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1、4Set-pointOptimization4.1Steady-stateOptimizationinMultilayerProcessControlStructureThetaskofset-pointoptimizationinamultilayercontrolstructureistopro-videthedirectlysubordinatefeedbackcontrollersofthelowerlayerswithbestpossibleset-pointvalues,seeFig.1.2inChapter1andthediscussiontherein.“Thebes
2、tpossibleset-pointvalues”meansoptimaldynamictrajectoriesoroptimalconstant(steady-state)valuesoftheset-pointsleadingtomaximalachievablevaluesoftheprescribedeconomiccriteriaoftheprocessoperation,whilekeepingtheprocessvariableswithinsafeoperationlimitsandsatisfyingcertainadditionalconstraintsofate
3、chnologicalnature.Thecaseofsteady-state(static)optimizationwillbeconsideredinthischapter,asitdominatesinpracticeinprocessindustries,foranumberofwell-knownreasons,seee.g.,[16].Thecontrollersundersupervisionoftheoptimizationunitaretheadvan-cedcontrollersoftheconstraintcontrollayerandcertaincontro
4、llersofthedirectcontrollayer.Thelocationofthesubordinatefeedbackcontrollersisnotessentialforthetaskoftheoptimizationlayer,asfromthislayertheplantisseentogetherwithallfeedbackcontrollers,thefeedbackcontrolledplantisbeingoptimized.However,theinformationsentfromtheoptimiza-tionlayertotheconstraint
5、controllersisdifferentthanthatsenttothedirectcontrollersonly,fromthepointofviewofthekindofprocessvariables.Therefore,considerfirstthecasewithouttheconstraintcontrollayer,withdirectcontrolandoptimizationlayersonly,asdepictedinFig.4.1(comparewithFig.1.2).Thesteady-stateoptimizationproblemcannowbefo
6、rmulatedas(1.21)orinanequivalent,butformallysimplerform(1.22),whichisrepeatedhereforconvenience2744Set-pointOptimizationwOPTIMIZATIONcyFeedbackcontrolledplantDIRECTCONTROL(BASICCONTROL)measurementscontrolinputsPROCESS(PLANT)disturbancesFig.4.1.Feedbackcontrolledplantasanobjectforset-pointoptimi
7、zationinthetwo-layerstructure(withouttheconstraintcontrollayer)minQ(c,y)subj.to:y=F(c,w)(4.1)c∈Cy∈YIntheabovedescription,Fdescribesthesteady-stateprocessmodel,cdeno-testhevectorofdecisionvariablesoftheoptimizationproblem,beinginth
