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LoadindependentcontrolofahydraulicexcavatorEugeniuszBudny,MiroslawChlosta,WitoldGutkowskiInstituteofMechanizedConstructionandRockMining,ul.Racjonalizacji6/8,02673Warsaw,PolandAccepted23August2002AbstractTheprimaryfocusofthisstudyistoinvestigatethecontrolofexcavationprocessesbyapplyingloadindependenthydraulicvalves.Thisapproachallowsavoidingclosedloopcontrolsystemwithsensorsandtransducersmountedontheexcavatorattachment.Thereare,then,nosensorcellsmountedonthemachineattachment.Theconsideredsystemiscomposedoftwosubsystemsamicrocomputerandahydraulicunitapumpandloadindependentvalves.Inthemicrocomputerunit,thebucketvelocityvectorisrelatedtotheoilflowintothreecylindersthroughtheapplicationofinversekinematics.Then,flowsaretransferredintotheelectricsignalsactuatingtheloadindependentvalves.Theirmotionispresentedbyapplyingtransferfunction.Theperformanceofthesystemisverifiedbyassuminganabruptchangeoftheoilflowintocylinders.Thelastpartofthepaperisdevotedtotheobtainedexperimentalresults.Thefirstresultdealswithverticaldrilling.Thesecondresultdealswithanexcavationalongahorizontaltrajectory.D2002ElsevierScienceB.V.Allrightsreserved.KeywordsExcavatorHydraulicsystemsControlTrajectoryexecution1.IntroductionDuetoencouragingresultsofrecentresearch,thereareincreasingpossibilitiesforenhancementofalargespectrumhumaneffortsinexcavationprocesses.Thismayoccurmainlythroughcontrolofrepetitiveworktasks,suchastrenchinganddrilling,requiringconstantattentionofmachineoperatorsduringtheperformanceofeachtask.Particularattention,inresearch,ispaidtoexcavationalongprescribedtrajectoriessubjectedtovaryingsoilenvironment.FundamentalsdealingwithcontrolledexcavationprocessesarediscussedbyVahaandSkibniewski1,Hemami2,andHillerandSchnider3.AninterestingapproachtopilingprocessesbyadirectangularsensingmethodisproposedbyKeskinenetal.8.BudnyandGutkowski4,6proposedasystem,applyingkinematicallyinducedmotionofanexcavatorbucket.Inthisapproach,influenceofasmallvariationofhydraulicoilflowintocylinders,applyingsensitivityanalysis,isdiscussedbyGutkowskiandChlgosta5.Huangetal.7presentedanimpedancecontrolstudyforaroboticexcavator.Theyappliedtwoneuralnetworksfirst,asafeedforwardcontrollerandthesecondasafeedbacktargetimpedance.Anotherimpedancesystem,applyingahybridposition/forcecontrol,isproposedbyHaetal.9.Thefirstgenerationofrobotswasconceivedasopenlooppositioningdevices.Thisimpliedthatallpartshadtobemanufacturedwithaveryhigh09265805/02/seefrontmatterD2002ElsevierScienceB.V.Allrightsreserved.PIIS0926580502000882Correspondingauthor.Emailaddressmchimbigs.org.plE.Budny.URLhttp//www.imbigs.org.pl.www.elsevier.com/locate/autconAutomationinConstruction122003245–254andcostlyaccuracy.Next,positioningrobots,withsensors,reducedthisaccuracyrequirementconsiderably.Herewereseveralapproaches,mentionedinabovereferences,toextendtheindustrialrobotscapabilitiestoroboticexcavator.Systemsofforcecells,longitudinalandangularsensorshavebeenapplied.However,twomaindifferencesbetweenrequirementsformanufacturingrobotsandroboticexcavatorsshouldbenoted.Thefirstdifferenceisthatmanufacturingrobotsareworkinginalmostperfectconditions,freeofvibrations,protectedagainstshocks,humidity,andotherpossibledamagingconditions.Theseconddifferenceistherequirementsforhighaccuracyofmanufacturingrobots,oftenwithinmicrons.Onthecontrary,roboticexcavatorsareworkinginverydifficultconstructionsiteconditions,andrequiredaccuracyoftheexecutedtrajectories,comparingwithindustrialrobots,islimited,saywithincentimetres.Withdifficultconditionsofexcavationsworks,allsensorsattachedtotheboom,arm,andbuckethavetobeverywellprotected.Bearinginmindtheabovedifferences,itwouldbeofinteresttoinvestigatethepossibilitiesofcontrollingexcavationtrajectorybyahydraulicmodulecomposedofapumpandloadindependentvalves.Inotherwords,toinvestigateasystemfreeofsensorcellsmountedattheexcavatorattachment,combinedwithafeedbackcontroller,includedinthehydraulicunitofthemachine.Themainobjectiveofthepresentpaperistoextendthediscussion,initiatedbytheauthors10,onthepossibilitiesofapplyingloadindependentvalvesinstalledinsideofoperatorcabinonly.Underthisassumption,thesystemisfreeofsensorslocatedontheexcavatorattachment.Afterdiscussingmathematicalmodelofthesystem,preliminaryexperimentalresultsarepresentedattheendofthepaper.2.StatementoftheproblemThepaperdealswithacontrolled,stablemotionofanexcavatorbucketalongaprescribedpath.Theproblemisbasedonpreviousauthorstheoreticalinvestigations4ofquasistatic,kinematicallyinducedexcavationprocessesforassumedtrajectories.Inthisstudy,thefollowingassumptionsaremade..Theexcavatorattachmentisaplanarmechanism,composedofaboom,anarm,andabucket.Three,independentlydriven,hydrauliccylindersoperatethesystem.Theyareassuringauniquerepresentationofthethreedegreesoftheplanarbucketmotion,twodisplacementsandarotation..Theexcavationprocess,intheexperimentsperformed,isassumedtobeslowenoughtoconsideritasaquasistaticone.Inertiatermsinmotionequationsofattachmentcanbethenneglected.Onlyspooloftheservomechanismisassumedtomovewithaccelerations,whichcannotbeneglected..Theforcepressuredisturbancesareassumedtohavesinusoidalform.Theacceptableparametersofthesinusoidaredefinedfromstabilityconditionsofthesystem..Thesoilisassumedhomogeneous.Somesmallinclusionsintheformofstonesareacceptable..Theproposedcontrolsystemofexcavationisoperatorassisted.Itmeansthatinacaseofalargerobstacle,theoperatorhastointervene..Ifsuccessful,theproposedcontrolsetupcouldapplytostandardexcavatorswiththeaimofenhancementofalargespectrumofhumaneffortsinrepetitiveprocessessuchastrenchinganddrilling..Theexperimentisconsideredasasystemcomposedofthreesubsystems,namelymicrocomputerwithPLChydraulicarrangementapump,valves,cylindersandthemechanismwiththreedegreesoffreedomofthebucket.Next,thesubsystemsareconsideredassetsofcomponents.Inthefirstsubsystem,thefollowingcomponentsarerecognisedpersonalcomputerwithappropriatesoftware,transformingintroducedequationsandinequalitiesofmotionandtrajectoryplanersintoelectricsignal.ThelatterissendtoaPLCunit,whichinturncausesanelectricalactuationofsolenoidvalves.Pressuresfromthesolenoidvalvesarecausingchangesinspoolpositions,assuringassumedflowofthehydraulicoilintocylinders.Thespoolposition,inturn,isconvertedthroughatransducertoanelectricfeedbacksignalsenttothesolenoidvalves.Openedspoolsarelettingthehydraulicoiltoflowintothethirdsubsystem,namelycylindersoftheexcavatormechanism.Finally,thelastsubsystemiscomposedofthreecomponentsthehydrauliccylinders,theboom,thearm,andthebucket.Withthemotionoftheexcavator,armsandthebucketitself,thepressuresincylindersE.Budnyetal./AutomationinConstruction122003245–254246arechanging.Informationaboutthesechangesissenttothesecond,hydraulicsubsystem,wherethefeedbacksignalcorrectspositionofspoolsassuringtheoilflowaccordingtothedesignedtrajectory.Inthepaper,transferfunctionsofallsystemcomponentsareinvestigatedfromthepointofviewofstability.Thefunctionsaredefinedtheoretically,ornumericallyfromdiagramspresentedincataloguesofhydraulicequipment.Joiningalltransferfunctionofparticularcomponent,thetransferfunctionofthewholesystemisdiscussedfromthepointofviewofperformanceunderabruptunitsignal.Severalexperimentswereperformed,showingthatitispossibletoassurestable,assumedmotionofthebucket.Amongexperiments,onewasdevotedtodrilling.Inotherwords,thekinematicallyinducedtrajectorywasastraight,verticalline.ExperimentallyobtainedlineispresentedinRefs.6and10.Itisinterestingtonotethatthevariationofexperimentallinedoesnotexceed10cm.3.ThreesubsystemsoftheexperimentalsetupThediscussedsystemisdividedinthreesubsystems,namelymicrocomputer,hydraulicvalves,andexcavatorarmswithabucket.Below,theyarediscussedseparatelyandthenajointcontrolproblemisdefined.3.1.MicrocomputerasasubsystemWestartwithdefiningamodeloftheendeffectorbucket,drill,hammermotion.Theendeffector,initsplanemotion,hasthreedegreesoffreedomajj1,2,3Fig.1.Theyarerotationsoftheboom,ofthearm,andoftheeffector.Denotingbyx1p,x2ppositionoftheendeffectortip,andbyx3itsrotation,thekinematicsoftheconsideredmechanismisrepresentedbyvectorrelationx1px2px3p266664377775¼c1c2c30s1s2s30000a3266664377775C1l1l2l3266664377775ð1Þwherecjandsjdenotecosajandsinaj,respectively.Infurtherconsiderations,thesubindexpisomittedasthepositionofonlyonepointisconsidered.VelocityofthepointP,vv1,v2,v3Tx˙1,x˙2,x˙3TisobtainedbytakingtimederivativeofEq.1,andbyreducing3C24matrixtoa3C23matrix˙x¼v¼A˙a¼Awð2ÞwhereA¼C0l1s1C0l2s2l3s3l1c1l2c2l3c3001266664377775ð3ÞTakinginverseofAmatrixequaltoAC01¼l2c2l1c10C0l2s2C0l1s10l2l3f23l1l3f13l1l2f12266664377775C11l1l2ðc1s2C0s1c2Þð4ÞwithfijsicjC0cisj,wefindtheinversekinematics,relatingangularvelocitiesofmechanismelementstothetipdisplacementvectorw¼AC01vð5ÞAngularvelocitiesxj,inturn,aredependentontheelongationvelocitiesh˙iofhydrauliccylinders.Thisdependencehastobedeterminedfromgeometricalrelationsbetweencylinderlengths,constantparametersofattachment,andaj.Westartwiththefirstcylinder.FromFig.2wefindcoordinatesoftwocylindershinges,A1andB1.Theyarex1A1¼a0x2A1¼b0x1B1¼b1c1þa1s1x2B1¼b1s1C0a1c1Takingh21¼ðx1B1C0x1A1Þ2þðx2B1C0x2A2Þ2E.Budnyetal./AutomationinConstruction122003245–254247aftertransformationweobtainh21¼p01þq01c1þr01s1ð6Þwherep01¼a20þa21þb20þb21q01¼2ða1b0C0a0b1Þr01¼C02ða0a1þb0b1ÞTakingtimederivativeofEq.6wefind˙h1¼C0q01s1þr01c12h1C1x1¼G1112h1C1x1ð7ÞRepeatingthesameconsiderationforthesecondcylinderlengthFig.3weobtainh22¼p02þq02f12þr02g12ð8Þwherep02¼a22þa23þb22þb23q02¼C02ða2a3þb2b3Þr02¼2ða2b3C0b2a3ÞFig.1.Theminiexcavatorconsidered.E.Budnyetal./AutomationinConstruction122003245–254248
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