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翻译部分英文原文NonlinearIdentificationofHydraulicServoDriveSystems1.IntroductionHydraulicservodrivesareusedinmanyindustrialplants,becausetheycanproducelargeforcesandtorqueswithhighspeed.However,therathercomplexstructuresofsuchdrivesystemsmakeitdifficulttodevelopsuitable,preferablylowordermodelsofthedynamicoftheplant.Themodelsareneededforthedesignofstateobservers,filtersandcontrollers.Thedesignismostsimplifiedifthemodeloftheplanthasanonlinearcanonicalform.Inactualhardivare,however,systemsrarelyhavethesesuitableforms.Nonlineartransformationsintocanonicalformsthereforemustfirstbedeterminedunderrigorousconditionsandwithconsiderablemathematicoeffortintegrationofpartialdifferentialequationsandinversionofnonlinearalgebraicequations.Toavoidthis,thepracticalapplicationofsystemidentificationtechniquesprovidessatisfactorymodelsofindividualunitsinsomedesiredform.Theaimoftheresearchpresentedinthisarticleistoobtainmodelsofahydraulicservodrivedirectly,inthenonlinearobservercanonicalform,viaparameteridentification.Inrecentyears,muchefforthasbeendevotedtomodelingofhydraulicsystemsusingbilinearmodels.Severalofthesemodelshavebeenevaluatedbytestsonrealplants,andarewellestablished.However,theidentificationmethodsused,themaximumlikelihoodmethodandpredictionerrormethod,requiresuitablyspecifiedagoodenoughinitialvaluesoftheunknownparametersandstatesofthesystem.Anunsuitablechoicecausesconvergenceandsingularityproblemsthat,inrealapplications,areverydifficulttosolve.Inthisarticle,theparameterestimationisbasedonamodifiedRecursiveInstrumentalVariablesalgorithmthatenablesustocvercomethedifficultiesmentionedabove.Weconsiderstatequadraticnonlinearitiesforbettermodelingoftherealdynamicsofhydraulicdrives.Forhandingtimederivativesofmeasurements,thesocalledLinearIntegral.FilterproposedbysagaraandZhaoisused.Theidentificationprocedureisappliedtoanexperimentalsetup.Agoodcorrespondenceisobtainedbetweenthedateandthemodelswhichareidentifieddirectlyinnonlinearespeciallyquadraticobservercanonicalform.2.DescriptionoftheHydraulicDriveThephysicalprocessusedastestingbenchconsistsofaservovalueandahydrauliccylindercoupledwithamovingmass.Iuustratestheteststandusedinthisstudy.Inordertoavoidtherepresentationofmanyequationswhichmaybefound,forinstance,inDietzandProchnioandKoeckemann,aschematicdiagramofthesystemisshowninandadetailedblockdiagramisgivenin.Theinputsignalofthesystemisthevoltageandtheoutputsignalisthepositionxofthemovingmass.ThestatevariablesarelistedinTable.Themostsignificantnonlinearitiesoftheplantarethemultipliers,thesquarerootfunctions,theoilelasticityandthefriction.Inpractice,itisdifficulttodeterminethephysicalparametersassociatedwiththesenonlinearities.Thussystemidentificationtechniquesareneededtoobtainapproximatemodelsofthesystemsuchthattheerrorbetweenmeasureddataandmodelisminimized.3.IdentificationThecontinuousparameterestimationfromsampleddataofinputoutputmeasurements.Forthis,SagaraandZhaoproposedanoperationofnumericalintegration,thesocalledLinearIntegralFilterLEforlineardifferentialequations.Thismethodwillbeextendedwiththegoaltoidentifysomelineatinparametersnonlinearsystemslikethoseinobservercanonicalform.4.LinearIntegralFilterCommonly,onlythelineartermsin10areconsidered.Thehigherordertermsarethusignoredfollowingtheassumptionthattheyarenegligiblewhenthesystemsstateclosetothereferencepointchosenforthelinearization.Inthisarticlewegotwostepsfurtherbytakingintoaccountalsothebilinearandthequadraticapproximationwhileaddingalottothecomputationalburden,theywillbeleftasideintheapplicationonthehydraulicdrivepresentedhere.Nevertheless,theidentificationmethodwillbederivedforany.Furthermore,thefilterparameter1affectsconsiderablytheaccuracyoftheparameterestimation.ItispointedoutbySagaraandZhao6thatshouldbechosensothatthefrequencybandwidthoftheLIFmatchesascloselyaspossiblethefrequencybandofthesystem.Inparacticaluse,however,aprioriinformationaboutthefrequencybandofthesystemareoftennotavailable.Therefore,manyidentificationexperimenttrialsmustbetaken.OneveryeffectivemethodistousetherecursiveinstrumentalvariableIVmethod,whichisasymptoticallylinbiasedforasuitablechoiceoftheIVanddoesnotrequireapricriknowledgeofthenoisestatistics.ThefollowingalgorithmisgivenbyLjungandsoederstrom.5.ExperinentalSetupandResultsTheexperimentalsetupconsideredhereiscomposedofahydrauliccylinder,aservovalveandadigitalcomputer,Theblockdiagramillustratesthedataacquisitionsystem.Thecylindermovesthemassm5kgdependingontheoilflowsQ1andQ2inthechambersAandBwhicharemanagedbythevalue.ThevoltageuoftheservovalueisobtainedviaaRTI815interfacecardAnalogDevicesthroughameasuringamplifier.TheRTI815worksasa12bitdigitaltoanalogD/Aconverterina386PC,whichisscaledtocommand10V.AnincrementalpositionmeasuringsystemIK120card,Heidenhainprovidesthepositionmeasurementxtothecomputer.Duetothefactthatthehydraulicsystemhasanintegratingbehaviorwithregardtothepositionofthecylinder,andsincetheidentificationhastobestableateachstepk,thevelocityisusedastheoutputsignalyfortheidentification.Thus,themeasuredpositionisnumericallydifferentiatedusingthedifferenceequation.Thisreconstructionenhanceshighfrequencynoise.ThesamplingratewasT1ms.Ofcourse,thehighfrequencynoisecanberemovedbysmoothingorfiltering.ThisisnotnecessaryheresincetheLIFworksasaprefitterandovercomesnoisysignals.Theinputsignalisnormalizedintheregion1,1.Inordertoobtainthemostinformationpossibleabouttherelevantplantdynamics,theinputtestsignalhastobedesigned,insuchawaythatitvariesovertheentireadmissibleregion.Arandomamplitudeinputwithconstantperiodwasappliedtotherealplant.Thegoodcorrespondencebetweenthemeasureddataandthequadraticapproximationdemonstratestheefficiencyofthepresentedidentificationmethod.Inordertocomparedifferentmodelsthemeannormalizederrorisconsideredwhereyisthemeasuredandjtheestimateddatavector.Thechoiceofthedesignparameters1andhaveagreatinfluenceonthequalityoftheidentifiedmodels.Forthehydraulicdrivepresentedhere,1shouldbebetween20and25andthedelayparameterbetween5and10.However,noteverycombinationinvolvesastablemodel.Thiscanbeshownbysimulation.Thequalityoftheidentifiedmodelsisworseforn4.Thebilinearandquadraticdynamicoftheplantmustbeconsideredforbettermodelingoftherealdynamicsofhydraulicdrives.Withtheintentionofassessingthetrueperformanceoftheidentificationmethod,acommonprocedurethatcanberegardedasatestofthemodelsvaliditywasapplied.Thatis,thesystemissimulatedwithinputsignalsotherthanthoseusedforidentificationandcomparemeasuredoutputwiththesimulatedmodeloutput.Exemplarycomparisonsbetweenthemeasuredoutputandthemodeloutputformodel3showstheinputsignalsused.Theseandothervalidationtestshaveconfirmedthegoodperformanceofthesystemidentificationmethodusedinthisstudy.Theerrorsintheresponsesofthesimulatedidentifiedmodeloutput,comparedwithmeasuredoutput,arecausedbythesomemodeledeffectslikestaticfriction,thedeviationbetweenthehydraulicandtheelectriczeropointofthedrive,aswellasthedecreasingofthesupplypressurewhichisneglectedhere.Nevertheless,theidentifiedquadraticmodelsenableustoavoidthecomplexphysicalmodelstructure,withmanyunknownparameters,anditcanbeproventhattheybringgreatimprovementtolinearapproximations.中文翻译液压伺服驱动系统的非线性识别1.简介工业设备中很多地方用到液压伺服驱动,因为它可以提供很大的压力而且速度很快。但是,液压伺服驱动系统自身结构相当复杂,这就使的它很难改进成适宜动态工作系统的低压或可执行的模型。设计观察元件过滤器。控制元件的时候需要这个模型。如果这个设备模型是一个非线性的标准的形式,这种情况下的设计是最简单的。然而在现实的设备中,系统仅有与这些标准形式相配合的形式。非线性的要转化成规范的形式,因此必须建立严格的条件和大量的细致的数字扶助下(偏微分方程和倒置非线性代数方程)。为了避免这些繁琐的计算,在实际应用中,系统的辨认技术提供了令人满意的模板,这些模板正是我们想得到的某作者写这篇文章陈述他的研究,而且的在于找到一种直接的液压伺服系统的模型,在非线性观察的语言语音的典型类型,并通过参数辨认。近年来,科学家们在建使用双线性模型的液压系统中,纷纷尝试这种方法。其中的一些模型已通过实际的设备使用情况进行评估,并且这些模型被很好的建立起来。可是,使用的这些辨认手段,对系统来说这些最大可能性的方法估计误差的方法,在初期需要详细的评估。不合适的选择会引起相互转向及其他异常问题,这些问题在实际使用中是非常难解决的。在这篇文章中,参数是建立在修改回归指令变量这一算法基础之上的,这样可以使我们找到一种解决上边提到的这些问题的方法。我们考虑建立更完善的实际动态,液压系统的模型建立方法非线性一次方程。为了处理测量时间带来的
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