機械制造及其自動化專業(yè)外文翻譯

外文原文VSSmotioncontrolforalaser-cuttingmachine^Ales\Hace,KarelJezernik*,MartinTerbucUniversityofMaribor,FacultyofElectricalEngineeringandComputerSciences,InstituteofRobotics,Smetanovaul.17,SI-2000Maribor,SloveniaReceived18October1999;accepted2June2000AbstractAnadvancedposition-trackingcontrolalgorithmhasbeendevelopedandappliedtoaCNCmotioncontrollerinalaser-cuttingmachine.Thedrivetrainsofthelaser-cuttingmachinearecomposedofbelt-drives.Theelasticservomechanismcanbedescribedbyatwo-masssysteminterconnectedbyaspring.Owingtothepresenceofelasticity,frictionanddisturbances,theclosed-loopperformanceusingaconventionalcontrolapproachislimited.Therefore,themotioncontrolalgorithmisderivedusingthevariablesystemstructurecontroltheory.Itisshownthattheproposedcontrole!ectivelysuppressesthemechanicalvibrationsandensurescompensationofthesystemuncertainties.Thus,accuratepositiontrackingisguaranteed.(2001ElsevierScienceJd.Allrightsreserved.)structurecontrol;Chattering;Disturbancerejection;Robustcontroll.Keywords:PositionKeywords:Positioncontrol;Drives;Servomechanisms;Vibrations;VariableIntroductionFormanyindustrialdrives,theperformanceofmotioncontrolisofparticularimportance.Rapiddynamicbehaviourandaccuratepositiontrajectorytrackingareofthehighestinterest.Applicationssuchasmachinetoolshavetosatisfythesehighdemands.Rapidmovementwithhighaccuracyathighspeedisdemandedforlasercuttingmachinestoo.Thispaperdescribesmotioncontrolalgorithmforalow-costlaser-cuttingmachinethathasbeenbuiltonthebaseofaplanarCartesiantablewithtwodegrees-of-freedom(Fig.1).Thedrivetrainsofthelaser-cuttingmachinearecomposedofbelt-driveswithatimingbelt.Theuseoftimingbeltsinthedrivesystemisattractivebecauseoftheirhighspeed,highefficiency,longtravellengthsandlow-cost(Haus,1996).Ontheotherhand,theyyieldmoreuncertaindynamicsandahighertransmissionerror(Kagotani,Koyama&Ueda,1993).Consequently,belt-drivessufferfromlowerrepeatabilityandaccuracy.Moreover,thebelt-drivedynamicsincludemoreresonancefrequencies,whichareadestabilisingfactorinafeedbackcontrol(Moon,1997).Therefore,aconventionalcontrolapproachlikePI,PDorPIDcontrolfailstoachieveacceptableperformance.Plantparametervariations,uncertaindynamicsandloadtorquedisturbances,aswellasmechanicalvibrations,arefactorsthathavetobeaddressedtoguaranteerobustsystemstabilityandthehighperformanceofthesystem.Anadvancedrobustmotioncontrolschemeisintroducedinthispaper,whichdealswiththeissuesrelatedtomotioncontrolofthedriveswithtimingbelts.ThecontrolschemeisdevelopedonthebasisofthemotioncontrolalgorithmintroducedbyJezernik,CurkandHarnik(1994).Itpossessesrobustpropertiesagainstthedisturbancesthatareassociatedwithanominalplantmodel,asithasbeendevelopedwiththeuseofthevariablestructuresystem(VSS)theory(Utkin,1992).Thecrucialpartofthecontrolschemeistheasymptoticdisturbanceestimator.However,asshowninthispaper,itfailstostabiliseresonantbeltdynamics,sinceitwasdevelopedforarigidrobotmechanism.Therefore,thispaperintroducesanimprovedmotioncontrolscheme,whichsuppressesthevibrationsthatwouldariseduetothenon-rigid,elasticdrive.Consequently,arapidresponsewithlowpositiontrackingerrorisguaranteed.Thepaperissetoutasfollows.Thelaser-cuttingmachineispresentedandthecontrolplantmodelofthemachinedrivesisdevelopedinSection2.InSection3,theVSScontrolregardingtheelasticservomechanismisdiscussedandthederivationofthemotioncontrolschemeisdescribed.Section4presentstheexperimentalresultsandafollow-updiscussion.ThepaperissummarizedandconcludedinSection5.2.Thecontrolplant2.1.ThemachinedescriptionThelaser-cuttingmachineconsistsoftheXYhorizontaltableandalasersystem(Fig.1).Thefundamentalcomponentsofthelasersystemare:thepowersupplyunit,whichisplacedoffthetableandthusisnotconsideredinthemotioncontroldesign;thelaser-beamsource,whichgeneratesthelaserbeam(thelaser-generator);?thelaser-head,whichdirectsthelaserbeamontothedesiredpositioninthecuttingplane.hrid皈Vgs；DCmoluraAflSIKl?CIlr1?|(nLihrid皈Vgs；DCmoluraAflSIKl?CIlr1?|(nLi做功"bF.潮WEminfflniptga!SJlilVOVaSinryn"m頑i曲rikxrs沁nnCEfTiSM網(wǎng)him蝠Y"imILSJ*124-iilgmot]od^)rilrn]]tr■L\M?k而Fig.1.Themachineandthecontrollerhardware.Thetablehastomoveandpositionthelaserheadinahorizontalplane.Thisisachievedbythemeansofadrivesystemwithtwoindependentmotionaxes.TheyprovidemovementalongtheCartesians'XYaxesof2and1m,respectively.TheX-driveprovidesthemotionofthelaser-headinX-direction.Thedriveandthelaser-headaswellasthelaser-generatorareplacedonthebridgetoensureahigh-qualityopticalpathforthelaser-beam.ThemovementofthebridgealongtheY-axisisprovidedbytheY-drive.Thelaser-headrepresentstheX-driveload,whiletheY-driveisloadedbythebridge,whichcarriesthecompleteX-drivesystem,thelaser-head,andthelaser-generator.Theloadsslideoverthefrictionlessslidesurface.Thepositioningsystemconsistsofthemotioncontroller,theamplifiers,theDC-motorsandthedrivetrains.TheX-drivetrainiscomposedofagearboxandabelt-drive(Fig.2).Thegearboxreducesthemotorspeed,whilethebelt-driveconvertsrotarymotionintolinearmotion.Thebelt-driveconsistsofatimingbeltandoftwopulleys:adrivingpulleyandadrivenpulleythatstretchthebelt.TheY-drivetrainismorecomplex.Theheavybridgeisdrivenbytwoparallelbelt-drives;eachbridge-sideisconnectedtooneofthebelt-drives.Thedrivingpulleysofthebelt-drivesarelinkedtothedrivingaxis,whichisdrivenviatheadditionalbelt-driveandthegearboxisusedtoreducethespeedofthemotor.loadFig.2.Thedrive.2.2.AssumptionsThemachinedrivesrepresentacomplexnon-lineardistributedparametersystem.Thehigh-ordersystempossessesseveralresonantfrequenciesthatcanbeobservedbythedrives'stepresponse(seeSection4).Fromacontroldesignperspective,difficultiesarisefrommechanicalvibrationsthataremetinthedesiredcontrolbandwidth(~10Hz).Ontheotherhand,thedesignobjectiveistohaveahigh-performancecontrolsystemwhilesimultaneouslyreducingthecomplexityofthecontroller.Therefore,asimplemathematicalmodelwouldonlyconsiderthefirst-orderresonanceandneglecthigh-orderdynamics.Inotherwords,thedesignmodelofthecontrolplantwillcloselymatchthefrequencyresponseoftherealsystemuptothefirstresonance.Next,thecontrollershouldbeadequatelydesignedtocopewiththehigher-orderresonanceinsuchawaythattheresonancepeaksdropsignificantlytomaintainthesystemstability.Thus,accordingtothesignalanalysisandthedrives'features,thefollowingassumptionscouldbemade:?theDC-servosoperatinginthecurrentcontrolmodeensureahigh-dynamictorqueresponseonthemotoraxiswithanegligibletimeconstant;?thesmallbacklashinthegearboxesandthebacklashofthebelt-drivesduetotheappliedpre-tensionofthetimingbeltsisnegligible;?arigidlinkbetweenamotorshaftandadrivingpulleyofthebelt-drivecouldbeadopted;?theinertiaofthebelt-drives'drivenpulleysisnegligibleincomparisontoothercomponentsofthedrivesystem.Usingtheassumptionsabove,dynamicmodelingcouldbereducedtoatwo-massmodelofthebelt-drivesthatonlyincludesthefirstresonance.Inthecontroldesign,

theuncertainpositioningoftheloadduetothelowrepeatabilityandaccuracyofthebelt-drivehastobeconsideredaswell.Note,thatnoattentionispaidtothecoupleddynamicsoftheY-driveduetotheparalleldriving,thus,thedoublebelt-driveisconsideredasanequivalentsinglebelt-drive.23.Thebelt-drivemodelThebelt-drivescouldbemodelledasamulti-masssystemusingmodalanalysis.Inthebelt-drivemodelwithconcentratedparameters,linear,masslessspringscharacterizetheelasticityofthebelt.Accordingtotheassumptionsabove,atwo-massmodelcanbeobtained.Thedriving-pulley,motorshaftandthespeedreducerareconsideredastheconcentratedinertiaofthedrivingactuator.Thedriven-pulleyandtheloadareconcentratedintheloadmass.Theinertiaandthemassarelinkedbyaspring.Frictionpresentinthemotorbearings,thegearbox,thebelt-drive,andnon-modelledhigher-orderdynamicsareconsideredasanunknowndisturbancethataffectsthedrivingsideaswellastheloadside.Themechanicalmodelofthetwo-masssystemanditsblockschemeareshowninFigs.3and4,respectively.Thebelt-stretchoccursduetotheinherentelasticityofthetimingbelts.However,accordingtoavibrationanalysisofbelt-drives(Abrate,1992),theobtainedmodelcouldberearranged.Assumetheunittransmissionconstant(L=1).Then,thecontrolplantmodelispresentedbyFig.5.Thecontrolplantconsistsoftwopartsconnectedinacascadedstructure.Thefirstpartisdescribedbypoorlydampeddynamicsduetotheelasticbelt.Thesecondpartconsistsoftheload-sidedynamics.Thebelt-stretchtforcedbytheappliedtorqueq.ThedynamicsaredescribedbyEq.(1)whereHw(s)denotesthebelt-stretchdynamicstransferfunction,(2)and*and(I-4--"一and*andisthenaturalresonantfrequency(3)ishtedisturbancethataffectsthebelt.Theload-sidedynamicsare(4)."?：'=/(4T廠、'?whereFwdenotestheforce,whichdrivestheloadFig.3.Themechanicalmodeloftheelasticdrive.Mistheloadsidemass;Jthedrivingsideinertia;Kthespringstiffness;一themotorshaftangularposition;xtheloadposition;wthebelt-stretch;tthemotorshafttorque;thedrivingsidedisturbancetorque;thefnL=cx/c(ploadsidedisturbanceforce;'"thespringforceand,thetransmissionconstant.Fig.4.Theblockschemeofthemechanicalmodel:symbolareasexplainedinFig.3.Fig.5.Theblockschemeofthecontrolplant-3.ThemotioncontrolalgorithmTheerroneouscontrolmodelwithstructuredandunstructureduncertaintiesdemandsarobustcontrollaw.VSScontrolensuresrobuststabilityforthesystemswithanon-accuratemodel,namely,ithasbeenprovenintheVSStheorythattheclosed-loopbehaviorisdeterminedbyselectionofaslidingmanifold.ThegoaloftheVSScontroldesignistofindacontrolinputsothatthemotionofthesystemstatesisrestrictedtotheslidingmanifold.Ifthesystemstatesarerestrictedtotheslidingmanifoldthentheslidingmodeoccurs.Theconventionalapproachutilisesdiscontinuousswitchingcontroltoguaranteeaslidingmotionintheslidingmode.Theslidingmotionisgovernedbythereducedordersystem,whichisnotaffectedbysystemuncertainties.Consequently,theslidingmotionisinsensitivetodisturbanceandparametervariations(Utkin,1992).TheessentialpartofVSScontrolisitsdiscontinuouscontrolaction.Inthecontrolofelectricalmotordrivespowerswitchingisnormal.Inthiscase,theconventionalcontinuous-time/discontinuousVSScontrolapproachcanbesuccessfullyapplied.However,inmanycontrolapplicationsthediscontinuousVSScontrolfails,andchatteringarises(S[abanovicH,Jezernik,&Wada,1996;Young,Utkin&OGzguKner,1999).Chatteringisanundesirablephenomenoninthecontrolofmechanicalsystems,sincethedemandedperformancecannotbeachieved,orevenworse-mechanicalpartsoftheservosystemcanbedestroyed.Themaincausesofthechatteringareneglectedhigh-ordercontrolplantdynamics,actuatordynamics,sensornoise,andcomputercontrolleddiscrete-timeimplementationinsampled-datasystems.SincethemainpurposeofVSScontrolistorejectdisturbancesandtodesensitisethesystemagainstunknownparametricperturbations,theneedtoevokediscontinuousfeedbackcontrolvanishesifthedisturbanceissufficientlycompensatedfor,e.g.bytheuseofadisturbanceestimator(Jezerniketal.,1994;Kawamura,Itoh&Sakamoto,1994).JezernikhasdevelopedacontrolalgorithmforarigidrobotmechanismbycombiningconventionalVSStheoryandthedisturbanceestimationapproach.However,therigidbodyassumption,whichneglectsthepresenceofdistributedorconcentratedelasticity,canmakethatcontrolinputfrequenciesoftheswitcherexciteneglectedresonantmodes.Furthermore,indiscrete-timesystemsdiscontinuouscontrolfailstoensuretheslidingmodeandhastobereplacedbycontinuouscontrol(Youngetal.,1999).Avoidingdiscontinuous-feedbackcontrolissuesassociatedwithunmodelleddynamicsandrelatedchatteringarenolongercritical.Chatteringbecomesanon-issue.Inplantswherecontrolactuatorshavelimitedbandwidththerearetwopossibilities:actuatorbandwidthisoutsidetherequiredclosed-loopbandwidth,or,thedesiredclosed-loopbandwidthisbeyondtheactuatorbandwidth.Inthefistcase,theactuatordynamicsaretobeconsideredasthenon-modelleddynamics.Consequently,theslidingmodeusingdiscontinuousVSScontrolcannotoccur,becausethecontrolplantinputiscontinuous.Therefore,thedisturbanceestimationapproachispreferredratherthanVSSdisturbancerejection.Inthesecondcase,theactuatordynamicsaretobelumpedtogetherwiththeplant.Thematchingconditions(Draz\enovicH,1969)fordisturbancerejectionandinsensitivitytoparametervariationsintheslidingmodeareviolated.Thisresultsfromhavingdominantdynamicsinsertedbetweenthephysicalinputtotheplantandthecontrolleroutput.WhenunmatcheddisturbancesexisttheVSScontrolcannotguaranteetheinvariantslidingmotion.Thisrestrictionmayberelaxedbyintroducingahigh-orderslidingmodecontrolinwhichtheslidingmanifoldischosensothattheassociatedtransferfunctionhasarelativedegreelargerthanone(Fridman&Levant,1996).SuchacontrolschemehasbeenusedinanumberofrecentlydevelopedVSScontroldesigns,e.g.inBartolini,FerraraandUsai(1998).Inthelatter,thesecond-orderslidingmodecontrolisinvokedtocreateadynamicalcontrollerthateliminatesthechatteringproblembypassingdiscontinuouscontrolactionontoaderivativeofthecontrolinput.ThesystemtobecontrolledisgivenbyEqs.(1)—(5)andthesystemoutputistheloadposition.Thecontrolobjectiveisthepositiontrajectorytracking.ThecontrolalgorithmthatisproposedinthispaperhasbeendevelopedfollowingtheideaoftheVSSmotioncontrolpresentedbyJezernik.Sincetheelasticbelt-drivebehavesasalowbandwidthactuator,theconventionalVSScontrolalgorithmfailedtoachievetheprescribedcontrolobjective.Thus,therobustpositiontrajectorytrackingcontrolalgorithmpresentedinthepaperhasbeenderivedusingsecond-orderslidingmodecontrol.Inordertoeliminatethechatteringproblemandpreserverobustness,thecontrolalgorithmusesthecontinuouscontrollaw.FollowingtheVSSdisturbanceestimationapproach,itwillbeshownthatthedisturbanceestimationfeatureoftheproposedmotioncontrolalgorithmissimilartothecontrolapproachofJezernik(Jezerniketal.,1994).Additionally,theproposedcontrolalgorithmconsiderstheactuatordynamicsinordertoreshapethepoorlydampedactuatorbandwidth.Consequently,theproposedmotioncontrollerconsistsofarobustposition-trackingcontrollerintheouterloopandavibrationcontrollerintheinnerloop(Fig.6).Thissectionisorganizedasfollows.Section3.1presentstheproposedVSScontroldesign.Section3.2describesthederivationoftherobustpositioncontroller.Section3.3providesadescriptionofthevibrationcontroller.Finally,theproposedcontrolschemeisdescribedinSection3.4.中文譯文激光切割機的傳動控制可變結(jié)構(gòu)系統(tǒng)艾力斯?霍斯，卡瑞爾?詰責(zé)尼克，馬丁?特布馬里博爾大學(xué)機器人學(xué)學(xué)院電氣工程系和計算機科學(xué)系截稿于1999年10月18日，出版與2000年6月2日.內(nèi)容摘要：一種先進的位置跟蹤控制算法已經(jīng)研制出來了，并將其應(yīng)用在激光切割機的數(shù)控運動控制器上。激光切割機的驅(qū)動機構(gòu)是由帶傳動機構(gòu)組成的。彈性伺服機構(gòu)可以看成是一個彈簧連接的雙量機構(gòu)。由于存在彈力,摩擦力和干擾，利用可行的傳統(tǒng)的控制方法得到的閉環(huán)回路是有限的。因此，利用可變系統(tǒng)結(jié)構(gòu)控制理論推導(dǎo)出運動控制算法。算例分析表明文中有效控制抑制機械振動和保證系統(tǒng)補償?shù)牟淮_定性。因此，確保準確的位置跟蹤。簡介：對許多工業(yè)驅(qū)動器，運動控制的性能具有非常重要性。最高的利益是快速動態(tài)行為與準確軌跡跟蹤。如應(yīng)用在機床必須滿足這些高的要求。激光切割機也是，它要求快速運動快速且高準確度。這篇論文講述了激光切割機的一種低成本的建立在有兩個自由度的二維笛卡爾表基礎(chǔ)上的運動控制算法（圖1）。激光切割機的驅(qū)動機構(gòu)由有一個正時帶的帶傳動組成的。驅(qū)動系統(tǒng)中的正時帶具有吸引力是因為它具有高速度、高效、遠距離行進和低成本特性（霍斯，1996）。另一方面，他們產(chǎn)生較多的不確定的動態(tài)和更高的傳動誤差。因此，傳動帶遭受較低的重復(fù)性和準確性。此外,帶傳動動力學(xué)包括很多諧振頻率，即反饋控制中的不穩(wěn)定因素。因此，傳統(tǒng)的控制方法像比例積分控制、比例微分控制或比例積分微分控制未達到可接受的性能。設(shè)備參數(shù)的變化、不確定的動態(tài)和負載轉(zhuǎn)矩的干擾，以及機械振動是必能保證系統(tǒng)的強穩(wěn)定性和系統(tǒng)的高性能的因素。在這片論文中講述了一種先進的穩(wěn)定的運動控制方案，內(nèi)容涉及到正時帶驅(qū)動的運動控制?？刂品桨甘窃谶\動控制算法的基礎(chǔ)上由詰責(zé)尼克、科克和哈尼克1994年研制出的。用變結(jié)構(gòu)系統(tǒng)（VSS）理論使其得到了強健的抵御與一個名義上的對象模型有關(guān)的干擾的性能。漸近線的擾動的估算是控制方案的關(guān)鍵的部分。然而，就像文章指出，因為是為剛性機器人機制而研制的故不是穩(wěn)定諧振帶動力學(xué)。因此，介紹了一種改進后的會出現(xiàn)非剛性、彈性傳動的振動運動控制方案。因此，保證其低位置跟蹤誤差的快速反應(yīng)。本文陳述如下。激光切割機的陳述和控制系統(tǒng)模型機械傳動在文章的第二節(jié)。在第三節(jié),對于關(guān)于系統(tǒng)彈性伺服機構(gòu)可變結(jié)構(gòu)系統(tǒng)控制進行了深入探討，并對運動的起源控制方案進行了闡述。第四節(jié)是實驗結(jié)果和后續(xù)討論。摘要在第五部分總結(jié)和歸納了。2.模型控制2.1.機床的描述激光切割機包括XY工作臺和激光系統(tǒng)（如圖1）。激光系統(tǒng)的基本組成：?因此沒有考慮運動控制設(shè)計所以電源設(shè)備被放置在后臺；?激光束來源即產(chǎn)生激光束（激光器）；?激光頭即引導(dǎo)激光到理想的剖切面。必須移坐標軸且與放置激光頭在水平面里。采用兩個獨立的運動軸的驅(qū)動系統(tǒng)實現(xiàn)這樣的水平面。他們提供沿卡迪爾XY軸和Z軸移動。X軸傳動使激光頭沿X軸方向的運動。驅(qū)動機構(gòu)、激光頭以及激光器放置在橋接器上，以確保激光束有一條高品質(zhì)的光路徑。Y軸運動是由Y傳動提供的。激光頭代表X驅(qū)動的負荷，它負載了全部X驅(qū)動系統(tǒng)，包括激光頭和激光器，而Y驅(qū)動由電機來負載。這些負載在無阻力的滑動面滑過。定位系統(tǒng)由運動控制器,放大器，直流電機與驅(qū)動系統(tǒng)。X驅(qū)動機構(gòu)是由一變速箱以及帶傳動（圖2）。當帶傳動由旋轉(zhuǎn)運動轉(zhuǎn)化為線性運動變速箱降低了電機的轉(zhuǎn)速。帶傳動由正時帶和兩個滑輪組成：讓皮帶運動的主動輪和從動輪。Y驅(qū)動機構(gòu)更為復(fù)雜。沉重的橋接器由兩條平行傳動帶驅(qū)動；每個橋面都連接到其中一個傳動帶上。傳動機構(gòu)通過減少馬達的速度的傳動帶驅(qū)動和變速箱來帶動的主動輪與傳動系聯(lián)系。2.2假設(shè)這臺機器驅(qū)動代表一個復(fù)雜的非線性分布參數(shù)系統(tǒng)。高階系統(tǒng)擁有多項的能被驅(qū)動器的階躍響應(yīng)觀測到的共振頻率（見第4部分）。根據(jù)控制設(shè)計觀點，困難產(chǎn)生于在所要控制帶寬（?10赫茲）出現(xiàn)的機械振動。另一方面，設(shè)計目的是得到一個高性能控制系統(tǒng)的同時降低控制器復(fù)雜性。因此，一個簡單的數(shù)學(xué)模型將只考慮它的一階共振，而忽視了高階動態(tài)。換句話說，控制設(shè)備的設(shè)計模型將密切配合真正系統(tǒng)頻率響應(yīng)直到第一階共振。其次，控制器設(shè)計應(yīng)充分地應(yīng)對多諧振峰值的大幅下降直到保持系統(tǒng)的穩(wěn)定性的情況下的高階共振。因此，根據(jù)信號分析與驅(qū)動裝置的特點,假設(shè)可制定為如下：?在電流控制方式里直流伺服系統(tǒng)的運作確保在電機軸上有一個忽略的時間常數(shù)的高動態(tài)扭矩。?變速箱里的小間隙和取決于應(yīng)用拉伸的正時帶的帶傳動機構(gòu)的間隙是可以忽略不計的。?電機軸和傳動機構(gòu)中的主動輪的剛性關(guān)聯(lián)是可采用的。?相對其他傳動系統(tǒng)中的部件從動帶輪的慣性是可以忽略不計的。用以上假設(shè),動態(tài)模型將縮減至一個有兩個傳動輪的只包含一階共振的傳動機構(gòu)。在控制設(shè)計，由于傳動機構(gòu)的可重復(fù)性和準確性都比較低，負載的不確定的位置必須加以考量。沒有注意到的耦合的動力學(xué)Y軸傳動由于平行傳動，因此,雙履帶傳動可看成同級別的單履帶傳動。2.3帶傳動模型可用一個多質(zhì)子系統(tǒng)仿制帶傳動機構(gòu)采用模態(tài)分析。在帶傳動機構(gòu)模型有著集中參數(shù)的、線性的、無質(zhì)量的彈簧表示履帶的彈性。根據(jù)以上的假設(shè)條件，可以得到輪-車架系統(tǒng)模型。主動輪、電機軸和減速機都被看作是驅(qū)動執(zhí)行機構(gòu)的集中慣量。從動輪及負載主要集中在負荷質(zhì)量上。慣量和負荷由彈簧聯(lián)系的。電機軸承、齒輪箱、傳動機構(gòu)以及非模型的高階動態(tài)里的摩擦力都被看作是一個影響著傳動方面還有負載方面的不為人知的干擾。輪-車架系統(tǒng)的力學(xué)模型系統(tǒng)及其方案分別顯示在圖3和圖4。皮帶的延展由于正時帶的固有彈性。但是，根據(jù)傳動機構(gòu)的振動分析，所得到的模型能夠調(diào)整。假設(shè)單位傳送值為常數(shù)(L=1)。然后，控制對象模型如圖5。控制設(shè)備包括兩個由一個串級結(jié)構(gòu)連接的部分。第一部分用取決于天性履帶的阻尼動力學(xué)差來描述。第二部分包括負載部分動力學(xué)。帶延伸t被迫通過應(yīng)用扭矩q。描述了動力式(1。Hw(s)表示帶張力動力學(xué)的傳遞函數(shù)Uf=—⑵S+叫K=I1—頊I"■是自然共振頻率(3)[%=」K是帶的阻力。負載動力公式是Fw