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PROCEEDINGSOFTHEAMERICANCONTROLCONFERENCEARLINGTON,VAJUNE2527,2001ASINGLEACTUATORCONTROLDESIGNFORHYDRAULICVARIABLEDISPLACEMENTPUMPSHONGLIUDUHYDRAULICSRLANTTO,ETAL,1989LINANDAKERS1990USINGAPROPORTIONALSOLENOIDVALVETOPROVIDECONTROLFLOWFORREGULATINGTHESWASHPLATEANGLE,ANONLINEARCONTROLSTRATEGYHASTEENDEVELOPEDFORPUMPDISCHARGEPRESSURECONTROLWHICHISCAPABLEOFONLINEADAPTIVECOMPENSATINGFORTHECHANGEOFTHEPRESSURECARRYOVERANGLEDUANDMANRING,2000TOFURTHERGETINSIGHTINTOTHESYSTEMDYNAMICS,ANDTOINVESTIGATETHEEFFECTSOFPARTICULARPARAMETERSONTHECONTROLDESIGN,ITWOULDBEUSEFULTOCLASSIFYTHESYSTEMSTATESINTODIFFERENTCATEGORIESBYDOINGTHIS,THEDOMINATING“SLOW”VARIABLESCANBEIDENTIFIEDANDTHELESSIMPORTANT“FAST”VARIABLESCANBENEGLECTEDTOREDUCESYSTEMCOMPLEXITYFORCONTROLDESIGNANDIMPLEMENTATIONPURPOSESINADDITION,AREASONABLEREDUCEDORDERMODELWILLREVEALTHEMOSTIMPORTANTASPECTSTHATAFFECTFUNDAMENTALCONTROLSYSTEMBEHAVIORSASSHOWNINFIGURE1,ANAXIALPISTONSWASHPLATEHYDRAULICPUMPNORMALLYCONSISTSOFSEVERALPISTONSWITHINACOMMONCYLINDRICALBLOCKTHEPISTONSARENESTEDINACIRCULARARRAYWITHINTHEBLOCKATEQUALINTERVALSABOUTTHESHAFTAXISTHECYLINDERBLOCKISHELDTIGHTLYAGAINSTAVALEPLATEUSINGTHEFORCEOFTHECOMPRESSEDCYLINDERBLOCKSPRINGANDALESSOBVIOUS07803649531011100002001AACCPRESSUREFORCEWITHINTHECYLINDERBLOCKITSELFABALLANDSOCKETJOINTCONNECTSTHEBASEOFEACHPISTONTOASLIPPERTHESLIPPERSTHEMSELVESAREKEPTINCONTACTWITHTHESWASHPLATEANDTHESWASHPLATEANGLE,AISCONTROLLEDBYASERVOMECHANISMBASEDUPONTHEREQUIREMENTSOFTHEDISCHARGEPRESSUREAND/ORDISCHARGEFLOWRATEFORPRACTICALAPPLICATIONS,THELOADSONANYHYDRAULICACTUATORCANCHANGEFROMTIMETOTIME,WHICHINTURNREQUIRESTHEHYDRAULICPUMPTOPROVIDEADIFFERENTOPERATINGPRESSUREACCORDINGLYSPECIFICALLY,FORAPRESSURECONTROL,THEOBJECTIVEISTOCONTROLTHEPUMPDISCHARGEPRESSURETOFOLLOWTHEDESIREDPRESSURETIMEHISTORYWHICHISDETERMINEDBYTHEWORKINGLOADSANDTHEENVIRONMENTWITHBOUNDEDTRACKINGERROR,WHILECONSIDERINGSYSTEMUNCERTAINTIESANDIMPLEMENTATIONLIMITATIONSTHEREARETWOMAINDRAWBACKSINTHECONVENTIONALCONFIGURATIONOFCONTROLACTUATORSFIRST,THEDISCHARGEPRESSUREFEEDBACKTOINCREASETHEPUMPDISPLACEMENTRESULTSINANOPENLOOPUNSTABLESYSTEM,WHICHIMPOSESINHERENTCONSTRAINTSONTHESTABILITYANDPERFORMANCEOFTHECLOSEDLOOPCONTROLDESIGNALTHOUGHTHISARGUMENTCANBERIGOROUSLYPROVEDASPRESENTEDINTHEFOLLOWINGSECTIONS,SOMEINTUITIVEANALYSESWOULDHELPTOREVEALTHEINSTABILITYPHYSICALLYASSUMINGTHATTHEPUMPDISCHARGEFLOWRATEDOESNOTCHANGE,ANDFEEDBACKCONTROLISNOTTAKINGPLACEOPENLOOP,ANEXTERNALDISTURBANCEISINTRODUCEDANDTHISCAUSESTHEDISCHARGEPRESSURETODEVIATEFROMITSOPERATINGPOINTANINCREASEINTHEPUMPDISCHARGEPRESSUREWILLBEFOLLOWEDBYANINCREASEOFTHESWASHPLATEANGLE,WHICHINTURNRESULTSINAFURTHERINCREASEINDISCHARGEPRESSURETHISPOSITIVEFEEDBACKPROCESSQUICKLYRAISESTHEPUMPDISCHARGEPRESSURETOITSMAXIMUMVALUECORRESPONDINGTOTHEMECHANICALLYSETMAXIMUMSWASHPLATEANGLE,WHICHMAKESAPRESSURERELIEFVALVEABSOLUTELYNECESSARYFORSAFETYFORTHESAMEREASON,ADECREASEINDISCHARGEPRESSUREWILLCAUSETHEOUTPUTPRESSURETODROPDOWNTOITSMINIMUMVALUESECOND,ALARGEFORCEISREQUIREDTOBALANCETHELOADGENERATEDBYTHETWOPARALLELACTUATORS,WHICHINTURNREQUIRESLARGESIZEBEARINGSTOHOLDTHESWASHPLATEINPLACETOOVERCOMEBOTHOFTHEDRAWBACKSINTHECONVENTIONALPUMPCONFIGURATION,ANOVELCONTROLCONFIGURATIONISPROPOSEDINTHISPAPERBYBALANCINGTHETORQUEINDUCEDFROMTHEPRESSURECARRYOVERANGLE,THEPRESENTEDCONTROLDESIGNUSESONLYONEACTUATORTHATISARRANGEDINAMERSUCHTHATTHEOPENLOOPDYNAMICSARESTABLEANDTHEFORCEEXERTINGONTHESWASHPLATEBEARINGSISSIGNIFICANTLYREDUCEDINTHISPAPER,TOMOREPHYSICALLYTRACKTHEPUMPPRESSUREDISCHARGECONTROLSYSTEM,AREDUCEDOPENLOOPMODELISDEVELOPEDUSINGASINGULARPERTURBATIONTECHNIQUEANANALYSISOFEACHSYSTEMSTATEANDTHEDESIGNDETAILSFORSYNTHESIZINGSYSTEMCONTROLLERSAREALSOPROVIDEDEXPERIMENTALRESULTSAREUSEDTOVALIDATETHEPROPOSEDCONTROLSYSTEMDESIGNTHEPAPERISORGANIZEDASFOLLOWSSECTION2DESCRIBESTHESERVOCONTROLCONFIGURATIONANDTHEDYNAMICSOFTHEVARIABLEDISPLACEMENTPUMPSECTION3DEVELOPSAREDUCEDORDERPUMPCONTROLMODEL,THEDYNAMICANALYSIS,ANDTHECONTROLDESIGNSECTION4PROVIDESTHEEXPERIMENTALRESULTSANDTHEDISCUSSIONTOVALIDATETHEPROPOSEDMODELREDUCTIONANDCONTROL4484AUTHORIZEDLICENSEDUSELIMITEDTOCENTRALSOUTHUNIVERSITYDOWNLOADEDONAPRIL18,2010AT010214UTCFROMIEEEXPLORERESTRICTIONSAPPLYDESIGNCONCLUSIONSAND,FINALLY,SECTION5SUMMARIZESTHEWORKWITH2SYSTEMMODELINGTHESCHEMATICOFTHEPRESSURESERVOCONTROLSYSTEM,WITHCONVENTIONALACTUATORSCONFIGURATION,FORVARIABLEDISPLACEMENTPUMPSISSHOWNINFIGURE2WITHTHECYLINDERBLOCKRUNNINGATACONSTANTANGULARVELOCITY,W,EACHPISTONSPERIODICALLYPASSESOVERTHEDISCHARGEANDINTAKEPORTSONTHEVALVEPLATETHEINCLINATIONOFTHESWASHPLATE,WITHAPOSITIVEANGULARPOSITION4MAKESTHEPISTONSUNDERGOANOSCILLATORYDISPLACEMENTINANDOUTTHECYLINDERBLOCKTHUSDRAWINGFLUIDFROMTHELOWPRESSUREINTAKEPORTANDPUMPINGITOUTTHROUGHTHEHIGHPRESSUREDISCHARGEPORTTHESWASHPLATEANGLECONTROLTORQUEISGENERATEDUSINGTWOSERVOSASSHOWNINTHEFIGUREASMALLSERVO,ALONGWITHASPRING,PROVIDESABIASTORQUETOINCREASETHEPUMPSTROKEANDALARGERSERVO,ONTHEOTHERHAND,ISUSEDTODECREASETHEPUMPSTROKETHEDISCHARGEPRESSUREOFTHEPUMPISDIRECTLYFEDBACKTOTHESMALLSERVOWHILETHEPRESSUREACTINGONTHELARGESERVOCOMESFROMTHEOUTPUTPORTOFACONTROLLEDSERVOVALVEINTHISRESEARCH,AFOURWAYSINGLESTAGESERVOVALVEWASPURCHASEDANDUSEDINTHECONTROLCONFIGURATIONONEOFTHEOUTPUTPORTSWASCONNECTEDTOTHELARGESERVOANDTHEOTHERWASBLOCKEDTOPREVENTOILLEAKAGEFORTHISCONTIGURATION,ONLYA3WAYVALVEISNEEDEDTHEPOSITIONOFTHEVALVESPOOLCONTROLSFLUIDFLOWINOROUTOFTHELARGESERVOCHAMBERTOGENERATETHECONTROLTOQUEFORPOSITIONINGTHESWASHPLATEANGLETHESERVOVALVEISASSUMEDTOHAVEAMUCHHIGHERBANDWIDTHTHANTHATOFTHEPUMPSUCHTHATITSDYNAMICSMAYBENEGLECTEDINTHEANALYSISOFTHESYSTEMDYNAMICSANDINTHECONTROLDESIGNTHUS,THETASKOFPRESSURESERVOCONTROLDESIGNBECOMESFINDINGANAPPROPRIATELAWTOPOSITIONTHESPOOLOFTHESERVOVALVESOTHATTHEPUMPDISCHARGEPRESSUREWOULDTRACKADESIREDPRESSURETIMEHISTORY21DYNAMICSOFAXIALPISTONSWASHPLATEHYDRAULICPUMPUSINGPREVIOUSRESEARCHUANDMANRING2000,MANRING1999ITCANBESHOWNFORTHECONFIGURATIONOFFIGURE2THATTHEEQUATIONOFMOTIONFORTHESWASHPLATEISGIVENBYWHERETFISTHENONLINEARFRICTIONEXERTINGONTHESWASHPLATE,TFIATISTHEMAGNITUDEOFTHECOULOMBFRICTIONBETWEENAPISTONANDITSBORE,ANDID2AVARIABLEDISPLACEMENTAXIALPISTONPUMPWITH9PISTONSANDAMAXIMUMDISPLACEMENTOF2473AMOOGD633DIRECTDRIVESERVOPROPORTIONALCONTROLVALVEWITHRATEDFLOWOF5VMINAT6895MP1000PSIOPERATINGPRESSURETOPROVIDETHECONTROLPRESSURE4AVARIABLEORIFICETORESTRICTTHEPUMPDISCHARGEFLOWRATEANDTOPROVIDEADISCHARGEPRESSUREANDAFLOWDISTURBANCE5APRESSURERELIEFVALVEWITHANADJUSTABLERELIEFPRESSUREFORSAFETYTHEPRESSURERELIEFVALVEISSETMUCHHIGHERTHANTHETESTPRESSURERANGEDURINGTHEEXPERIMENTALTESTS6APENTIUMI1BASED333MHZCOMPUTERWITHWITHUSBDT9802DATAACQUISITIONSYSTEMUSEDFORDATAACQUISITIONANDCONTROL7TWOPRESSURETRANSDUCERSANDANANGULARPOSITIONSENSORTOMEASURETHESYSTEMVARIABLESAND8CUSTOMBUILTSIGNALCONDITIONERS1OWHYDRAULICOILISUSEDINTHEEXPERIMENTALTESTSANDTHETEMPERATUREOFTHEOILISCONTROLLEDANDLIMITEDTOLESSTHAN650OTHERRELATEDPARAMETERSARELISTEDINTABLE1THEVOLTAGEOUTPUTFROMTHECOMPUTERISLIMITEDTOFLOV20MAADIGITALBUTTERWORTHLOWPASSFILTERWITHA50HZCUTOFFFREQUENCYISIMPLEMENTEDTOREMOVETHEEFFECTSOFHIGHFREQUENCYELECTRICALNOISETHEAIDBOARDHAS16BITRESOLUTIONONDOGINPUTSAND12BITRESOLUTIONONTHEANALOGOUTPUTSTHECONTROLSOFTWAREWASDEVELOPEDUSINGVCLANGUAGEEXDENMENTALRESULTSFORTHEPDCONTROLDESIGN,GENERALLYSPEAKING,THESMALLERRANDTHELARGERKPTHEFASTERSYSTEMRESPONSEANDTHEBETTERPERFORMANCE,PROVIDEDUNMODELEDDYNAMICSARENOTEXCITEDANDTHEACTUATORSATURATIONISPREVENTEDINTHETESTS,THETWOPARAMETERSARESELECTEDAS01SECANDTHEPROPORTIONALGAINKPL2E105“/KPATHEREGULATIONPERFORMANCEISSTUDIEDUSINGASQUAREWAVETRAJECTORYFORPDOFAMPLITUDE3MPACENTEREDAT17MPAANDWITHAPERIODOF4OR8SECONDSTHESAMPLINGFREQUENCYISLIMITEDBY60HZTHEPUMPRUNNINGSPEEDISSETAT2000RPM,1900RPM,1800RPMAND1700RPMRESPECTIVELYALARGENUMBEROFEXPERIMENTALTESTSHAVEBEENCONDUCTEDANDTHETESTRESULTSAREVERYCONSISTENTFIGURES7AND8SHOWTHETYPICALCLOSEDLOOPCONTROLSYSTEMPERFORMANCEFORHARDWAREIMPLEMENTATIONOFTHEPROPOSEDSTRATEGIESANDALGORITHMSINTHEFIGURES,THEHIGHFREQUENCYCOMPONENTCORRESPONDSTOTHEPRESSUREFLUCTUATIONCAUSEDBYTHECYCLINGOFTHEPISTONSWHICHUSUALLYISNOTMODELEDITCANBESEENFROMTHEFIGURESTHATFORAPDCONTROLLER,ASPREDICTEDINTHEANALYSIS,NOOVERSHOOTOCCURSFORTHESTEPCOMMANDINPUTSANDTHESYSTEMISSTABLEWITHTRACKINGERRORSBEINGBOUNDEDTHERELATIVELYSLOWERDESTROKINGOFTHESWASHPLATE,WHICHCANBEIMPROVEDWITHAGAINSCHEDULINGSCHEME,BASICALLYCAUSESTHEOFFSETOFTHESTEADYSTATEAVERAGEERRORITSHOULDALSOBENOTEDTHATTHEHIGHERPUMPRUNNINGSPEEDCORRESPONDSTOAQUICKERSYSTEM4487AUTHORIZEDLICENSEDUSELIMITEDTOCENTRALSOUTHUNIVERSITYDOWNLOADEDONAPRIL18,2010AT010214UTCFROMIEEEXPLORERESTRICTIONSAPPLYRESPONSEWHENPUMPSWASHPLATEDESTROKINGISREQUIREDDURINGTHETESTSITHASALSOBEENFOUNDTHATIFTHEFEEDBACKGAINSAREKEPTASCONSTANTSATDIFFERENTPRESSUREOPERATINGPOINTS,THETRACKINGERRORANDTHESYSTEMRESPONSETIMEBECOMELARGERANDLONGERRESPECTIVELYGAINSCHEDULINGBASEDONDIFFERENTOPERATINGPOINTSIMPROVESTHEPERFORMANCESIGNIFICANTLY5CONCLUSIONINTHISPAPERADISCHARGEPRESSURECONTROLOFHYDRAULICVARIABLEDISPLACEMENTPUMPSUSINGSINGLEACTUATORISPROPOSEDTHECONTROLDESIGNSPRESENTEDINTHISPAPERPROVIDEANAPPROACHFORCONTROLLINGTHEDISCHARGEPRESSUREOFVARIABLEDISPLACEMENTPUMPSTOTRACKTHEDESIREDPRESSURETIMEHISTORYUSINGSINGLEACTUATORITHASBEENSHOWNTHAT,USINGTHEREDUCEDSECONDORDERSYSTEMMODEL,THELOCALLYLINEARIZEDOPENLOOPSYSTEMISSTRICTLYSTABLEAPROPORTIONALCONTROLCPCONTROLORPROPORTIONALPLUSDERIVATIVECONTROLPDCONTROLWILLBEABLETOFORMASTRICTLYSTABLECLOSEDLOOPSYSTEM,PROVIDEDTHATTHECONTROLGAINSAREPROPERLYCHOSENSUCHTHATTHEHIGHFREQUENCYUNMODELEDSYSTEMUNCERTAINTIESARENOTEXCITEDWITHPROPERLYSELECTEDPDGAINS,THECLOSEDLOOPTRANSFERFUNCTIONISESSENTIALLYAFIRSTORDERDYNAMICSYSTEM,WHICHIMPLIESTHATNOOVERSHOOTFORSTEPRESPONSECANBEEXPECTEDFORTHISESSENTIALFIRSTORDERSYSTEM,THESYSTEMRISINGTIMEANDSTEADYSTATETRACKINGERRORWILLBEBASICALLYDETERMINEDBYFEEDBACKGAINSFORHIGHPRESSUREAPPLICATIONS,BETTERPERFORMANCECANBEOBTAINEDSINCETHEUNMODELEDDYNAMICS,ESPECIALLYTHESWASHPLATEKINEMATICS,AREMUCHLESSIMPORTANTANDAWIDERRANGEOFCONTROLTORQUECANBEOBTAINEDEXPERIMENTALRESULTSAREPROVIDEDTOVALIDATETHEPROPOSEDCONTROLAPPROACHES5REFERENCESLAKERSAANDLIN,SJ1988“OPTIMALCONTROLTHEORYAPPLIEDTOAPUMPWITHSINGLESTAGEELECTROHYDRAULICSERVOVALVE,”ASMEJOURNALOFDYNAMICSYSTEM,MEASUREMENT,ANDCONTROL,VOL110,NO2,PP1201252DU,HANDMANRINGND,2000,“ANADAPTIVEPRESSURESERVOCONTROLDESIGNFORVARIABLEDISPLACEMENTPUMPS,”PROCEEDINGSOFTHEASMEINTEMIONALMECHANICALENGINEERINGCONGRESSANDEXPOSITION,2000,DSCVOL961,PP3053123LMTTO,B,JANSSON,AANDPALMBERG,JO,1989,“ANEWCONCEPTOFCOMPUTERCONTROLLEDELECTROHYDRAULICSYSTEMTHEPQPUMPCOMBINEDPUMPANDVALVECONTROL,”SECONDBATHINTERNATIONALFLUIDPOWERWORKSHOPFLUIDPOWERCOMPONENTSANDSYSTEMS4LIN,SJANDAKERS,A,1990,“OPTIMALCONTROLTHEORYAPPLIEDTOPRESSURECONTROLLEDAXIALPISTONPUMPDESIGN,”ASMEJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROL,VOL112,NO3,PP4754815MANRING,NDANDJOHNSON,R1996,“MODELINGANDDESIGNINGAVARIABLEDISPLACEMENTOPENLOOPPUMP,”ASMEJOUR