翻譯部分英文原文：NonlinearIdentificationofHydraulicServo-DriveSystems1.IntroductionHydraulicservo-drivesareusedinmanyindustrialplants,becausetheycanproducelargeforcesandtorqueswithhighspeed.However,therathercomplexstructuresofsuchdrivesystemsmakeitdifficulttodevelopsuitable,preferablylow-or-dermodelsofthedynamicoftheplant.Themodelsareneededforthedesignofstateobservers,filtersandcontrollers.Thedesignismostsimplifiedifthemodeloftheplanthasanonlinearcanonicalform.Inactualhardivare,however,systemsrarelyhavethesesuitableforms.Nonlineartransformationsintocanonicalformsthereforemustfirstbedeterminedunderrigor-ousconditionsandwithconsiderablemathematicoeffort(inte-grationofpartialdifferentialequationsandinversionofnonlinearalgebraicequations).Toavoidthis,thepracticalapplicationofsystemidentificationtechniquesprovidessatisfactorymodelsofindividualunitsinsomedesiredform.Theaimoftheresearchpresentedinthisarticleistoobtainmodelsofahydraulicservo-drivedirectly,inthenonlinearobservercanonicalform,viaparameteridentification.Inrecentyears,muchefforthasbeendevotedtomodelingofhydraulicsystemsusingbilinearmodels.Severalofthesemodelshavebeenevaluatedbytestsonrealplants,andarewellestablished.However,theidentificationmethodsused,themaximumlikelihoodmethodandpredictionerrormethod,requiresuitablyspecified(agoodenough)initialvaluesoftheunknownparametersandstatesofthesystem.Anunsuitablechoicecausescon-vergenceandsingularityproblemsthat,inrealapplications,areverydifficulttosolve.Inthisarticle,theparameterestimationisbasedonamodifiedRecursiveInstrumentalVariablesalgorithmthatenablesustocvercomethedifficultiesmentionedabove.Weconsiderstatequadraticnonlinearitiesforbettermodelingoftherealdynamicsofhydraulicdrives.Forhandingtimederivativesofmeasure-ments,theso-calledLinearIntegral.FilterproposedbysagaraandZhaoisused.Theidentificationprocedureisappliedtoanexperimentalsetup.Agoodcorrespondenceisobtainedbetweenthedateandthemodelswhichareidentifieddirectlyinnonlinearespeciallyquadraticobservercanonicalform.2.DescriptionoftheHydraulicDriveThephysicalprocessusedastestingbenchconsistsofaservovalueandahydrauliccylindercoupledwithamovingmass.Iuustratestheteststandusedinthisstudy.Inordertoavoidtherepresentationofmanyequationswhichmaybefound,forinstance,inDietzandProchnioandKoeckemann,aschematicdiagramofthesystemisshowninandadetailedblockdiagramisgivenin.Theinputsignalofthesystemisthevoltageandtheoutputsignalisthepositionxofthemovingmass.ThestatevariablesarelistedinTable.Themostsignificantnonlinearitiesoftheplantarethemulti-pliers,thesquarerootfunctions,theoilelasticityandthefriction.Inpractice,itisdifficulttodeterminethephysicalparametersassociatedwiththesenonlinearities.Thussystemidentificationtechniquesareneededtoobtainapproximatemodelsofthesystemsuchthattheerrorbetweenmeasureddataandmodelisminimized.3.IdentificationThecontinuousparameterestimationfromsampleddataofinput-outputmeasurements.Forthis,SagaraandZhaoproposedanoperationofnumericalintegration,theso-calledLinearIntegralFilter(LE)forlineardifferentialequations.Thismethodwillbeextendedwiththegoaltoidentifysomelineat-inparametersnonlinearsystemslikethoseinobservercanonicalform.4LinearIntegralFilterCommonly,onlythelineartermsin(10)areconsidered.Thehigher-ordertermsarethusignoredfollowingtheassumptionthattheyarenegligiblewhenthesystemsstateclosetothereferencepointchosenforthelinearization.Inthisarticlewegotwostepsfurtherbytakingintoaccountalsothebilinearandthequadraticapproximationwhileaddingalottothecomputationalburden,theywillbeleftasideintheapplicationonthehydraulicdrivepresentedhere.Nevertheless,theidentificationmethodwillbederivedforany.Furthermore,thefilterparameter1affectsconsiderablytheaccuracyoftheparameterestimation.ItispointedoutbySagaraandZhao6thatshouldbechosensothatthefrequencybandwidthoftheLIFmatchesascloselyaspossiblethefrequencybandofthesystem.Inparacticaluse,however,a-prioriinformationaboutthefrequencybandofthesystemareoftennotavailable.Therefore,manyidentificationexperimenttrialsmustbetaken.Oneveryeffectivemethodistousetherecursiveinstrumentalvariable(IV)method,whichisasymptoticallylinbiasedforasuitablechoiceoftheIVanddoesnotrequireapricriknowledgeofthenoisestatistics.ThefollowingalgorithmisgivenbyLjungandsoederstrom.5.ExperinentalSetupandResultsTheexperimentalsetupconsideredhereiscomposedofahydrauliccylinder,aservovalveandadigitalcomputer,Theblockdiagramillustratesthedataacquisitionsystem.Thecylindermovesthemass(m=5kg)dependingontheoilflowsQ1andQ2(inthechambersAandB)whicharemanagedbythevalue.ThevoltageuoftheservovalueisobtainedviaaRTI-815interfacecard(AnalogDevices)throughameasuringamplifier.TheRTI-815worksasa12-bitdigital-toanalog(D/A)converter(ina386-PC),whichisscaledtocommand+10V.Anincrementalpositionmeasuringsystem(IK-120card,Heidenhain)providesthepositionmeasurementxtothecomputer.Duetothefactthatthehydraulicsystemhasanintegratingbehaviorwithregardtothepositionofthecylinder,andsincetheidentificationhastobestableateachstepk,thevelocityisusedastheoutputsignalyfortheidentification.Thus,themeasuredpositionisnumericallydifferentiatedusingthedifferenceequation.Thisreconstructionenhanceshigh-frequencynoise.ThesamplingratewasT=1ms.Ofcourse,thehigh-frequencynoisecanberemovedbysmoothingorfiltering.ThisisnotnecessaryheresincetheLIFworksasapre-fitterandovercomesnoisysignals.Theinputsignalisnormalizedintheregion-1,+1.Inordertoobtainthemostinformationpossibleabouttherelevantplantdynamics,theinputtestsignalhastobedesigned,insuchawaythatitvariesovertheentireadmissibleregion.Arandomamplitudeinputwithconstantperiodwasappliedtotherealplant.Thegoodcorrespondencebetweenthemeasureddataandthequadraticapproximationdemonstratestheefficiencyofthepresentedidentificationmethod.Inordertocomparedifferentmodelsthemeannormalizederrorisconsideredwhereyisthemeasuredandjtheestimateddatavector.Thechoiceofthedesignparameters1and&haveagreatinfluenceonthequalityoftheidentifiedmodels.Forthehydraulicdrivepresentedhere,1shouldbebetween20and25andthedelayparameterbetween5and10.However,noteverycombinationinvolvesastablemodel.Thiscanbeshownbysimulation.Thequalityoftheidentifiedmodelsisworseforn4.Thebilinearandquadraticdynamicoftheplantmustbeconsideredforbettermodelingoftherealdynamicsofhydraulicdrives.Withtheintentionofassessingthetrueperformanceoftheidentificationmethod,acommonprocedurethatcanberegardedasatestofthemodelsvaliditywasapplied.Thatis,thesystemissimulatedwithinputsignalsotherthanthoseusedforidentificationandcomparemeasuredoutputwiththesimulatedmodeloutput.Exemplarycomparisonsbetweenthemeasuredoutputandthemodeloutputformodel3showstheinputsignalsused.Theseandothervalidationtestshaveconfirmedthegoodperformanceofthesystemidentificationmethodusedinthisstudy.Theerrorsintheresponsesofthesimulatedidentifiedmodeloutput,comparedwithmeasuredoutput,arecausedbythesomemodeledeffectslikestaticfriction,thedeviationbetweenthehydraulicandtheelectriczeropointofthedrive,aswellasthedecreasingofthesupplypressure(whichisneglectedhere.)Nevertheless,theidentifiedquadr