structures are entering the system. (ii) On the other hand, we would like to yz =fdC 1,C*,h1 ;BI ,B 2) monitor the process almost continuously by observing all those Ci =f3(Cl,hi;F,C~) outputs which are critical for system performance. Page 232 March,- 1980 c, = f,(C 1,Cz,h,;BAlChE 1) Journal (Vol. 26, No. 2) The concepts of complete state controllability and observ- h, = f5(C 1 ,h 1;F,TF3 1 ability are generally believed to provide the necessary and where: sufficient conditions for a control structure to achieve the above holdup in the first effect W1 two objectives. This is not so, and in the following paragraphs, holdup in the second effect Wz WP discuss the shortcomings of these concepts. CI concentration in the first effect concentration in the second effect C2 CONTROLLABILITY AND OBSERVABILITY IN RELATION TO h, enthalpy in the first effect PROCESS CONTROL STRUCTURES F feedflowrate Cp concentration in feedstream The concept of controllability was introduced by Kalman TF feed temperature (1960) and states that a linear system with the state differential S1 steam rate equation outlet flowrate of first effect B1 i(t) = A(t) x (t) + B(t) u(t) (1) B2 outlet flowrate of second effect The structural matrix of this system is is said to be completely controllable if the state of the system can be transferred from the zero state at any initial time, to any W2 CV Si B2 1 W1 C1 C, hi I F TP B1 terminal state x(tJ = xi within a finite time tl - to, through the wx I X xlx x use of a piecewise continuons control input u(t). w; xxx xx IfA and B are constant matrices, it is well known that the pair Cl X xxx (A,B)is completely controllable if and only if cz xxx X rank (B, AB, A2B, . . . , A"-'B) = n (3) h'l X xx xx The mathematical implications of controllability with respect to The first part corresponds to the system matrix A, the con- existence and uniqueness of an optimal feedback control, eigen- troller matrix B will consist of a subset of the columns of the value assignment using state variable feedback etr. are available second part (e.g., Bl,Bz, F)while the remaining columns indi- in any textbook (Kwakernaak and Sivan 1972). We would like to cate the influence ofdisturbances. We can associate a graph with explore the usefulness of controllability for the synthesis of the system matrix which shows the mutual influence of the control structures. To avoid common misunderstandings, let us variables. The system variables form the state-nodes of the clarify the deficiencies of the definition and theorem above for graph. There is a directed edge from node i to node i, if the our purposes: structural system matrix has a nonzero entry in the ithrow and 1. The path for going from xo toxl is not completely arbitrary. thejthcolumn. The graph corresponding to the structural matrix Any practical control input might result in intolerably large above is shown in Figure 2. Each manipulated variable and deviations before we reach x, from xo. disturbance can be represented by a node, and its influence on 2. If the control u is bounded, we might not be able to reach the state variables shown graphically. The structural representa- xi in the specified amount of time, or not at all. tion ofa staged system gives rise to large matrices with repeated 3. We have no information concerning regulation, ~e.,what common structural elements. This observation has been used to to do when disturbances enter the system. reduce the size of the representation of complex staged systems, 4. Assuming that we are just interested in keeping a subset of without losing the fundamental information about the system the outputs at their setpoints in the face of disturbances by structure (see Appendix C). constructing feedback loops using the available manipulated In connection with structural matrices and their associated variables, we cannot deduce if and how this can be achieved. graphs, we define the generic rank pu of a structural matrix to 5. The rank test gives us no quantitative clues as to "how be the maximal rank a matrix achieves as a function of its free controllable" a system is. parameters, e.g., the matrix 6. The rank test might fail because of some unfortunate pa- rameter choice. In reality, most of the system parameters are determined experimentally and not known exactly. An arbi- trarily small variation in some of the parameters might make the has a generic rank of 2 despite the fact that one of the diagonal system controllable.

Page 234 March, 1980 AlChE Journal (Vol. 26, No. 2) Control Structures

Automatica 37 (2001) 487}510

Survey Paper A review of methods for input/output selectionଝ Marc van de Wal! , Bram de Jager" * !Philips CFT, Mechatronics Motion, P.O. Box 218, SAQ-2116, 5600 MD Eindhoven, Netherlands "Faculty of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, Netherlands Received 11 June 1998; revised 3 July 2000; received in "nal form 6 September 2000

Abstract

Control system design involves input/output (IO) selection, that is, decisions on the number, the place, and the type of actuators and Computers and Chemical Engineering 28 (2004) 219Á/234 sensors. The choice of inputs and outputs a!ects the performance, complexity, and costs of the control system. Due to the www.elsevier.com/locate/compchemeng combinatorial nature of the selection problem, systematic methods are needed to complement one's intuition, experience, and physical insight. This paper reviews the currently known IO selection methods, which aids the control engineer in picking a suitable method for the problem at hand. The methods are grouped according to the control system property that is addressed and applications are grouped accordingControl to the considered structure control systems. design A set forof criteria complete is proposed that chemical a good IO selection plants method should possess. It is used to assess and compare the methods and it could be used as a guideline for new methods. The state of the art in IO selection is sketched and directions for further research are mentioned.Sigurd Skogestad! 2001 Elsevier+ Science Ltd. All rights reserved.

Keywords: ControlDepartment system of Chemicaldesign; Structural Engineering, properties; Norwegian Input University signals; of OutputScience and signals; Technology Controllability; (NTNU), Observability; 7491 Trondheim, Relative Norway gain array; Robust control

Abstract 1. Introduction (PID, LQG, adaptive control, H optimization, etc.) Control structure design deals with the structural decisions of the controldepends system, on including aspects like what the to control control and goal, how model to pair accuracy, the vControlariables to system form control design loops. could Although be split theseinto the are followingvery important issues,and these restrictions decisions areon in the most implementation. cases made in an ad Fifth, hoc the fashion, based on experience and engineering insight, without considering the details of each problem. In the paper, a systematic sixprocedure steps. First, for control the structure control design goals for are complete formulated. chemical This plants (plantwideclosed-loop control) system is presented. is evaluated It starts with via carefully simulations defining or pilot involvesthe operational choosing and and economic characterizing objectives, andthe exogenousthe degrees of vari- freedom avplantailable experiments. to fulfill them. InOther the issues, last discussed step, the in controller the paper, and ablesincludew and inventory choosing and production and imposing rate control, requirements decentralized onv theersus multihardwarevariable control, like sensors, loss in performance actuators, by and bottom-up control design, processors controlledand a definition variables of a thez, ‘‘complexity see Fig.number’’ 1. Thefor control the control goals system.are implemented in the real plant. Iterative re"nements of should# 2003 be Else quantivier Ltd."ed All rightsin the reserved. time and/or frequency these steps are often necessary, e.g., meeting the control domain. The choice of z may be a!ected by the outcome goal might call for a more accurate model or a modi"ca- Keywords: Control structure design; Chemical plants; Plantwide control; Process control of the other steps of control system design, like the choice tion of controller parameters. of the plant model G in the second step of control system The third step of control system design, i.e., control design.1. Introduction The techniques used in other steps also determine controllerstructure design, selection, and is inv usuallyolves the split following into twotasks separate the model type, e.g., linear or nonlinear, time-invariant or (Foss,problems 1973); which (Skogestad are then & Postlethwaite, solved successively: 1996): input/out- time-varying,A chemical physical plant may principles have thousands or black of box. measure- In the put (IO) selection, which is the focus of this paper, and thirdments step, and the control control loops. structure In practice, is selected. the control Fourth, system the 1.control selection con of" manipulatedguration (CC)variables selection.m (‘‘inputs’’); Approaches to controlleris usuallyK diisvided designed. into se Theveral choice layers, of separated the design by method time 2.solve selection IO and of controlledCC selectionvariables jointly (‘‘outputs’’; are seldomlyvari- encoun- scale, including (see Fig. 1): teredables in with the setpoints); literature. Here, the IO selection problem is 3.posed selection as follows: of (extra) measurements (for control . scheduling (weeks), purposes including stabilization); ଝ . Thissite-wide paper was optimization not presented (days), at any IFAC meeting. This paper was 4. selection of control configuration (the structure of recommended for publication in revised form by Editor Manfred Select suitable variables u to be manipulated by the . local optimization (hours), the overall controller that interconnects the con- Morari. controller (plant inputs) and suitable variables y to be supervisory (predictive, advanced) control (minutes), trolled, manipulated and measured variables); .* Corresponding author. Tel.: #31-40-2472784; fax: #31-40- supplied to the controller (plant outputs). 2461418.. regulatory control (seconds) 5. selection of controller type (control law specifica- E-mail addresses: [email protected] (M. van de Wal), tion, e.g. PID, decoupler, LQG, etc.). a.g.de.jagerHere, we@ considerwfw.wtb.tue.nl the (B. lower de Jager). three layers. Both the inputs and the outputs of G are divided into two  http://www.wfw.wtb.tue.nl/english/research/control/The local optimization layer typically recomputes new Controlclasses, structurebut in this design paper for the complete terms chemical`inputsa plantsand `out- marcw/.setpoints only once an hour or so, whereas the feedback isputs alsoa knownare reserved as plantwide for u controland y.. Each In practice, combination the of layers operate continuously. The layers are linked by the problem is usually solved without the use of existing 0005-1098/01/$-controlled variables see front, whereby matter ! the2001 setpoints ElsevierScience are computed Ltd. All rightstheoretical reserved. tools. In fact, the industrial approach to PII:by S the 0 0 upper0 5 - 1 0 layer 9 8 ( 0 0and ) 0 0 implemented 1 8 1 - 3 by the lower layer. plantwide control is still very much along the lines An important issue is the selection of these variables. described by Buckley in 1964 in his chapter on Overall Control structure design deals with the structural process control. The realization that the field of control decisions that must be made before we start the structure design is underdeveloped is not new. Foss (1973) made the observation that in many areas application was ahead of theory, and stated that:  Extended version of this paper ‘‘Plantwide control: towards a systematic procedure’’ from ESCAPE 12 Symposium, Haag, May 2002. The central issue to be resolved by the new theories

* Tel.: /47-7349-4154; fax: /47-7349-4080. is the determination of the control system struc- E-mail address: [email protected] (S. Skogestad). ture. Which variables should be measured which

0098-1354/03/$ - see front matter # 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.compchemeng.2003.08.002 Major Themes of George’s Research Program in the 1970s

“The Research Community is studying the wrong problem”

• Architectures – Control Structure – Decomposition for optimization • Design for Control Design for Control Design for Control Design for Control Outline • My Time with George at U of MN • Past Attempts to Predict the Future • Predicting the Future Predicting the future in 1990 Digital Equipment Corp. (DEC) and DuPont

Voice Control Finger Print ID Video Phone Operator Screen Predicting the future in 1990 Digital Equipment Corp. (DEC) and DuPont

Voice Control Finger Print ID Video Phone Operator Screen Outline • My Time with George at U of MN • Past Attempts to Predict the Future • Predicting the Future Status Assessment and Trends • Interest in control is at an all-time high Graduate Course Enrollments ETH

2008 2009 2010 2015/16

MPC 32 44 67 149

Linear Systems 34 42 59 63

Dynamic 72 101 140 218 Programming Status Assessment and Trends • Interest in control is at an all-time high • Interest in computer science is at an all-time high CS Majors at Caltech Status Assessment and Trends • Interest in control is at an all-time high • Interest in computer science is at an all-time high • Interest in traditional positions in “hot” areas is low Raff D’Andrea PhD students & Post-Docs since moving to ETH

Federico Augugliaro startup Mark Muller assistant professor (Berkeley) Philipp Reist startup Luca Gherardi startup Gajamohan Mohanarajah startup (founder) Markus Waibel startup (founder) Markus Hehn startup (founder) Sergei Lupashin startup (founder) Raymond Oung startup Sebastian Trimpe group leader (Max Planck) Angela Schoellig assistant professor (U. of Toronto) Michael Sherback startup Frederic Bourgault startup Guillaume Ducard assistant professor (U. of Nice) Oliver Purwin startup Status Assessment and Trends • Interest in control is at an all-time high • Interest in computer science is at an all-time high • Interest in traditional positions in “hot” areas is low • Interest in predictive control is at an all-time high American Control Conference 2017

• 65 / 900 papers on MPC Mark W. Mueller Example problem PhD Thesis, ETH (w/ Raff D’Andrea) ● Hit back a thrown ball ● Implicit feedback law updated at 20ms – Try 10’000 trajectories

● Sample different ways to hit the ball – Apply first 20ms of the best one

10 Evaluation

● Algorithm evaluated in the Flying Machine Arena

● System limits

11

MPC@MHz Jerez, Goulart, Richter, Constatinides, Kerrigan, Morari, IEEE TAC 2014

Motivation Prove feasibility of online optimization@MHz sampling rate

Setup - Algorithms: first-order methods (FGM, ADMM) - Implementation: hand-crafted fixed-point VHDL design on high-end FPGA (Xilinx Vertex 7)

Case study deflection Control of Piezo-electric plate actuator signal in high-speed AFM (provided by IBM Zurich)

Objective: Maintain constant loading force actuation signal sample Piezo plate actuator scan direction Status Assessment and Trends • Interest in control is at an all-time high • Interest in computer science is at an all-time high • Interest in traditional positions in “hot” areas is low • Interest in predictive control is at an all-time high • Trends in software and hardware – Optimization software – Data and Connectivity – Validation and Verification Speedup of software for MIPs

Progress in MIP Solvers MILP Speedups

Calculations

Improvement in MIP Software from 1988-2017 Algorithms: 147650x Machines: 17120x

http://preshing.com/20120208/a-look-back-at-single-threaded-cpu-performance/ NET: (Algorithm Machine): 2,527,768,000x ⇥

What Does This “Mean”? A “typical” MILP that would have taken 124 years to solve in 1988 will solve in 1 second now. This is amazing, but your mileage may vary

Linderoth (UW ISyE) Quo Vadis MIP FOCAPO 12 / 58 Control and Optimization Control and Optimization Abundance of Data and Connectivity The New Opportunity

Price of sensors that make up the IoT will keep falling

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https://www.insightfromhbr.org/0210camp/voucher.cfm?cntry=SWITZ Page 1 of 1 Formal Verification of Embedded Software in Model Based Design • Model checking of safety properties for Simulink Models • Avionics distributed control system complexity: – 10K-250K simulink blocks – 40k-150K binary raw variables – Hundred to few thousand bin’s after simplification/abstraction • Automotive single controller complexity: – 5K-80K simulink blocks – Few thousand bin’s after simplification/abstraction • FormalSpecsVerifier tool environment (NuSMV)

Source: Alberto Ferrari Advanced Laboratory on Embedded Systems S.r.l. A Research and Innovation Company Status Assessment and Trends • Interest in control is at an all-time high • Interest in computer science is at an all-time high • Interest in traditional positions in “hot” areas is low • Interest in predictive control is at an all-time high • Trends in software and hardware – Optimization software – Data and Connectivity – Validation and Verification Dear George:

Thank you! Happy Birthday! Happy Retirement!