啤酒发酵过程的多变量开关控制仿真研究

442()Vol.44No.220053JournalofXiamenUniversity(NaturalScience)Mar.2005:2004202225:(1978-),,.3Correspondingauthor,Tel:[phone],E2mail:[e-mail],3,(,361005):,(Bang2Bang),Smith,,PID.,,,.:Bang2Bang;;;;:TS262.5:A:043820479(2005)0220246204,.[1]:.;,,,,,.,,.,M2PID[2][3][4][5][6][7].,,,(Bang2Bang).[8],,.,[9,10]Bang2Bang,,,,,Smith[11],,.11.1Bang2Bang,,,.,;(U,C,F],U,,C,F.C,.(U),C(),1)C={},.2)U={u1,u2,,un}.3)U={f1,,fm},X(fj),j=1,2,,m.4)fj,uixij=fj(ui),i=1,2,,n,j=1,2,,m,1ui:1(ui)={f1(ui),f2(ui),,fm(ui)}={xi1,xi2,,xim},xij=fj(ui).(1)5),uiX(1)B(1).B(1)X(1)[0,1],X(1).6)1-1(B(1)),UuiA-1-1(B(1))(ui)=B(1)(1(ui))(2)'1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.)ug(1gn).1.2,4)5).;,PID,e(k)e(k)2e(k),U={},xij(i=1,2j=1,2,3),.,,,Mm(1),Mm(x1,x2,,xm)=(x1,x2,,xm)=mj=1wjxj(3)wj[0,1](j=1,2,wj)mj=1wj=1..wj,(3)..X=(x1,x2,,xm),W=(w1,w2,,wm),.pi:eec,,w1=w2=0.5M2(e,ec)=0.5e+0.5ec.(e,ec)=(0.5,0.5),M2=0.5(0.5+0.5)=0.5;(e,ec)=(0.8,0.2),M2=0.5(0.8+0.2)=0.5.,eec.e,e,e;e,,,ec.,.[9,10]:w3ij=wijQ/xijij[0,0.5)wijQ/xij+ij[0.5,1]wijxij0xij0.5wijijzij[0,0.5)wijQ/xij+zij[0.5,1]wijxij0.5xij1.0(4)xij,¢ij,Q=zij[0,0.5]xij.:M3m(x1,x2,,xm)=(x1,x2,,xm)=mj=1w3ijxj(5),uiB(1)(1(ui)),.1.3Smith,;,,Smith.Smith,,.,[11],,,,,.,,Smith,.Smith1.2.,,.[1],G(s)=G11(s)G12(s)G21(s)G22(s)=-0.615915e-240s4844.18s2+286.25s+1-0.859148e-240s6241.28s2+450.76s+1-0.914839e-480s8147.96s2+515.95s+1-0.416558e-540s7679.75s2+444.95s+1(6)G3(s)G311(s)G312(s)G321(s)G322(s)=-82700s+1-52700s+1-52700s+1-82700s+1(7)7422:©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.:,ui:,Gij:,yij:,Yi:,G3ij:(i=1,2j=1,2)Fig.1multivariableon2offcontrolwithSmith2searchpredictort/h2PIDFig.2SimulationofconventionalPIDcontrolt/h4SmithPIDFig.4SimulationofconventionalPIDcontrollcombiningwithSmith2searchingpredictor25:A:,B:,C:,D:,E:t/h3Fig.3Simulationofon2offcontrolbasedonthefactorspacet/h5SmithFig.5Simulationofon2offcontrolbasedonthefactorspaceandcombiningwithSmith2searchingpredictor,F:.842()2005©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=u1u210s,PID2010.2,PID010.010,0.48.23,,Smith,PIDBang2Bang,,0.5.45SmithPID,(7),30min.4,PIDSmith,,,PID,.5,Smith,,,,,.SimulationofMultivariableOn2offTemperatureControlSysteminBeelFermentationProcessJIJun,JIANGQin2yin3,CAOZhi2kai(DepartmentofChemical&BiochemicalEngineering,XiamenUniversity,Xiamen361005,China)Abstract:Beerfermentationprocessisamultivariablecouplingsystemwithlargetimeconstantandlargedelaytime.Toensurethequalityofbeer,thefermentationtemperatureisdemandedtobecontrolledwithintherangeof0.5,butitsdifficulttobedone.Ontheotherhand,mostBeerfermentationtemperaturecontrolsysteminrecentreportswerecontinuouscontrolsystemusingtheservovalve.Butmostfactoriesinourcountrywouldliketousetheon2offvalvebecauseitischeaperthantheservovalve.SotheBang2Bangcontrolismoresuitableforthefermentationtemperaturecontrol.HowevertheresearchaboutBang2Bangcontrollerisfewintheinternalandoverseaspublication.ThispaperintroducesanewBang2Bangcontrolalgorithmbasedonthefactorspace.Variableweightisusedtodeterminetheswitchtimeandavoidtheshakeofcontroller.Itisnotnecessarytoadjustthecontrolparameter,soitseasytoberealized.Todealwiththedelaytimeincontrolsystem,conventionalSmithpredictoriscommonlyregardedasaneffectivemethod,buttherobustnessofconventionalSmithpredictorsispoor.SoaSmith2searchingpredictorisusedtoimprovetherobustnessoftheSmithcontroller.CombiningthefactorBang2BangcontrolandtheSmith2searchingpredictcontrol,anewbeerfermentationtemperaturecontrolsystemissuggestedinthispaper.Simulationshowsthatthisnewcontrolalgorithmisbetterthantheconvention2alPIDcontrolandismoreavailableforindustryapplication.Keywords:Bang2Bangcontrol;factorspace;variableweight;beerfermentation;multivariable3SmithBang2Bang,,,,.:[1],,.[J].,2001,31(4):502-508.[2],,.M-PID[J].,1999,20(1):87-89.[3].PID2P[J].(),1999,17(3):14-21.[4],,.PID[J].,2001,18(2):40-43.[5],,.[J].,2000:17(4):4-6.[6],,.[J].,1987,13(6):441-444.[7]IoanCristianTrelea,MarianaTitica.Predictivemodellingofbrewingfermentation:fromknowledge2basedtoblack2boxmodels[J].MathematicsandComputersinSimula2tion,2001(56):405-424.[8],.[M].:,1992.[9].()-[J].,1995,9(3):1-9.[10],,.[J].(),2002,41(4):448-452.[11].[J].,1997,1(1):107-111.9422:©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.