自动化专业毕业论文外文文献翻译Word格式.docx
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Abstract:
Theauthorsofthispapertrytoanalyzethedynamicbehavioroftheproduct-sumcrisptypefuzzycontroller,revealingthatthistypeoffuzzycontrollerbehavesapproximatelylikeaPDcontrollerthatmayyieldsteady-stateerrorforthecontrolsystem.ByrelatingtotheconventionalPIDcontroltheory,weproposeanewfuzzycontrollerstructure,namelyPIDtypefuzzycontrollerwhichretainsthecharacteristicssimilartotheconventionalPIDcontroller.Inordertoimprovefurthertheperformanceofthefuzzycontroller,weworkoutamethodtotunetheparametersofthePIDtypefuzzycontrolleronline,producingaparameteradaptivefuzzycontroller.Simulationexperimentsaremadetodemonstratethefineperformanceofthesenovelfuzzycontrollerstructures.
Keywords:
Fuzzycontroller;
PIDcontrol;
Adaptivecontrol
1.Introduction
Amongvariousinferencemethodsusedinthefuzzycontrollerfoundinliteratures,themostwidelyusedonesinpracticearetheMamdanimethodproposedbyMamdaniandhisassociateswhoadoptedtheMin-maxcompositionalruleofinferencebasedonaninterpretationofacontrolruleasaconjunctionoftheantecedentandconsequent,andtheproduct-summethodproposedbyMizumotowhosuggestedtointroducetheproductandarithmeticmeanaggregationoperatorstoreplacethelogicalAND(minimum)andOR(maximum)calculationsintheMin-maxcompositionalruleofinference.
Inthealgorithmofafuzzycontroller,thefuzzyfunctioncalculationisalsoacomplicatedandtimeconsumingtask.TagagiandSugenoproposedacrisptypemodelinwhichtheconsequentpartsofthefuzzycontrolrulesarecrispfunctionalrepresentationorcrisprealnumbersinthesimplifiedcaseinsteadoffuzzysets.Withthismodelofcrisprealnumberoutput,thefuzzysetoftheinferenceconsequencewillbeadiscretefuzzysetwithafinitenumberofpoints,thiscangreatlysimplifythefuzzyfunctionalgorithm.
BoththeMin-maxmethodandtheproduct-summethodareoftenappliedwiththecrispoutputmodelinamixedmanner.Especiallythemixedproduct-sumcrispmodelhasafineperformanceandthesimplestalgorithmthatisveryeasytobeimplementedinhardwaresystemandconvertedintoafuzzyneuralnetworkmodel.Inthispaper,wewilltakeaccountoftheproduct-sumcrisptypefuzzycontroller.
2.PIDtypefuzzycontrollerstructure
Asillustratedinprevioussections,thePDfunctionapproximatelybehaveslikeaparametertime-varyingPDcontroller.Sincethemathematicalmodelsofmostindustrialprocesssystemsareoftype,obviouslytherewouldexistansteady-stateerroriftheyarecontrolledbythiskindoffuzzycontroller.ThischaracteristichasbeenstatedinthebriefreviewofthePIDcontrollerintheprevioussection.
Ifwewanttoeliminatethesteady-stateerrorofthecontrolsystem,wecanimaginetosubstitutetheinput(thechangerateoferrororthederivativeoferror)ofthefuzzycontrollerwiththeintegrationoferror.Thiswillresultthefuzzycontrollerbehavinglikeaparametertime-varyingPIcontroller,thusthesteady-stateerrorisexpelledbytheintegrationaction.However,aPItypefuzzycontrollerwillhaveaslowrisetimeifthePparametersarechosensmall,andhavealargeovershootifthePorIparametersarechosenlarge.Sotheremaybethetimewhenonewantstointroducenotonlytheintegrationcontrolbutthederivativecontroltothefuzzycontrolsystem,becausethederivativecontrolcanreducetheovershootofthesystem'
sresponsesoastoimprovethecontrolperformance.Ofcoursethiscanberealizedbydesigningafuzzycontrollerwiththreeinputs,error,thechangerateoferrorandtheintegrationoferror.However,thesemethodswillbehardtoimplementinpracticebecauseofthedifficultyinconstructingfuzzycontrolrules.Usuallyfuzzycontrolrulesareconstructedbysummarizingthemanualcontrolexperienceofanoperatorwhohasbeencontrollingtheindustrialprocessskillfullyandsuccessfully.Theoperatorintuitivelyregulatestheexecutortocontroltheprocessbywatchingtheerrorandthechangerateoftheerrorbetweenthesystem'
soutputandtheset-pointvalue.Itisnotthepracticefortheoperatortoobservetheintegrationoferror.Moreover,addingoneinputvariablewillgreatlyincreasethenumberofcontrolrules,theconstructingoffuzzycontrolrulesareevenmoredifficulttaskanditneedsmorecomputationefforts.HencewemaywanttodesignafuzzycontrollerthatpossessesthefinecharacteristicsofthePIDcontrollerbyusingonlytheerrorandthechangerateoferrorasitsinputs.
OnewayistohaveanintegratorseriallyconnectedtotheoutputofthefuzzycontrollerasshowninFig.1.InFig.1,
and
arescalingfactorsforeand~respectively,andflistheintegralconstant.Intheproceedingtext,forconvenience,wedidnotconsiderthescalingfactors.HereinFig.2,whenwelookattheneighborhoodofNODEpointinthee-~plane,itfollowsfrom
(1)thatthecontrolinputtotheplantcanbeapproximatedby
(1)
Hencethefuzzycontrollerbecomesaparametertime-varyingPIcontroller,itsequivalentproportionalcontrolandintegralcontrolcomponentsareBK2DandilK1Prespectively.WecallthisfuzzycontrollerasthePItypefuzzycontroller(PIfc).WecanhopethatinaPItypefuzzycontrolsystem,thesteady-stateerrorbecomeszero.ToverifythepropertyofthePItypefuzzycontroller,wecarryoutsomesimulationexperiments.Beforepresentingthesimulation,wegiveadescriptionofthesimulationmodel.InthefuzzycontrolsystemshowninFig.3,theplantmodelisasecond-orderandtypesystemwiththefollowingtransferfunction:
(2)
WhereK=16,
=1,and
=0.5.Inoursimulationexperiments,weusethediscretesimulationmethod,theresultswouldbeslightlydifferentfromthatofacontinuoussystem,thesamplingtimeofthesystemissettobe0.1s.Forthefuzzycontroller,thefuzzysubsetsofeanddaredefinedasshowninFig.4.Theircores
ThefuzzycontrolrulesarerepresentedasTable1.Fig.5demonstratesthesimulationresultofstepresponseofthefuzzycontrolsystemwithaPlfc.Wecanseethatthesteady-stateerrorofthecontrolsystembecomeszero,butwhentheintegrationfactorflissmall,thesystem'
sresponseisslow,andwhenitistoolarge,thereisahighovershootandseriousoscillation.Therefore,wemaywanttointroducethederivativecontrollawintothefuzzycontrollertoovercometheovershootandinstability.WeproposeacontrollerstructurethatsimplyconnectsthePDtypeandthePItypefuzzycontrollertogetherinparallel.WehavetheequivalentstructureofthatbyconnectingaPIdevicewiththebasicfuzzycontrollerseriallyasshowninFig.6.Where~istheweightonPDtypefuzzycontrollerandfiisthatonPItypefuzzycontroller,thelargera/fimeansmoreemphasisonthederivativecontrolandlessemphasisontheintegrationcontrol,andviceversa.Itfollowsfrom(7)thattheoutputofthefuzzycontrolleris
(3)
3.Theparameteradaptivemethod
Thusthefuzzycontrollerbehaveslikeatime-varyingPIDcontroller,itsequivalentproportionalcontrol,integralcontrolandderivativecontrolcomponentsarerespectively.WecallthisnewcontrollerstructureaPIDtypefuzzycontroller(PIDfc).Figs.7and8arethesimulationresultsofthesystem'
sstepresponseofsuchcontrolsystem.Theinfluenceof~andfltothesystemperformanceisillustrated.When~>
0and/3=0,meaningthatthefuzzycontrollerbehaveslikePDfc,thereexistasteady-stateerror.When~=0andfl>
0,meaningthatthefuzzycontrollerbehaveslikeaPIfc,thesteady-stateerrorofthesystemiseliminatedbutthereisalargeovershootandseriousoscillation.
When~>
0and13>
0thefuzzycontrollerbecomesaPIDfc,theovershootissubstantiallyreduced.Itispossibletogetacomparativelygoodperformancebycarefullychoosingthevalueof
.
4.Conclusions
Wehavestudiedtheinput-outputbehavioroftheproduct-sumcrisptypefuzzycontroller,revealingthatthistypeoffuzzycontrollerbehavesapproximatelylikeaparametertime-varyingPDcontroller.Therefore,theanalysisanddesigningofafuzzycontrolsystemcantakeadvantageoftheconventionalPIDcontroltheory.AccordingtothecoventionalPIDcontroltheory,wehavebeenabletoproposesomeimprovementmethodsforthecrisptypefuzzycontroller.
IthasbeenillustratedthatthePDtypefuzzycontrolleryieldsasteady-stateerrorforthetypesystem,thePItypefuzzycontrollercaneliminatethesteady-stateerror.Weproposedacontrollerstructure,thatcombinesthefeaturesofbothPDtypeandPItypefuzzycontroller,obtainingaPIDtypefuzzycontrollerwhichallowsthecontrolsystemtohaveafastriseandasmallovershootaswellasashortsettlingtime.
ToimprovefurthertheperformanceoftheproposedPIDtypefuzzycontroller,theauthorsdesignedaparameteradaptivefuzzycontroller.ThePIDtypefuzzycontrollercanbedecomposedintotheequivalentproportionalcontrol,integralcontrolandthederivativecontrolcomponents.Theproposedparameteradaptivefuzzycontrollerdecreasestheequivalentintegralcontrolcomponentofthefuzzycontrollergraduallywiththesystemresponseprocesstime,soastoincreasethedampingofthesystemwhenthesystemisabouttosettledown,meanwhilekeepstheproportionalcontrolcomponentunchangedsoastoguaranteequickreactionagainstthesystem'
serror.Wit