外文翻譯-動(dòng)態(tài)自適應(yīng)粒子群算法和它的應(yīng)用程序來(lái)優(yōu)化PID參數(shù)

2023屆電子信息工程學(xué)院外文文獻(xiàn)及譯稿外文文獻(xiàn)題目：DynamicalAdaptiveParticleSwarmAlgorithmandItsApplicationtoOptimizationofPIDParameters姓名：學(xué)號(hào)：專業(yè)班級(jí)：自動(dòng)化B095學(xué)院〔部〕：電子信息工程學(xué)院指導(dǎo)教師：2023年5月30日AmericanJournalofOperationsResearch,2023,2,448-451doi:10.4236/ajor.2023.23053PublishedOnlineSeptember2023DynamicalAdaptiveParticleSwarmAlgorithmandItsApplicationtoOptimizationofPIDParametersJiminLi,GuolinYuResearchInstituteofInformationandSystemComputationScience,TheNorthUniversityforNationalities,Yinchuan,ChinaReceivedJune15,2023;revisedJuly18,2023;acceptedAugust5,2023ABSTRACTBasedonanewadaptiveParticleSwarmOptimizationalgorithmwithdynamicallychanginginertiaweight(DAPSO),itisusedtooptimizeparametersinPIDcontroller.ComparedtoconventionalPIDmethods,thesimulationshowsthatthisnewmethodmakestheoptimizationperfectlyandconvergencequickly.Keywords:ParticleSwarmOptimization;DynamicalAdaptive;PIDAutomaticRegulationSystem1.IntroductionParticleSwarmOptimizationisakindofsimulationgroup(Swarm)intelligentbehavioroftheOptimizationofthealgorithmproposedbyKennedyandEberhart[1]andothers.Itsthoughtsourcefrombirdpreyonbehaveiorresearch.ContrastingPSOwiththegeneticalgorithmandtheantcolonyalgorithm,thePSOmethodissimpleandeasytoimplement,anditcanbeadjustedlessparameterscharacteristics.So,itiswidelyappliedinthestructuraldesign[2],electromagneticfield[3]taskscheduling[4]engineeringoptimizationproblems.Intheparticleswarmalgorithm,theadjustedparame-tersarethemostimportantpartintheinertiaweights.Inordertofindainertiaofweightsselectionmethodwhichcangetthebestbalancebetweentheglobalsearchandlocalsearch,theresearchershaveputforwardtothelin-eardecreaseweights(LDIW)strategy[5],fuzzyinertiaweights(FIW)strategy[6],andrandominertiaweights(RIW)strategy[7],andsoon. Inthebasicthoughtofdiminishinginertiavalueguidance,thispaperintroducesanewadaptiveself-adaptinginertia,whichisbasedonexpectationsofsurvivalrate.Whentheexpectedsurvivalrategetssmaller,itshowsthattheoptimalparticledistancetopositionisfurther,atthistime,weshouldmakeparticlesintothelocalsearchrapidly,theauthorsshallproposeanewdynamicadaptiveparticleswarmoptimizationalgorithm(DAPSO),andusingthisalgorithmtocalculateoptimizerinthePIDregulatorparametersofindustrialcontrolsystem.Thispaperisdividedintofivesections.Section2includespreliminariesandrelatedresultswhichwillbeusedinlatersections.Section3isdevotedtointroducedynamicadaptiveparticleswarmoptimizationalgorithm.InSection4,weshallusethedynamicadaptiveparticleswarmoptimizationalgorithmtooptimizethePIDpa-rameters.Section5istheconclusionandworkingdirectioninthefurther.2.BasicPSOAlgorithmandtheRelatedConceptParticleswarmoptimizationwasfirstlyproposedin1995byKennedyandEberhart[1],usingthefollowingfor-mulaintheparticlegroupofoperation:(1)(2)which=1，2……，=1，2…….;Learningfactor,isnegativeconstants；Theparameters,isbetweentherandomnumbers=[–];isconstant.Thei-thparticlesinaD-dementionalvectoris,Inthespaceofflightspeedisand;Thei-thknownsofartosearchtheoptimumpositionis,theparticleswarmsofartosearchtheoptimalpositionis.Intheliterature[7],thespeedEquation(1)havemadethefollowingchanges:(3)wherewisinertiacoefficient，,arenonnegative,Equations(1)and(3)arebasicPSOiterativeformula.Experimentalresultsshowtheparticleswarmoptimizationalgorithmwhetherprematureconvergenceorglobalconvergence,particleswarmofparticleswillappear“together〞phenomenon.Therefore,westudythechangeoftheaffinitybetweenparticles,particleswarmstatecanbetrack,theaffinitybetweenparticlesreflectthesimilaritybetweentheparticle,whenaffinityislarge,andthenumberparticlesaremoresimilar.Conversely,similardegreeispoor.Weshallmakethepartsthoughtofimmunealgorithmtofusetheparticleswarmoptimizationalgorithm,andgivethenewdefinitionofaffinityandtheconceptofantibodyconcentration,theconstructionmethodofnonlinearadaptiveinertiatheweights,andbasedonthis,itimprovesthedynamicadaptiveparticleswarmoptimizationalgorithmin[8].3.DynamicAdaptiveParticleSwarmOptimizationAlgorithmNow,weintroducethedynamicadaptiveparticleswarmoptimizationalgorithm:DAPSOStep1:TheparticlepositionandspeedofRandominitialparticleswarm.Step2:Maketheparticles,tobethecurrentposition,settothebestpositionofparticlesininitialpopulation.Step3:Judgalgorithmconvergencecriteriawhethermeet,ifmeet,truetoStep5;or,executeStep4.Step4:Totheallparticlesofparticleswarm,executethefollowingoperations:1)Accordingtothetype(1),(2),(3)updatetheparticle’spositionandspeed;2)Accordingtothetypeofabove,deduceadynamicadaptiveinertiaweights,turntoStep2.Step5:output,thealgorithmtorunisend.4.UsingtheDynamicAdaptiveParticleSwarmOptimizationAlgorithmtoOptimizethePIDParameters4.1.PIDRegulatorParameters’OptimizationProblemIntheindustrialcontrolsystem,lotsofcontrolobjectsundertheactionofsteprepresentationtheoutputsignalisSformrisescurve,rightnow,canuseasecondorderinertiaanddelayedmodeltodescribeit.Itstransferfunctionis:(4)Inordertomakethecontrolobject’soutputyindisturbanceactionmaintain,weusuallyuseproportion,integral,differential(P,I,D)regulatortoformaconstantadjustmentsystem.Whentheproductionprocessisstable,whichobjectcharacteristicsarestable,、、和rebasicallyconstant,atthistime,PIDparameterswhichareonceadjustedwouldnotbecharged,but,whentheproductionprocessisinaconstantlychangedsituation,thereactionconditionssuchaschemicalengineeringchange,powerplantandthechangeofload,sosomeobject,,andwillhaveacorrespondingchanged,atthistime,ifwestillkeepPIDparametersunchanged,itwillbedifficulttoachievetheoptimalregulationeffect.Intheconditionofconstantfluctuation,becausethecomputerhasstrongabilityofcalculationandcontrolonflexibility,wecanachievetheadjustmenttypeDDCcontrol.Therefore,usingthecomputertocarryonthePIDregulatorparametersadjustmentandcontrolsystemhastheverystrongsuperiority[9].NowusingacomputertoachieveP,I,D,adjustmentthenwecontroluanddeviationbetweenetosatisfythe\(5)Or(6)Amongthem,u(n)forthecontroleffect;u(n–1)forthepreviouscontrolfunction;e(n)forthedeviation;ande(n–1)forthepreviousdeviation;ande(n–2)foragainthefirstdeviation.Tisthesamplingperiod,isgaincoefficientratio,isintegraltimeconstant,isdifferentialtimeconstant.Nowthetaskistosearchthebest:seekthePIDthreeparameters、、tomaketheobjectivefunctionisthesmallestItbelongstononlinearplanninginthemultivariatefunctionoptimizationproblem,andcannotuseamathematical(7)4.2.TheResultsoftheSimulationExperimentIfweinputthefollowingdata:VariablenumberN=3;thecalculationprecisionE=0.01;Compressionfactoris0.618;Expansionfactoris1.5.Theparametersofthecontrolledobjects=0.44s;=0.44s;=0.12s;ThetotalnumberofprintL3=30;agivennumberofcontrolsystem’sinputvalueR=10;PIDparameters、、initialvalueX(1,0)=1.5;X(2,0)=0.88;X(3,0)=0.11.ForDAPSO,thesizeofthegroupsetto30,theterminatealgebrais50,setforthisdrangeof15%,c1,c2areall2,amaximumofself-adaptinginertiais0.8,minimumnumberis0.2.Thecalculatedparameterscorrespondtothecontrolobject、andiswithagivennumber,theoptimalnumberofPIDregulatorparameters、、:=1.69764,=0.772662s,=0.229209s.Inaddition,when、、isthebestnumber,westillobtainallsamplingmomentsofoutputX1,anddeviationquantityX5,asisshowninTable1.ThesystemoutputovershootsisE=1.42%,thetransitionprocesstimeisTP=1.1s.Table1.Theoutputresultsofsystemsimulation.AccordingtothestandardoftheengineeringdesignmethodIsystem,thesystemoftheoutputovershootisE=4.3%,thetransitionprocesstimeisTP=1.76s.Contrastwiththeresults,itshowstheparameterswhichgetbyusingthisalgorithmaremuchsuperior5.ConclusionandWorkingDirectionThispaperputsforwardadynamicchangingtheinertiaweightsoftheadaptiveparticleswarmalgorithm(DAPSO),andusingthealgorithmtooptimizethePIDparameters,thesimulationresultsshowthatthismethod,contrastedwitharelativelyroutineofthesimplexmethod,hasalotofadvantages,suchasthefastspeed,accuracy,theoptimalspeed,accurate,toimprovethedynamicsystem,etc.Havingtheprospectofthegoodapplicationandthefurtherresearch,however,forthefunction,whichisverycomplexandexistsmanylocaloptimizationsneartheoptimalsolution,theresultsarenotveryideal.Therefore,furtherworkdirectionis:expandingthescopeofthealgorithmtesting,seekingthecooperatewaysbetweenparticles,andtoacertainextent,analysis,theconvergenceandrobustnessofPAPSO.6.AcknowledgementsThisworkissupportedbyNaturalsciencefoundationoftheStateEthnicAffairsCommissionofPRC;ZizhuNaturalScienceFoundationofBeifangUniversityforNationalities.Minis-tryofEducationScienceandtechnologykeyprojectsNaturalScienceFoundationfortheYouth.REFERENCES[1]J.KennedyandR.Eberhert,“ParticleSwarmOptimization,〞IEEEInternationalConferenceonNeuralNetworks,IEEEServiceCenterPress,IV.Piscataway,NewJersey,1995,pp.1942-1948.[2]C.Elegbede,“StructuralReliabilityAssessmentBasedonParticlesSwarmOptimization,〞StructuralSafety,Vol.27,No.2,2005,pp.171-186.doi:10.1016/j.strusafe.2004.10.003[3]J.PobinsonandY.Rahmat-Samii,“ParticleSwarmOptimizationinElectromagnetics,〞IEEETransactionsonAntennasandPropagation,Vol.52,No.2,2004,pp.397-406.doi:10.1109/TAP.2004.823969[4]A.Salman,I.AhmadandS.Al-Madani,“ParticleSwarmOptimizationforTaskAssignmentProblem,〞Micro-processorsandMicrosystems,Vol.26,No.8,2002,pp.363-371.doi:10.1016/S0141-9331(02)00053-4[5]Y.ShiandR.Eberhart,“EmpiricalStudyofParticleSwarmOptimization,〞InternationalConferenceonEvolutionaryComputation,IEEEServiceCenterPress,WashingtonDC,1999,pp.1945-1950.[6]Y.ShiandR.Eberhart,“FuzzyAdaptiveParticleSwarmOptimization,〞TheIEEECongressonEvolutionaryCompution,IEEEServiceCenterPress,SanFrancisco,2001,pp.101-106.[7]R.EberhartandY.Shi,“TrackingandOptimizingDynamicSystemswithParticleSwarm,〞TheIEEECongressonEvolutionaryComputation,IEEEServiceCenterPress,SanFrancisco,2001,pp.94-100.[8]J.M.Li,C.M.LeiandY.Qiao,“BasedonExpectationsofSurvivalRateDynamicAdaptiveParticleSwarmAlgorithm,〞JournalofNingxiaUniversity,Vol.12,2023,pp.347-350.[9]Y.X.YuanandW.Y.Sun,“OptimizationTheoryandMethod,〞SciencePress,Beijing,1999,pp.69-75.《美國(guó)運(yùn)籌學(xué)雜志》，2023.2:448–451動(dòng)態(tài)自適應(yīng)粒子群算法和它的應(yīng)用程序來(lái)優(yōu)化PID參數(shù)李繼民，郭林宇信息和系統(tǒng)計(jì)算科學(xué)研究所，北方民族大學(xué)，銀川，中國(guó)電子郵件2023年6月15日收到，2023年7月18日修訂，2023年8月5日接受摘要基于一種動(dòng)態(tài)改變慣性權(quán)重(DAPSO)的新的自適應(yīng)粒子群優(yōu)化算法，它用于優(yōu)化PID控制器參數(shù)。相比傳統(tǒng)的PID控制方法,仿真結(jié)果說(shuō)明,這種新方法使其優(yōu)化完全并且收斂得也很快。關(guān)鍵詞：粒子群優(yōu)化；動(dòng)態(tài)適應(yīng)性；PID自動(dòng)調(diào)節(jié)系統(tǒng)1.引言粒子群算法是一種模擬組(群)智能行為的優(yōu)化算法，是被尼肯迪和埃伯哈特等人提出來(lái)的，其思想來(lái)源是鳥類的捕食行為。與遺傳算法和蟻群算法相比擬，粒子群優(yōu)化算法的方法比擬簡(jiǎn)單并且容易實(shí)現(xiàn)，它可以實(shí)現(xiàn)調(diào)整較少參數(shù)的特征。因此，它被廣泛應(yīng)用于結(jié)構(gòu)設(shè)計(jì)、電磁場(chǎng)等工程優(yōu)化問題中。粒子群算法中,在慣性權(quán)重中最重要的局部是調(diào)整參數(shù)。為了找到一個(gè)最好的平衡全球搜索和本地搜索的慣性權(quán)重選擇方法，研究人員已經(jīng)提出了線性遞減權(quán)重〔LDIW〕的策略，模糊的慣性權(quán)重(FIW)策略和隨機(jī)慣性權(quán)重(RIW)策略等等。本著減少慣性權(quán)重的思想，本篇文章介紹了一種新的自適應(yīng)慣性權(quán)重，這是基于預(yù)期的存活率來(lái)的。當(dāng)預(yù)期的存活率變小，它進(jìn)一步顯示了最優(yōu)的粒子距離位置，在這時(shí)，我們應(yīng)該使粒子迅速進(jìn)入本地搜索。作者將提出一種新的動(dòng)態(tài)的粒子群算法(DAPSO)和使用該算法來(lái)計(jì)算優(yōu)化的PID調(diào)節(jié)器參數(shù)的工業(yè)控制系統(tǒng)。本文分為五個(gè)局部。第二局部和相關(guān)結(jié)果將在后面的局部中使用。第三局部是專門介紹動(dòng)態(tài)自適應(yīng)粒子群優(yōu)化算法的。第四局部中,我們將使用動(dòng)態(tài)自適應(yīng)粒子群優(yōu)化算法優(yōu)化PID參數(shù)。第五局部是結(jié)論和進(jìn)一步優(yōu)化的工作。2.根本的粒子群算法和相關(guān)的概念粒子群優(yōu)化算法是在1995年首先由由肯尼迪和埃伯哈特提出的。在粒子群操作中使用以下公式〔1〕〔2〕其中，=1，2……，=1，2…….，因子,是負(fù)常數(shù)，參數(shù)和是[–]之間的隨機(jī)數(shù)，是常數(shù)，i個(gè)粒子構(gòu)成了D維的矢量，在空中飛行的速度是，且;第i個(gè)粒子迄今為止搜索到的最優(yōu)的位置是，而整個(gè)粒子群迄今為止搜索到的最優(yōu)的位置，在文獻(xiàn)[7]中，速度方程(1)進(jìn)行了以下更改：〔3〕w是慣性系數(shù)，是負(fù)常數(shù)，方程(1)和(3)是根本粒子群優(yōu)化算法的迭代公式。實(shí)驗(yàn)結(jié)果說(shuō)明，粒子群優(yōu)化算法不管是早熟收斂還是全局收斂性，粒子群粒子總是呈現(xiàn)出在一起的現(xiàn)象。因此，我們需要研究有變化關(guān)系的粒子，粒子群狀態(tài)才可以被追蹤。粒子之間的密切關(guān)系反映了粒子之間的相似性，當(dāng)關(guān)系越密切，粒子之間越相似。相反，似相度是不高的。我們應(yīng)當(dāng)使局部免疫思想算法融合到粒子群優(yōu)化算法中，并給出了密切關(guān)系和群體凝聚度的新概念，非線性自適應(yīng)慣性權(quán)重就是基于此，并在此根底上，提高了動(dòng)態(tài)自適應(yīng)參數(shù)優(yōu)化算法。3.動(dòng)態(tài)自適應(yīng)粒子群算法和它的應(yīng)用程序來(lái)優(yōu)化PID參數(shù)現(xiàn)在介紹動(dòng)態(tài)自適應(yīng)粒子群優(yōu)化算法：動(dòng)態(tài)自適應(yīng)粒子群優(yōu)化算法第一步：隨機(jī)的粒子群初始位置和初始群速度；第二步：使是粒子當(dāng)前的位置，為當(dāng)前整個(gè)粒子群的最正確初始位置；第三步：判斷算法收斂條件是否符合,如果符合