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Proceedingsofthe2001IEEEInternationalSymposiumonIntelligentControlSeptember5-7,2001MexicoCity,MexicoGeneticAlgorithmsforOptimalControlofBeerFermentationG.E.Carrillo-Ureta,P.D.Roberts*andV.M.Becema**g.camllo@city.ac.uk,p.d.roberts@city.ac.ukandv.m.becerra@reading.ac.uk*CityUniversity,ControlEngineeringResearchCentre,NorthamptonSquare,LondonEClVOHB,U.K.UniversityofReading,DepartmentofCybernetics,ReadingRG66AY,U.K**Abstract-Thispaperusesgeneticalgorithmstooptimisethemathematicalmodelofabeerfermentationprocessthatoperatesinbatchmode.Theoptimisationisbasedinadjustingthetemperatureprofileofthemixtureduringafixedperiodoftimeinordertoreachtherequiredethanollevelsbutconsideringcertainoperationalandqualityrestrictions.IndexTerms-batchfermentation,beerfermentationmodelling,geneticalgorithms,optimalcontrolI.INTRODUCTIONThemodellingoffermentationprocessesisabasicpartofanyresearchinfermentationprocesscontrol.Sincealltheoptimisationworktobedoneisbasedonthereliabilityofthemodelequations,theyareimportantfortherightdesign.Theseequationsaregenerallynon-linear.Inbatchorfedbatchfermentationprocesses,thereisnosteadystate.Thecontrolofafermentationprocessisbasedonthemeasurementofphysical,chemicalorbiochemicalpropertiesofthefermentationbrothandthemanipulationofphysicalandchemicalenvironmentalparameters[8],[l11.Theheuristicmethodoftrialanderror,whichisusedtofindanoptimalorpseudo-optimaloperatingregimebymanipulatingtheprocesstechnologicalparameters,isoneoftheoldestoptimisationmethods.GeneticAlgorithmsarerandomsearchmethodsbasedonthemechanicsofnaturalselection,andnaturalgenetics.InordertouseGeneticAlgorithms,asolutiontotheproblemasagenome(orchromosome)mustberepresented.Thegeneticalgorithmthencreatesapopulationofsolutionsandappliesgeneticoperatorssuchasmutationandcrossovertoevolvethesolutionsinordertofindthebestone(s).AppropriateimplementationofGeneticAlgorithmsincludesthefollowingthreeaspects:definitionoftheobjectivefunction,definitionandimplementationofthegeneticrepresentation,anddefinitionandimplementationofthegeneticoperators.ThesimulationoftheselectedmodelhasbeenaccomplishedwiththehelpofSIMULINK(Version2.2)underMATLAB(version5.2)environmentasamodemandimprovedwayforprocesssimulationandpossiblecontrol.TheoptimisationoftheprocesshavebeenaccomplishedwiththeSHEFFIELDMATLABGENETICALGORITHMTOOLBOXVersion1.2whichisanovelinstrumentforimplementinggeneticalgorithmmethodsasscriptfilesthatcanbechangedaccordingtotheproblemrequirements[3].ArefiningprocedureforsmoothingthetemperatureprofileobtainedwiththeGeneticAlgorithmoptimisationhasalsobeenincludedtoachieveimplementableresults.11.DESCRIPTIONOFTHEPROCESSFermentationhascometohavedifferentmeaningstobiochemistsandtoindustrialmicrobiologists.Itsbiochemicalmeaningrelatestothegenerationofenergybythecatabolismoforganiccompounds,whereasitsmeaninginindustrialmicrobiologytendstobemuchbroader.Batchfermentationreferstoapartiallyclosedsysteminwhichmostofthematerialsrequiredareloadedontothefermentor,decontaminatedbeforetheprocessstartsandthenremovedattheend.Conditionsarecontinuouslychangingwithtime,andthefermentorisanunsteady-statesystem,althoughinawell-mixedreactor,conditionsaresupposedtobeuniformthroughoutthereactoratanyinstantoftime[5].Alcoholicbreweryfermentationisthemainobjectiveofthiswork.Brewingandtheproductionoforganicsolventsmaybedescribedasfermentationinbothsensesofthewordbutthedescriptionofanaerobicprocessasfermentationisobviouslyusingtheterminthemicrobiologicalcontext.Themicroorganismsorbiomassconcentrationsarethecentralfeatureoffermentationaffectingtheratesofgrowth,substrateconsumptionandproductformation.Growthandproductformationratesvarywithtimeduetoadependenceonthepresentstateofthebatch;characterisedbybiomass,substrateandproductconcentrations,dissolvedoxygentension,nutrientfeedratesandalsoontheconditionoftheculture[7],[lo].111.MATHEMATICALMODELInfermentation,anaccuratemathematicalmodelisindispensableforthecontrol,optimisationandthesimulationofaprocess.Modelsusedforon-linecontrolandthoseusedforsimulationwillnotgenerallybethesame(eveniftheypertaintothesameprocess)becausetheyareusedfordifferentpurposes;nomodelcanbesaidtobethebest.Themodelisnotexpectedtobeareconstructionoftheprocess,ratheritisintendedtoserveasasetofoperatorsontheidentifiedsetofinputs,producingsimilaroutputasexpectedfromtheprocess.Theproblemisthatinreallifetheprocessoutputisusuallycontaminatedwithnoiseandotherdisturbances,whereasideallythemodelshouldfollowthetrueoutputoftheunderlyingrepresentativeprocess,whichisunknown.Estimationalgorithms,ifproperlychosen,yieldtheparameter0-78034722-7/01/$10.0002001IEEE391valuesafterprocessingofdatacomingfrommeasurementsonthesystem.Forthepurposeofthiswork,akineticmodelhasbeenchosentobepartofthesimulationandoptimisation.Thismodelwasdevelopedandpublishedin[2].ThemodelwasobtainedfrommanyexperimentalstudiesatlaboratoryscalewiththenecessaryequipmentascanbeseeninFigure1.Themodelhasshowngoodresults,anditshouldbenotedthatittakesintoaccountrealisticaspectsoftheprocess,suchasthecharacteristicsofwortandyeast