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1913©Vol.19No.1320077JournalofSystemSimulationJuly,2007•2995•PID1122111.201900;2.200030PIDPIDTP13A1004-731X(2007)13-2995-04OptimalPIDControlandSimulationforTime-delaySystemsWANGJian-guo1,GUTing-quan1,CAOGuang-yi2,ZHUXin-jian2,TANGCheng-long1,CHENPei-lin1(1.InstituteofEquipmentResearch,ShanghaiBaosteelTechnologyCenter,Shanghai201900,China;2.InstituteofFuelCell,ShanghaiJiaoTongUniversity,Shanghai200030,China)Abstract:Optimalcontrolfortwoclassesoftypicaltime-delaysystemsundercontrolenergyconstraintinprocesscontrolwasinvestigated.Anintegralsquareperformancecriterioncontainingtrackingerrorandcontrolenergywasdefined.SpectralfactorizationtominimizingtheperformanceindexfordifferentsystemswasappliedandcorrespondingparametertuningmethodsofPIDcontrollerwasderived,whichcouldbeusedtoobtainoptimalcontrolperformanceundercontrolenergyconstraint.Thevalidityoftheobtainedmethodscouldbeillustratedbysimulationresearch.Keywords:optimalPIDcontrol;controlenergyconstraint;spectralfactorization;time-delay1PID[1-4][5][6]Zigler-NicholsPID[7-8]PID[9]PID[10-11][12-13]2006-05-022007-04-25863(2003AA517020)(1974-),,,,;(1970-),,,,,;(1940-),,,,,[14]PIDPID11r(t)y(t)e(t)u(t)d(t)G(s)C(s)r(t)u(t)e(t)y(t)d(t)C(s)G(s)1DOI:10.16182/j.cnki.joss.2007.13.0291913Vol.19No.1320077July,2007•2996•Youla()()1()()QsCsGsQs=−(1)Q(s)()1()()SsGsQs=−(2)()()uSsQs=(3)2200(1)()()()Jetdtutudtεε∞∞=−+−∞∫∫(4)ε0ε1u(∞)Parseval(4)2222()1(1)2()(0)12uuSjJdSjSdωεωπωωεωπω∞−∞∞−∞=−+−∫∫(5)2PIDPID2.11()sGseTsτ−=(6)Pade1()(1)/(1)22GsssTsττ=−+(7)Q(s)'()()QssQs='()Qsu(∞)=0Su(0)=0(2)(3)(4)'()()QssQs=G(s)(7)2'2'11112(1)()212()jJQjjjTjQjdτωεωτπωωωεωω∞−∞−=−−++∫(8)'2|()|QjωH1111()()()()ssTTHsHsssεεεεεε−−+−−=(9)[15]467J2'21()()()2()()()()FjJQjHjHjFjDjdHjωωωπωωωωω∞−∞=++−−−∫(10)21()(1)(1)/(1)22FsssTsττε=−+−(11)2(1)()Dssε−=−(12)2222()(1)()()(1)FsTDsHsTsεεεε−−=−−−(10)'()Qjω[15]16.2(10)'()Qs'1()()()()stablepartFsQsHsHs⎧⎫=−⎨⎬−⎩⎭(13)'()QsQ(s)()11TsQsTsεε=+−(14)Q(s)Ts/(1)Tλεε=−(14)(1)PID11()(1)1PDFCsKTsTs=++(15)1PTKTετε=+−2DTτ=12()1FTTTετεετε−=+−(16)2.2()1sKGseTsτ−=+(17)Pade()(1)/(1)122KGsssTsττ=−++(18)K()1/uK∞=(0)1/uSK=(2)(3)(18)(4)222211(1)21()21121()jKJQjjTjQjdKτωεωτπωωωεωωω∞−∞−−=−+++−∫(19)2|()|Qjω1913Vol.19No.1320077PIDJuly,2007•2997•H221(1)()()()1()1(1)()1()KsTHsHsssTKsTssTεεεεεεεε+−+−=++−−−−(20)221()()()2()()()()FjJQjHjHjFjDjdHjωωωπωωωωω∞−∞=++−−−∫(21)21112()[(1)]112sKFssTsKsτεετ+=−+−+−(22)21()[(1)]DssKεε=−−+(23)2()()()FsDsHs−−(21)(13)(21)Q(s)21()(1)(1)TsQsKTsKεεε+=++−(24)Q(s)(1)/TsK+'2/[(1)]TKλεεε=+−(24)(1)PID211()(1)1PDIFCsKTsTsTs=+++(25)'''2,,,()22()2()2PIDFTTKTTTTKTτττλττλτλτ+==+==+++(26)3Q(s)G(s)PIDεPIDQ(s)εεPID4PID[13]31()101sGses−=+(27)ε=0.010.10.5(24)'λ(25)PIDPID23ε(ε=0.010.10.5)01020304050T/SU1086420201020304050T/SY10.80.60.40.203T=050E(T)()()uutu∆=−∞ε1PID22||||u∆12.5ε0.11913Vol.19No.1320077July,2007•2998•1εε0.01ε0.1ε0.522||||u∆40.3912.395.60822||||e3.5564.6046.5472222||||(1)||||ueεε∆+−3.9745.3836.076εPID5PID:[1],,.PID[J].,2000,26(3):347-355.[2],.PID[J].,2003,15(3):389-392.(WANGYin-song,LiuWu-lin.AKindofPID-TypedFuzzyNeuralNetworkController[J].JournalofSystemSimulation,2003,15(3):389-392.)[3],,,.PID[J].,2004,16(6):1330-1332.(WANGJian,CAOBing-gang,WANGKun,CHANGDong-ying.ASeeker-angle-tracingSystemonFuzzyPID[J].JournalofSystemSimulation,2004,16(6):1330-1332.)[4],,.PID[J].,2006,18(6):1729-1732.(WANGShuang-xin,JIANGYan,LIYa-guang.ChaosOptimizationStrategyonFuzzy-immune-PIDControlofTurbineRegulatingSystem[J].JournalofSystemSimulation,2006,18(6):1729-1732.)[5].[M].:,1993.[6]TyreusBD,LuybenWL.TuningPIcontrollersforintegrator/deadtimeprocesses[J].Ind.Eng.Chem.Res.(S0088-5885),1992,31(10):2625-2628.[7],,.PID[J].,1999,25(4):518-523.[8]ZhangWD.Quantitativeperformancedesignforintegratingprocesseswithtimedelay[J].Automatica(S0005-1098),1999,35(7):719-723.[9],,.PID[J].,2002,17(6):886-889.[10]BiQ,CaiWJ,LeeEL,WangQG,HangCC,ZhangY.RobustIdentificationofFirst-orderPlusDead-timeModelfromStepResponse[J].ControlEngineeringPractice(S0967-0661),1999,7(1):71-77.[11],,.[J].,2003,30(5):25-27.[12]HangCC,KJAstrom,WKHo.RefinementsoftheZiegier-Nicholstuningformula[J].IEEProc-D(S1025-8973),1991,38(2):111-118.[13]HungHP.AModifiedSmithPredictorwithanApproximateInverseofDead-time[J].AICHEJ.(S0001-1541),1990,36(5):1025-1031.[14]ChenJ,HaraS,ChenG.BestTrackingandRegulationPerformanceUnderControlEnergyConstraint[J].IEEETrans.Automat.Contr.(S0018-9286),2003,48(8):1320-1336.[15]GoodwinGC,GraebeSF,SalgadoME.ControlSystemDesign[M].UpperSaddleRiver,NJ:Prentice-Hall,2002.2975CAD:[1].[M].:,2004.[2].[M].:,2003.[3],.[J].,1999,11(3):145-151.[4],,,.[J].,2005,17(4):789-792.(SHAZhi-hua,GEYan-jun,ZHAOLiang,ZHANGSheng-fang.AReviewonModelingTechnologytoMachiningSimulation[J].JournalofSystemSimulation,2005,17(4):789-792.)[5]WiensGJ.Anoverviewofvirtualmanufacturing[C]//VirtualManufacturing-Proceedingof2ndAgileManufacturingconference(AMC’95),Albuquerque,NewMexico,USA:ERIPress.1995.[6]MichaelWeyrich,PaulDrews.Aninteractiveenvironmentforvirtualmanufacturing:thevirtualworkbench[J].ComputersinIndustry(S0166-3615),1999,(38):5-15.[7],,,.[J].,20