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BIRGITTALANTTOPETTERKRUSJANOVEPALMBERGDIVISIONOFFLUIDPOWERTECHNOLOGY,DEPARTMENTOFMECHANICALENGINEERING,LINKDPINGUNIVERSITY,S58183LINKOPING,SWEDENDYNAMICPROPERTIESOFLOADSENSINGSYSTEMSWITHINTERACTINGCOMPLEXMECHANICALLOADSALOADSENSINGFLUIDPOWERSYSTEMISAFEEDBACKSYSTEMWITHSEVERALTYPESOFINSTABILITYMODESTHISPAPERDEALSWITHONEOFTHEM,WHERELOADINTERACTIONTHROUGHAMECHANICALSTRUCTUREANDTHEFLUIDPOWERSYSTEMMAYCAUSEINSTABILITY,EGINALORRYCRANECRITERIAFORINSTABILITYAREEVALUATEDTHISPAPERALSOPROPOSESSOMEMETHODSHOWTOAVOIDTHISTYPEOFINSTABILITYINTRODUCTIONTHEHIGHENERGYSAVINGPOTENTIALOFLOADSENSINGSYSTEMSISASPECIALADVANTAGE,ESPECIALLYWHENTHECONFIGURATIONINCLUDESAVARIABLEPUMPCONTROLLABILITYOFSUCHSYSTEMSMAYBEENHANCEDBYPRESSURECOMPENSATEDCONTROLVALVESSINCEINTERACTIONBETWEENTHEACTIVATEDLOADSCANBEAVOIDEDSEEFIG1HOWEVER,THISTYPEOFSYSTEMISAFEEDBACKSYSTEMAND,UNFORTUNATELY,ALSOEXTREMELYUNDAMPEDTHEREFORE,ITISNOTUNLIKELYTHATINSTABILITYTAKESPLACEINSUCHSYSTEMSGENERALLY,THEMOSTRISKYFEEDBACKISTHEPUMPPRESSUREANDHIGHESTLOADPRESSUREFEEDBACKSCONTROLLINGTHEPUMPREGULATORWHICHCOULDLEADTOTHESOCALLEDPUMPANDPUMPLOADINSTABILITIES,SEEKRUS1989THEREISALSOARISKOFINSTABILITYATTHELOADIFAFEEDBACKCOMPONENTSUCHASANOVERCENTREVALVECONTROLSTHEACTUATORATHIRDTYPEOFINSTABILITYISDISCUSSEDINLANTTO1992WHENSEVERALACTUATORSCONTROLTHESAMEMECHANICALSTRUCTURE,EGACRANEARM,THEYINTERACTTHROUGHTHESTRUCTUREANDTHEFLUIDPOWERSYSTEMTHEN,AFEEDBACKCOULDBECREATEDASINFIG2WHEREAMOVEMENTOFTHEACTUATORWITHTHELOWESTLOADCHANGESTHEHIGHESTLOADPRESSUREANDTHEREFORETHELOADSENSINGPUMPPRESSUREWHICHCHANGESTHEFLOWTOTHELOWESTLOADSUCHDESTABILIZINGINTERACTIONHASEARLIERBEENANALYZEDBYEGRAMACHANDRAN1982ANDPANNALA1985THISPAPERGIVESADEEPERDISCUSSIONABOUTTHISTHIRDTYPEOFINSTABILITYRISK,MAINLYFOUNDINLOADSENSINGSYSTEMSTHESTABILITYANALYSISINTHISPAPERISBASEDONKRUS1988,KRUS1989,PALMBERGETAL1985,ANDLANTTO1992ANDCONCERNSMAINLYSYSTEMSWITHNONCOMPENSATEDCONTROLVALVESONLYSYSTEMSWITHANUNSATURATEDLOADSENSINGPUMPAREDISCUSSEDHEREMOREOVER,ONLYPOSITIVEMASSANDINERTIALOADSARECONSIDEREDINSTABILITYBECAUSEOFLOADINTERACTIONTHROUGHTHEMECHANICALSTRUCTUREINTHISSECTION,WEWILLSHOWHOWINSTABILITYCANBEEVALUATEDFORASTRUCTURECONTROLLEDBYANIDEALLOADSENSINGSYSTEMTHISCONTRIBUTEDBYTHEDYNAMICSYSTEMSANDCONTROLDIVISIONFORPUBLICATIONINTHEJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROLMANUSCRIPTRECEIVEDBYTHEDYNAMICSYSTEMSANDCONTROLDIVISIONMARCH25,1991;REVISEDMANUSCRIPTRECEIVEDJULY1992ASSOCIATETECHNICALEDITORAAKERSSECTIONWILLALSODISCUSSWHENANORMALLORRYCRANEREACHESINSTABILITYSINCETHISTYPEOFINSTABILITYISDEPENDENTONBOTHTHEFLUIDPOWERSYSTEMANDTHEGEOMETRYOFTHEMECHANICALSTRUCTURE,THEDESIGNOFTHESTRUCTUREANDTHEFLUIDPOWERSYSTEMWILLBEDISCUSSEDTHEANALYSISWILLSHOWTHATTHISINSTABILITYGENERALLYMAYOCCURIF1APOSITIVEORNEGATIVEMOVEMENTOFTHELOWESTLOADWILLCAUSEANEGATIVEAPOSITIVE,RESPECTIVELYMOVEMENTOFTHEHIGHESTLOADTHROUGHTHEMECHANICALSTRUCTUREAND2IFAFEEDBACKCOMPONENTCONTROLSTHESYSTEMSOTHATANINCREASEOFTHEHIGHESTLOADPRESSUREWILLCAUSEANINCREASEOFTHELOADFLOWTOTHELOWESTLOADTHROUGHTHEFLUIDPOWERSYSTEMINSTABILITYINALOADSENSINGSYSTEMTHESIMPLESTRUCTUREINFIG3,CONTROLLEDBYTWOCYLINDERSINALOADSENSINGSYSTEMWITHNONCOMPENSATEDCONTROLVALVES,HASTHEFOLLOWINGEQUAFIG1LOADSENSINGSYSTEMINCLUDINGCONTROLVALVESWITHCONVENTIONALPRESSURECOMPENSATORSPOOLS////VHIGHESTLOADLOADFLOWFRLOWESTLOAD\4LOADSENSINGPRESSURE4FIG2FEEDBACKTHROUGHTHEMECHANICALSTRUCTUREJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROLSEPTEMBER1993,VOL115/525COPYRIGHT1993BYASMEDOWNLOADED22MAR2009TO20219846187REDISTRIBUTIONSUBJECTTOASMELICENSEORCOPYRIGHT;SEEHTTP//WWWASMEORG/TERMS/TERMS_USECFMFIG3LOADSENSINGSYSTEMWITHLOADINTERACTIONTHROUGHASIMPLIFIEDMECHANICALSTRUCTURETIONSOFMOTION,DESCRIBINGTHESMALLMOVEMENTSOFTHETWOPISTONSINTHEFREQUENCYDOMAINS2/AXLJ\AXL2,00B2\AXI2,ALLJLLAOLUPOLAL2APL2A02AP01THEYFORMTHETRANSFERFUNCTIONSGMAANDG„H2OFTHEMECHANICALLOADINAPPENDIXWHEREMMLM2,BIBI,M2M2ANDB2B2,WHILEMFI1MKI2M2FORMSTHETRANSFERFUNCTIONSOFTHEMECHANICALCOUPLINGASG,GK2AL1AL2M2SALXALLM2S23THESEEQUATIONSANDTHEAPPENDIXFORMTHEBLOCKDIAGRAMINFIG4WHICHDESCRIBESAGENERALLOADSENSINGSYSTEMWITHLOADINTERACTIONTHROUGHTHEMECHANICALSTRUCTUREBLOCKSGKILANDGKI2ANDTHEFLUIDPOWERSYSTEMRFFKEFIG4BLOCKDIAGRAMOFALOADSENSINGSYSTEMWITHLOADINTERACTIONTHENEXTSTEPISTOANALYZETHISFEEDBACKSYSTEMBYREDUCINGTHEBLOCKDIAGRAMINTOCLOSEDLOOPTRANSFERFUNCTIONSWHERETHEOUTPUTSIGNALSAXLIANDAXL,2AREFUNCTIONSOFAXVIIANDAA,SEELANTTO1992THEN,THECHARACTERISTICEQUATIONISFOUNDAS1H,IIG,NI1G;GMLHMGNFLSCGMXGVHL2GMIRTC/J2J/PUMPGM2G„\FLSGN1HL\GKJ1HL2GK1G„G„HMHMGPLFLSGPGMIG„GMIHMH,,LHSPGNG„2GP045AB,BCDPDLFSGSHSJKKCAREA,M2VISCOUSDAMPINGCOEFFICIENTOFACTUATOR,NS/MVOLUMECAPACITANCEV7/3E,M3/PAVOLUMETRICGRADIENTOFPUMPDISPLACEMENT,MVREVMOTORLOADDISPLACEMENT,MVREVFILTERTRANSFERFUNCTIONTRANSFERFUNCTIONWHEREOUTPUTISNORMALLYFLOWWHILEINPUTISPRESSURETHEFLOWISOUTPUTANDVALVEDISPLACEMENTINPUTWHENTHESUBSCRIPTISXTRANSFERFUNCTIONWHEREOUTPUTISPRESSUREWHILEINPUTISFLOWINERTIA,KGMSPRINGCOEFFICIENT,N/MFLOWPRESSURECOEFFOFORIFICEDQ/DPMPOM,M3/SPAKQL,LM,MNPQSVXHE6APE01FLOWGAINOFVALVEORIFICE3/DXVALVE,M2/SLENGTH,MMASS,KGPUMPSPEED,REV/SPRESSURE,PAFLOW,M3/SLAPLACETRANSFORMOPERATOR,RAD/SVOLUME,M3DISPLACEMENT,MEFFECTIVEBULKMODULUS,PADAMPINGRATIOSMALLVARIATIONINALINEARIZEDVARIABLEDENSITY,KG/M3ANGLE,RADFREQUENCY,SUBSCRIPTINDICATESABREAKFREQUENCY,RAD/SCAPITALLETTEROFAVARIABLEMAYINDICATEALAPLACETRANSFORMEDVARIABLESUBSCRIPTLLSM0PREGTVK12JMETERINSIDEOFCYLINDERLOADSENSINGLINEMECHANICALLOADMETEROUTSIDEOFCYLINDERPUMPPUMPREGULATORPUMPSUPPLYVOLUMETANKCONTROLVALVEORVALVEPACKAGELOADWHICHCOUPLESTHEACTUATORSTHROUGHTHESTRUCTURETHEHIGHESTLOADTHESECONDHIGHESTLOADSHORTNOTEINSUBSCRIPT,EG,L,IMEANSU526/VOL115,SEPTEMBER1993TRANSACTIONSOFTHEASMEDOWNLOADED22MAR2009TO20219846187REDISTRIBUTIONSUBJECTTOASMELICENSEORCOPYRIGHT;SEEHTTP//WWWASMEORG/TERMS/TERMS_USECFMAFIRSTGLANCEATTHISEQUATIONUSINGTHEFOLLOWINGSIMPLIFICATIONS9ANINFINITELYFASTPUMPPRESSURECONTROLWITHOUTLEAKAGEMODELLEDASANINDUCTANCE,GPL/LPSOOWHICHLEADSTOPUMP1/GP,ANDCONSEQUENTLYAPSAPLII9NOORIFICEINTHELOADSENSINGLINE,FLS18CONSTANTPRESSUREONTHEMETEROUTSIDEOFTHEPISTONS,AP0IL0OTAOA0LEADINGTOG„,AGM1RESPECTIVELYAP0I20ORAOI20LEADINGTOG™,2GM,28ONLYMASSLOADSWITHOUTSPRINGFORCESANDWITHTHEONLYVISCOUSFRICTIONAPPEARINGINTHECYLINDERSAREANALYZEDWHICHLEADTOGKAALAALA/MK2SANDGK1ALAAL1/{MKAS8NODYNAMICSINTHECONTROLVALVESLEADINGTOG„AJJGJSANDKCIVY2,RESPECTIVELY9B2KC,V,IA2LTLOFTHELOWESTLOADGIVESTHEFOLLOWINGCHARACTERISTICEQUATIONWHEREALAAL,2/MKACLAAND4,IALAALA/MK2CL,22512I228,WI2L2KFNA2LLM2AL2MKASAF,J7MKCNB\AL,_06FINDINGTHEROOTSTOTHISEQUATIONWILLSHOWIFSTABILITYISACHIEVEDORNOTTHECHARACTERISTICEQUATIONMAYBEREWRITTENASS26,4,TS10WB7IDENTIFICATIONOFTHESTERMSGIVESWAANDOBASSUMETHAT\\825ILL,KCBXJ1THEN,UAANDWFIWILLBEACHIEVEDFROMEQS6AND7AS9UA210,/WIV1VW2,22,WAWI2IF,/WIVV1/1WL\2MK1MNIC2JWJMM2MKLMK2MXM211WHERECOIJIILCOFLANDCOUII2WBEQUATIONS6AND7GIVETHEDAMPINGRATIOS8,4ANDBBNEGATIVEDAMPINGRATIOSSHOWONINSTABILITYHERE,ITISPOSSIBLETOSHOWTHAT5BWILLBEPOSITIVESINCETHEMASSMATRIXINEQ1MUSTBEPOSITIVESEMIDEFINITEORMKLMK2MLM212MOTORSPEED9LRAD/S15MOTORSPEED0RAD/SISM45CM3/ROVTIMES10TA/2IC152HZJSK100HZ500155CM/IW5TIMES10OIA/2170HZEG/FA110HZS0005FIG5TIMESIMULATIONSOFALOADSENSINGSYSTEMWITHTWOINTERACTING,FIXEDDISPLACEMENTMOTORSWITHTHEDISPLACEMENTSDTI1HIGHESTLOADANDDL2WHENDT|1DL2ANDDL|1DL2THEHIGHESTLOADSTARTSAT0S,THEOTHERAT5SECKCNM2MKLALLI40LHWA2IA12UBKCN\M,ALLA72M2\21DL2WB13THEEQUATIONSHOWSONSTABILITYONLYWHENM212L22ALLAL2BICLJKC2UA20LXB2CL2KR2A214ASSUMINGNOVISCOUSFRICTIONINTHECYLINDER,B20,ANDNT\0INTHESIMPLIFIEDCASEINFIG3,WHEREMKAM2M2,LEADSUSTOTHEFOLLOWINGCRUDECRITERIONSINCEWAWLAANDOBOOIFINSTABILITYSHALLOCCURINTHESYSTEM,THEPISTONAREAAL,2OFTHELOWESTLOADMUSTBELARGERTHANTHEPISTONAREAALAOFTHEHIGHESTLOADTHISMEANSTHATFORTHEMECHANICALSTRUCTUREINFIG3,INSTABILITYWILLALWAYSOCCURSINCETHEACTUATORWITHTHEHIGHESTPRESSUREHASTHESMALLESTPISTONAREA,SEEFIG5INREALITY,THISMAYNOTALWAYSHAPPENSINCETHESIMPLIFICATIONSPRECEDINGEQ6NORMALLYARENOTFULFILLEDWHICHINCREASESTHEDAMPINGANDCONSEQUENTLYTHESTABILITYMARGINOFTHESYSTEMDESIGNASPECTSOFAVOIDINGINSTABILITYTHISINSTABILITYTYPEHASITSORIGININEFFECTIVENEGATIVEDAMPINGRATIOOFTHELOWESTLOADINTHETWOLOADSITUATIONTOINCREASETHEDAMPINGRATIOOFTHEACTUATORISCONSEQUENTLYSTABILIZINGEGWITHTHEMETEROUTORIFICEASMENTIONEDEARLIER,THEFEEDBACKNORMALLYPASSESBETWEENTHEACTUATORSTHROUGHTHEMECHANICALSTRUCTURE,BUTALSOTHROUGHTHELOADSENSINGLINETOTHEPUMPANDPUMPPRESSUREVOLUMETHEBESTWAYTOREDUCETHEINSTABILITYRISKSHOULDTHEREFOREBETODESIGNTHEMECHANICALSTRUCTUREPROPERLYTHISREQUIRESTHATALARGEMASSORINERTIAOFTHEDYNAMICCOUPLINGFROMTHELOWESTLOADTOTHEHIGHEST,MKUMUSTBEAVOIDEDHOWTOCALCULATETHISMASSANDOTHERSISGIVENASANEXAMPLEINTHENEXTCHAPTERFORALORRYCRANEARMAFLEXIBLESTRUCTUREJOURNALOFDYNAMICSYSTEMS,MEASUREMENT,ANDCONTROLSEPTEMBER1993,VOL115/527DOWNLOADED22MAR2009TO20219846187REDISTRIBUTIONSUBJECTTOASMELICENSEORCOPYRIGHT;SEEHTTP//WWWASMEORG/TERMS/TERMS_USECFMFIG6MODELOFALORRYCRANESTRUCTURETOTALLENGTHOFCYLINDER1MHIGHESTHADMAXTOTALLENGTHOFCYLINDER2MHIGHRISKFIG7VARIOUSVALUESOF2BALVAA\JMKCV2ASAFUNCTIONOFTHEPISTONDISPLACEMENTSOFTHELORRYCRANENEGATIVEVALUESINDICATEDESTABILIZATIONOFTHEOSCILLATIONS,WHILEPOSITIVEVALUESINDICATESTABILIZATIONISALSOSTABILIZINGCOMPAREDWITHASTIFFONETHEFEEDBACKSIGNALTHROUGHALOADSENSINGPUMPISALSOSTOPPEDBYALOWPASSFILTER,THATISANORIFICE,INTHELOADSENSINGLINESINCEITHASTOPASSTHISLINEITALSOSEEMSASIFAFASTPUMPPRESSURECONTROLINTHELOADSENSINGSYSTEMMAYEASETHEINTERACTIONBETWEENTHEACTUATORSTHROUGHTHEFLUIDPOWERSYSTEMANDINCREASETHERISKOFINSTABILITYTOPRESSURECOMPENSATETHECONTROLVALVEOFTHELOWESTLOADSINTHELOADSENSINGSYSTEMREDUCESTHEINSTABILITYRISKSINCEKC„2ISCLOSETOZEROOFAVALVEPACKAGEWITHAFASTANDIDEALPRESSURECOMPENSATORSPOOLSUCHASINFIG1ANEXAMPLEINSTABILITYOFALORRYCRANEARMWILL2HA/WAINEQ13BEPOSITIVEFORTHELORRYCRANESTRUCTUREINFIG6AROUGHCRITERIONOFACRANEARMISACHIEVEDIFTHEFOLLOWINGASSUMPTIONSAREMADETHESTRUCTUREISSTIFFTHEMASSOFTHESTRUCTUREISLUMPEDINTOTHELOADMASSM9THEBOOMISTHEHIGHESTLOADONLYPOSITIVELOADSAREDISCUSSED,9290DEGTHELAGRANGEEQUATIONDESCRIBESTHEMOVEMENTSOFTHESTRUCTURETISTHEKINETICENERGYANDMEJTHETORQUEFORTHEANGLE0,DDF\DT,JT{WWME,12MKLEUE2Y2MEUE215TLLCOSDLL2COS62JLISINOZSIN1617TIMESECTIMESECFIG8MEASUREMENTSONTHELORRYCRANETHE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