Introduction
Inactualproblems,theperturbationofsystemcharacteristicsorparametersisofteninevitable.Therearetwomainreasonsfortheperturbation:oneisduetoinaccuratemeasurementTheactualvalueofthecharacteristicorparameterwilldeviatefromitsdesignvalue(nominalvalue),andtheotheristheslowdriftofthecharacteristicorparametercausedbytheinfluenceofenvironmentalfactorsduringtheoperationofthesystem.
Currentresearchonrobustnessismainlylimitedtolinearsteadycontrolsystems,andtheissuesinvolvedincludestability,nostaticerror,adaptivecontrol,etc.Therobustnessproblemiscloselyrelatedtotherelativestabilityofthecontrolsystem(aperformanceindexthatcharacterizesthestabilitymarginofthecontrolsysteminthefrequencydomain)andtheprincipleofinvariance(thetheoryofcontrollingandeliminatingtheinfluenceofdisturbancesonthecontrolsystemintheautomaticcontroltheory).Theestablishmentoftheinternalmodelprinciple(adesignprincipleofimplantingthedynamicmodelofexternallyactingsignalsintothecontrollertoformahigh-precisionfeedbackcontrolsystem)hasplayedanimportantroleintheresearchofrobustness.Earlyrobustcontrolfocusedonthesensitivityofsmallperturbationanalysis.Modernrobustcontrolfocusesontheanalysisanddesigntheoryandmethodsundernon-micro-boundedperturbationinthecontrolsystemandthenon-fragilecontrolmethodwithnon-micro-boundedperturbationinthecontroller.
Analysisanddesignmethodsofuncertainsystemsmustbeestablishedtomakethesystemrobust.Theuseoffeedbacktodesignarobustcontrolsystemisbasedonanincompletedescriptionofthecontrolledobject.Thisisdifferentfromthedesignofalinearmultivariablecontrolsystem,whichrequiresthemathematicalmodeloftheobjecttobeaccuratelyknowninadvance.
Classification
Robustnessincludesstabilityrobustnessandqualityrobustness.Whetheracontrolsystemisrobustornotisthekeytoitsactualapplication.Therefore,thedesignofmoderncontrolsystemshastakenrobustnessasoneofthemostimportantdesignindicators.
Inordertosolvetherobustnessproblemofcontrolsystems,twomaindirectionshaveemergedinrecentyears:oneisactiveadaptationtechnology,whichiscommonlycalledadaptivecontrolsystemdesigntechnology.Itusesidentificationmethodstocontinuouslyunderstandtheuncertaintyofthesystem,andadjuststhestructureandparametersofthecontrolleronthisbasis,sothatthesystemmeetstheperformanceindexrequirements.Theotherispassiveadaptationtechnology,whichisgenerallycalledrobustcontrol.Designtechnology.Designacontrollerforthesystemwithuncertainty,sothatwhenthesystemworkswithintheuncertaintyrange,itcanmeetthedesignperformanceindexrequirementsofthesystem.
Therobustnessofthecontrolsystemreferstotheabilityofthesystemtokeepcertainperformanceunchangedunderthedisturbanceofuncertainty.Iftheuncertaintyoftheobjectcanbedescribedbyaset,examinecertainperformanceindicatorsofthecontrolsystem,suchasstabilityqualityindicators,etc.,anddesignacontroller.IfthecontrollercanmeetthegivenrequirementsforeachobjectintheobjectsetPerformanceindex,thecontrollerissaidtoberobusttothisperformanceindex(characteristic).Therefore,whentalkingaboutrobustness,acontrollermustberequired,asetofobjectsandcertainsystemperformance.Forthecontrolsystem,twoimportantconceptsofrobustnessare:
StableandrobustRobustness:AcontrollerisrobustandstableifitcanensurethestabilityofthesystemforeachobjectinthesetP.
Qualityrobustness:AcontrollerisconsideredtobequalityrobustifitcanensuresystemstabilityandaspecificqualityforeachobjectinthesetP.
Robustcontrol
Robustcontrolisacontrollerdesignmethodthatfocusesonthereliabilityofcontrolalgorithms.Robustnessisgenerallydefinedastheminimumrequirementthatthecontrolsystemmustmeetinordertoensuresafetyintheactualenvironment.Oncethecontrollerisdesigned,itsparameterscannotbechangedandthecontrolperformanceisguaranteed.
Therobustcontrolmethodgenerallyassumestheinformationofthedynamiccharacteristicsoftheprocessanditsvariationrangeinthetimedomainorfrequencydomain.Somealgorithmsdonotrequireanaccurateprocessmodelbutsomeofflineidentification.Thedesignofgeneralrobustcontrolsystemisbasedonsomeworstcases,sothegeneralsystemdoesnotworkintheoptimalstate.
Therobustcontrolmethodissuitableforapplicationswherestabilityandreliabilityaretheprimarygoals.Atthesametime,thedynamiccharacteristicsoftheprocessareknownandtherangeofuncertainfactorscanbeestimated.Thecontrolofairplanesandspacevehiclesareexamplesofsuchsystems.Inprocesscontrolapplications,somecontrolsystemscanalsobedesignedwithrobustcontrolmethods,especiallyforthosethataremorecriticalandhave(1)awiderangeofuncertainfactors;(2)objectswithsmallstabilitymargins.
However,thedesignofarobustcontrolsystemmustbecompletedbyseniorexperts.Oncethedesignissuccessful,toomuchmanualinterventionisnotrequired.Ontheotherhand,ifyouwanttoupgradeormakemajoradjustments,thesystemmustberedesigned.
Usually,systemanalysismethodsandcontrollerdesignaremostlyestablishedbasedonmathematicalmodels,andvariousmethodshavebecomematureandperfect.However,therearealwaysuncertaintiesofonekindoranotherinthesystem.Whenmodelingthesystem,sometimesonlythesituationneartheoperatingpointisconsidered,resultinginartificialsimplificationofthemathematicalmodel;ontheotherhand,therearemanufacturingtolerancesbetweentheexecutivecomponentsandthecontrolcomponents,andthesystemoperationprocessalsohasaging,wear,andenvironmentandoperation.Deterioratingconditionsandotherphenomenamakemostsystemshaveuncertaintiesintheirstructureorparameters.Inthisway,theanalysisresultsofthesystemwithaccuratemathematicalmodelsorthedesignedcontrollersoftendonotmeettheengineeringrequirements.Inrecentyears,peoplehavecarriedoutresearchontherobustcontrolofuncertainsystems,andobtainedaseriesofresearchresults.Hoorobustcontroltheoryandμanalysistheoryarecurrentlyoneofthemostactiveresearchfieldsincontrolengineering,andhavebeenfavoredbycontrolresearchersformanyyears.Theauthorsystematicallystudiestherobuststabilityoflinearuncertainsystems,time-lagsystems,intervalsystems,anddiscrete-timesystems,andputsforwardtheanalysisanddesignmethodsoftherobuststabilityofthesystem.
Robustcontrolsystemdesign
Therearemanywaystodesignarobustcontrolsystem,includingrootlocusmethod,frequencyresponsemethodandITAE.Thetwobasictasksofrobustcontrolsystemdesignaretodeterminethecontrollerstructureandadjustthecontrollerparameterstoobtainthe"optimal"systemperformance.Intheprocessofrobustcontrolsystemdesign,itisusuallyassumedthatthecontrolledobjecthasacomprehensiveUnderstandingisaprerequisite,andthecontrolledobjectisusuallydescribedbyalineartime-invariantcontinuousmodel.Thechoiceofthecontrollerstructureisgenerallybasedonthestartingpointthatthesystemresponsecanmeetacertainperformancecriterion.
Inmanyoccasions,theidealdesigngoalofthecontrolsystemisthatthesystemcanaccuratelyandtimelyreproducetheinput.Correspondingly,theBodediagramofthesystemshouldbeveryflat,thatis,ithasaninfinitebandwidthof0dBgainandthephaseangleisalways0.However,sinceanysystemcontainsinductiveorcapacitivecomponentsthatstoreenergy,thereisnosuchidealsysteminpractice.Theseenergystorageelementsandtheirconnectionwithenergy-consumingcomponentsdeterminethedynamiccharacteristicsofthesystem.Suchasystemcanreproducesomeinputsquiteaccurately,butcannotreproduceotherinputsatall,thatis,thebandwidthoftheactualsystemisalwayslimited.
Robustdesign
Whenoptimizingthedesignbymakingtheproductperformancereachthetargetvalueandreducingtheirdeviation,therobustdesigntechnologyusesbothtraditionalideasandnewThought.Thefollowingaresomeoftheseideas.
Lossfunction
Thelossfunctionisaquadraticformulausedtoestimatethecostcausedbythedeviationofthemeanvaluefromthetargetvalueandproductperformance.Thiscostisbasedontheuser’sopinionTheeconomiclosscausedbyproductdefects.Thetraditionalmethodonlycalculatesthislosswhentheproductperformanceexceedstheuser'sspecificationrequirements.Therobustdesignmethodestimatesthislossonthebasisofthecurrentproductperformancedistribution(distributionnearthemeanvalue).
Orthogonalarray
Orthogonalarrayhasseveraluniqueproperties.Theycanworkinseveralranges,butthemostcommonareintwoorthreeranges.Oneoftheirmostimportantpropertiesisbalance:whentherangeinonecolumnisconstant,allotherrangesintheothercolumnswillbeobtainedbyrotatingtheirvalues.Byusingthisbalanceofthearray,theinfluenceofeachfactorcanbeeffectivelydetermined.
Signal-to-noiseratio
Thesignal-to-noiseratioisameasureoftheoutputperformancedeviationofarobustdesignexperiment.Thepurposeofthesignal-to-noiseratio(S/N)istoexpresstherepeatabilityoftheoutputperformanceasanumber.Thisnumbercanthenbetreatedinasimilarway,asinthecaseofbondingstrength,inordertoincreasethemeanvalue.
Robustdesignexperiment
Performingrobustdesignexperimentinvolvestheuseofmanyqualityengineeringtoolsmentionedearlier.Thesuccessofthisworkdependsonthecorrectselectionofteammembers,focusingonoptimizingandtestingappropriateperformance,andfollowingmethodologicalguidelines.Thestepsforasuccessfulrobustdesignexperimentareasfollows.
1.Problemdefinition.Thefirststepinconductingarobustdesignexperimentistooutlinetheobjectivesoftheexperimentanddefinetheprocessordesignperformancetobeoptimized.However,onlyoneperformancecanbeoptimizedatatime,andmanyperformancescanbemeasuredduringexperimentsandthenanalyzedseparately.Thefinalparameterselectionisamixtureofvariousrecommendedparameters,whichdependsonthecompromiseofdifferenttargetsforeachtargetperformancelevel.
Itisimportanttogeneratetheboundariesoftheproductordesigntobeoptimized.Theexperimentshouldbelimitedtoasmallrangeofdesign.Inotherwords,experimentsshouldnotattempttooptimizeallstepsoftheproductorprocess.
2.Theestablishmentandstabilityofthegroup.Aprojectteamshouldbeselectedforexperimentationandanalysis.Theteamshouldbecomposedofpeoplewithproductandprocessknowledge,andsolicittheopinionsofallpersonnelrelatedtotheoptimizationdesign.Theydonotneedtohavein-depthtechnicalunderstandingofthesubjectrelatedtotheproblem,buttheteammembersshouldhaveexperienceinsimilardesigns.Theteamshouldbeabletoobtainknowledgeofstatisticalmethodsandspecialrobustdesigntechniquesthroughstatisticiansorpersonnelwhohavereceivedrobustdesigntraining.
3.Parameterselection.Therobustdesignmethoddoesnotincludescreeningexperimentstonarrowtheselectedparametersetoftheoptimaldesign.However,teammembersmayregardthisprogramasanopportunitytotestmoreparametersordifferentlevelsandcombinationsofthesameparameters.Inthiscase,ascreeningexperimentmayberequiredtonarrowdowntheselectionofparameters.
Robustnessapplication
Inpractice,robustnessiswidelyused.Duetotheinaccuracyofmeasurementandtheinfluenceofenvironmentalfactorsduringoperation,itwillinevitablycausethesystemCharacteristicsorparametersdriftslowlyandirregularly,sorobustnessmustbeconsideredwhendesigningvarioustypesofcontrolsystemsusingcomplexityparadigms.Suchasorganizationalbehaviormanagement,formulationofstrategicplanning,provisionofdecision-makingplans,restorationofecosystems,dynamicbalance,geneticnetworks,dampingofgeneticvariation,developmentofbiologicalcomplexity,automaticselectionofdirectedevolutionaryevolution,anddistributedfeedbackintheimmunesystem.Nervoussystem,computernetworksystem,economicgameofeconomicandsocialsystem,socialsystem,politicalagreement,institutionalmechanism,etc.
Itisworthmentioningthatwiththeprocessoffinancialliberalizationandglobalization,thetrendoffinancialinnovationhasgraduallystrengthened,theuncertaintyofthefinancialsystemhasincreasedsignificantly,thefinancialdecision-makingenvironmenthasbecomemorecomplex,thefinancialmarketenvironmentandfinancialFundamentalchangeshavetakenplaceintheoperatingcharacteristicsofinstitutions.Manyscholarshaveacceleratedtheirresearchontherobustnessofthefinancialsystem,usingtheirresearchresultsintheeffectivenessofinvestmentdecision-making,financialriskmanagement,assetallocation,etc.,andachievedsignificantresults.
Themosttypicalapplicationisincomplexadaptivesystems.However,itwillhavepracticalsignificanceonlywhenitcanbeusedinsomeenvironmentstoachieveeffectsthatcannotbeachievedinotherways.Atthesametime,wemustpayattentiontotheissuesofcostandbenefit.Asauniversallaw,therearestrictconservationlawsinrobustsystemsthatrequirehightoleranceforcertainscenariosandnecessarilylowtoleranceforotherscenarios.Forexample,anaircraftiseitherhighlymaneuverable,orverycapableofresistinganti-aircraftgunfire,butnotboth.Anotherexampleisthatthereisagameproblembetweeneconomicgrowthandenvironmentalprotection,andtheeconomymustdevelopfasterandinanorderlymanner.Toconsumeresourcesandhaveacertainimpactontheenvironment,andemphasizingenvironmentalprotection,tosomeextent,willrestricteconomicgrowth.Whendesigningandusingrobustnesstosolvetheaboveproblems,itisnecessarytoconsidercostandbenefitissues.