外文翻译一种采用现代先进控制算法的3轴台式数控系统铣床

外文翻译--一种采用现代先进控制算法的3轴台式数控系统铣床Developmentofa3-axisDesktopMillingMachineandaCNCSystemUsingAdvancedModernControlAlgorithmsByung-SubKim,Seung-KookRoandJong-KweonPark1NanoConvergenceManufacturingSystemsResearchDivision,KoreaInstituteofMachinery&Materials,Daejeon,SouthKorea,305-343CorrespondingAuthor/E-mail:bkim@//0>.,TEL:+82-42-868-7109,FAX:+82-42-868-7180Inthispaper,weintroduceadesktop-size3-axismillingmachineandaCNCsystemwhichwasdevelopedtooperatethe3-axismillingmachine.The3-axismillingmachinehasamini-desktopsizeof200×300×200mm3anditscuttingvolumeis20×20×20mm3.TheverticallyinstalledXYstageisdrivenbyvoice-coilmotors,andforthez-axis,amagneticallypreloadedairbearingandalinearmotorareused.Theairspindlerunsatupto160,000rpm.Thegravityforceisactingonthey-direction,soaweightbalancerusinganairbearingcylinderisinstalledtocanceloutthegravityforceactingontheXYstageinthey-direction.TheCNCsystemdesignedforthe3-axismillingmachineconsistsoftwoparts.TheoneisagraphicaluserinterfaceprogramwhichrunsunderMicrosoftWindowsandtheotherisaDSPprogramwhichisimplementedonaDSPboardwithTITMS320C6701chips.AG-codeinterpreterisincludedintheCNCsystemwhichcaninterpretandinterpolateabasicsetofG-codesandM-codesinreal-time.ToimprovetheperformanceofservocontrolloopintheCNCsystembeyondthetraditionalPID-typecontrol,severalmoderncontrolalgorithmshavebeentestedincludingcontrol,inputshapingcontrol,disturbanceobserverandcross-coupledcontrolonthe3-axismillingmachine.Experimentalresultsshowtheeffectivenessanddrawbacksofeachcontrolschemewhentheyareappliedtothe3-axisdesktopmillingmachine.KEYWORDS:3-axismillingmachine,CNCsystem,Hcontrol,Inputshaper,Cross-coupledcontrol1.IntroductionAsnewfieldssuchasITInformationTechnology,BTBioTechnologyandNTNanoTechnologyemergeasadrivingforceintheindustry,theinterestsinmicro-factorysystemhavebeengrowing.Themicro-factoryisaminiaturizedflexiblemanufacturingsystemwhichconsumesminimalspaceandenergycomparedtotheconventionalone,anditisdesiredtoproducemicro/mesosizemechanicalcomponentsnecessaryforIT,BTandNTapplications.Majortechnicalunitscontributingtomicromechanicalmachiningsystemsare,tonameafew,highspeedspindlesystems,microhighprecisionfeedingsystems,controlsystemstogeneratecoordinatedmotions,toolingandchuckingsystems,framedesignandmoduleallocationschemesbaseduponoptimizationforhighstiffness.Researchershavebeentryingtoputmicrotechnologiestogethertobuildmicro-factorysystemswhichmakemicro/mesosizeprecisionpartstomeettheneedsfromthemanufacturingInthispaper,wepresentaminiaturized3-axismillingmachineandadedicatedCNCsystemforthemachine.The3-axismillingmachineisconstructedasoneofmicro-factorymoduleanddesignedtoproducehighprecisionmicroparts.Ithasadesktopsizeof200×300×200mm3andisservingasourtestbedmachine.Fromfiniteelementanalysisandanimpacthammertest,wehaveverifiedthatithasagoodstructuralstiffnessandhighnaturalfrequencies.Ahighspeedairturbinespindleonthehorizontalz-axiscanrunatupto160,000rpm.This3-axismillingmachinewasputunderrealmachiningtestsanditsuccessfullydemonstrateditsmachiningcapabilities.ACNCsystemwasdevelopedforoperationofthe3-axisdesktopmillingmachine.TheCNCsystemincludesaG-codeinterpreterwhichcanprocessabasicsetofG-codesandM-codesinreal-time.TheCNCsystemconsistsoftwoparts.TheoneisagraphicaluserinterfacewhichrunsunderMicrosoftWindows,andtheotherisaDSPprogramwhichinterpolatescommandsandexecutesareal-timeservocontrol.TwopartscommunicateeachotherthroughadualportRAMRandomAccessMemory.Jobassignmentsforthetwopartsarediscussedindetailinthispaper.ToimprovetheperformanceoftheCNCsystemforthe3-axismillingmachinebeyondthetraditionalPID-typecontrol,differentcontrolschemeshavebeentestedincludingcontrol,inputshapingcontrol,disturbanceobserverandcross-coupledcontrolonthe3-axismillingmachine.Therestofthispaperisorganizedasfollows.Sec.2presentsthedesignofthe3-axismillingmachine.Theresultsofthefiniteelementanalysisandthenaturalfrequenciesobtainedfromtheimpacthammertestaregiveninthissection.InSec3,aPC-basedCNCsystemdevelopedforthe3-axismillingmachineisdiscussed.Severalmoderncontrolschemesincludingcontroldesign,inputshapingcontrol,disturbanceobserver,andcross-coupledcontrolarediscussedwiththeirexperimentalresultstoshowtheireffectivenessanddrawbacksinSec4.TheconcludingremarkswillbegiveninSec.5.2.Designofa3-axisMillingMachineMicromachinetoolsarerequiredtohavehighmachiningaccuracywhileprovidingenoughstiffness.Toestimatebasicmachiningperformanceandstiffnessofamicromachinetool,aminiaturized3-axismillingmachinewasbuiltandusedasatestbed.Fig.1showsthe3-axismillingmachineanditsspecifications.Ithasamini-desktopsizeof200×300×200mm3anditscut-tingvolumeis20×20×20mm3.TheverticallyinstalledXYstageisdrivenbyvoice-coilmotors,andforthez-axis,amagneticallypreloadedairbearingandalinearmotorareused.Theairspindlerunsatupto160,000rpmanditisfastenoughforhighprecisionmachining.AweightbalancerusinganairbearingcylinderisinstalledtocounteractthegravityforceactingontheXYstageinthey-direction.Asmallcuttingforcedynamometerisalsoinstalledunderneaththeworktabletomonitorthecuttingprocess.Fig.2showsapictureofthe3-axismillingmachine.2.1StaticandDynamicAnalysisFiniteelementanalysiswasdonetoinvestigatethestaticanddynamiccharacteristicsofthedesigned3-axismillingmachineusingafiniteelementmodelasshowninFig.3.Thecomputationalresultsshowedthatthedeflectionduetoitsownweightwasnegligible.Whena10Nforcewaslocatedatthemachiningpositioninz-direction,thenumericalresultsshowedthatthedisplacementchangeattheworktablewouldbeabout0.07?,andthebackfamewouldundergolessthan0.02deflectioninz-direction.Itseemsthatthe3-axismillingmachinehasgoodstiffnessduetogoodframedesignandapairofsmallLMguidessupportingeachx-andy-direction.Themodalanalysisrevealedmanyimportantdynamicmodesofthe3-axismillingmachine.Weusedtheimpacthammertesttoverifythecomputednaturalfrequencies.Themeasurednaturalfrequenciesdonotexactlymatchthecomputedones,buttheindicatedfrequencyrangefromthefiniteelementmodalanalysiswassimilartothatfromtheimpacthammertest.Fig.4andTable1showthemeasurednaturalfrequenciesandcorrespondingfrequencyresponsefunctionofthe3-axismillingmachine.Itcanbeseenthatthenaturalfrequenciesofz-axisstage,whichissupposedtobelowinstiffnessduetoitsairbearing,locateatarangeof250~390Hz.ThenaturalfrequencyoftheXYstageshowsatabout400and710Hzand,forthebackframe,itisaround440and640Hz.Itseemsthatthedesignedminiaturized3-axismillingmachinehashighernaturalfrequenciesthanconventionalmachinetools.3.ACNCSystem3.1GraphicalUserInterfaceProgramAPC-basedCNCsystemwasdevelopedforthe3-axismillingmachine.ThedevelopedCNCsystemhastwoparts,agraphicaluserinterfaceprograminthePCpartandaDSPprogramintheDSPpart.ThePCpartrunsonMS-Windowsandprocessesuserinputs.TheDSPpartreceivesthousandstimerinterruptspersecondandinterpretscommandsinreal-timeforeachaxisofamachineandexecutesservocontrolloops.TwopartsshareadualportRAMandcommunicateeachotherthroughit.Fig.5showsthegraphicaluserinterfaceofthedevelopedCNCsystemanditsbriefexplanations.Oneofthemajorfeaturesoftheuserinterfaceprogramisa3DplotwindowatthebottomrightcornerinFig.5.ItdisplaysthetoolpathdescribedinG-codeswhentheuserinterfaceprogramreadsinaG-codefile.ThecurrenttoolpositionalsoappearsasasmallreddotonthescreensothatCNCuserscaneasilyidentifywherethemachiningprocessgoesintheG-codefile.Userscanalsousecontouringfunctionwhichmergeslinesegmentsandarcswhicharetangent,ornearlytangent,intoasinglesmoothmotionwithoutstoppingateachend-point.Contouringcanbeturnedonandoffmanuallywhileaprogramisrunning,oritcanbeturnedonandoffbytheprogramitselfusingM-codesM21andM22.CurrentlyimplementedG-codesandM-codesareG00RapidMotion,G01LinearMotion,G02CWCircularArc,G03CCWCircularArc,G04Dwell,G17X-YPlaneSelection,G18Z-XPlaneSelection,G19Y-ZPlaneSelection,M21ContouringOn,M22ContouringOff,M30ProgramEnd&Reset.WhenauserclicktheOpenG-codebutton,awholeG-codefileisreadinandsavedinamemoryarea,andthentheG-codesappearatthebottomleftlistbox.WhentheStartG-codebuttonisclicked,theuserinterfaceprogramtakesoutalinefromthememoryandchecksitssyntaxandidentifiesallthemeaningfultokens.DuringpreprocessingaG-codeline,theuserinterfaceprogramissupposedtocompute,amotionplane,adrivingaxis,imumallowablevelocityandacceleration,thestartingpositionofthedeceleration,directionalcosines.IftheG-codelineisaboutcircularmotion,thecenterpointofthearc,thenormaldirectionofthearc,andstartandendanglesarealsocomputedbytheuserinterfaceprogram.AllthepreprocessedinformationisenteredintheDPRAMandhandedtotheDSPprogram.AcircularbufferintheDPRAMhasroomsforonly4linesofG-codes,sotheuserinterfaceprogramneedstokeepmonitoringthecircularbufferusage.WhentheuserinterfaceprogramfindsthattheDSPprogramfinishescarryingoutaG-codelineandemptiesitsspace,itfillsintheemptyspaceinthecircularbufferwithanewpreprocessedG-codelineintheorderinwhichtheyoccur.3.2DSPProgramTheDSPprograminterpolatesthepreprocessedG-codesinreal-timeandgeneratespositioncommandsformultipleaxestofollow.Italsoclosesservocontrolloops.Generallyasamplingrateissettobetentimeslargerthanthebandwidthofaplanttobecontrolled.ThedevelopedCNCsystemadoptedasamplingrateof2,000Hzfortheservoloops.TheDSPprogramtakesoutaG-codelinefromthecircularbufferandcomputestheanglebetweentwosuccessiveG-codelines.Iftheangleislessthanacertainpredefineddegreeandthecontouringison,itsetsaflagsothatthetoolpathdoesnotreduceitsvelocitywhenitentersintothenextsegment.Whenatimerinterruptoccurs,theDSPprogramcomputesthedesiredvelocityandpositionofeachaxisandgeneratescommandsfortheservocontrolloop.Thecomputedvelocityshouldbelessthantheimumallowablevelocitycomputedbytheuserinterfaceprogramandstartdecreasingwhenthepositionreachesthepositionofdecelerationtomakeacompletestopattheendpointifcontouringfunctionisnotused.Ifthecurrentmotionislinear,allthecomputationsareforthedrivingaxisandcommandsfortheotheraxesarecalculatedfromstraight-lineequationsrelatedtothedrivingaxis.Ifthecurrentmotioniscircular,angularvelocityandangularaccelerationaresimilarlyusedasinthelinearmotionandthefinalcommandsaremadefromthepolarcoordinatetotheCartesiancoordinatetransformation.Aftergeneratingreal-timecommandsforeachaxistheDSPprogramdrivestheservocontrolloopsofthe3-axis.TheerrorswhicharedifferencesbetweenthecommandsandtheactualfeedbackpositionsarefedintoacontrolalgorithmsuchasPIDandthecontrolsignalsforthemotordrivesarecomputed.4.ControlSystemDesignToimprovetheperformanceofservocontrolforthe3-axismillingmachine,severalcontrolalgorithmshavebeentestedonthe3-axismillingmachine.TheyincludePID,H∞control,inputshapingcontrol,disturbanceobserver,andcross-coupledcontrol.ThesecontrolschemesweredigitallyimplementedonaDaytonaDSPboardfromSpectrumsignalCo.TheDSPboardhastwoTI320C6701chipsonitandasamplingrateof2,000Hzhasbeenused.Thedesignprocedureandexperimentalresultsfromeachcontrolaredescribedasfollows.4.1OptimalControlDesignUsingaconventionalPIDcontrollerforthez-axiswhichhasalinearmotorandair-bearing,itseemedthathighgainPIDeasilystartedoscillations.Asanalternative,ancontrollerwasdesignedandappliedtothez-axisandperformanceofhandtunedPIDandcontroliscompared.Anopen-loopplantmodelforcontroldesignwasobtainedfromexperimentalfrequencyresponsedata.Thefrequencyresponsesweremeasuredwithadynamicsignalanalyzerusingasweptsinemethodthatgeneratesfixed-amplitudesinewavesofvaryingfrequencies.Fromthefrequencyresponsesfordifferentinputamplitudes,anaveragedfrequencyresponsewascomputedandanominalcontinuous-timeplantmodelwasfitted.Fig.6showstheaveragedfrequencyresponseandanominalopen-loopplantmodel.Asecondorderplantmodelwasobtainedfromthecurvefit.Theidentifiedopen-loopplantmodelGsforthez-axiswasWecanseethatthez-axishasacomplexpolepairataround4.5Hz.WhenaPID-typecontrollerinatypicaldigitalformof,whereukiscontrolleroutput,ekiserrorsignal,Tissamplingperiod,andzisadelay,isappliedtotheplant,itturnsoutthatahighgainPIDcaneasilyexcitetheoscillatorymodeoftheplant.Toavoidso-calledderivativekick,thederivativegainKdwasforcedtoactonthederivativeoftheactualposition,notonthederivativeofthepositionerror,i.eismultipliedbythenegativepositionfeedback,?ykinsteadofekatEq.2.Forthez-axis,usingthederivativeofpositioninsteadofthatofpositionerrorallowedmoreaggressivePIDgains.BasedontheplantmodelatEq.1,thecontrolloopemployedanrobustcontrollerat2kHzsamplingfrequency.AmixedsensitivityproblemwassolvedtodesignanH∞controllerincontinuous-timeandtheresultingcontinuoustimecontrollerwasconvertedtoadiscrete-timemodel.Themixedsensitivityspecificationforcontroldesignincontinuous-timewas,whereSsisthesensitivityfunction,Tsisthecomplementarysensitivityfunction,Ksisthedesiredcontroller,,andputupperboundsonthemagnitudeofSsforperformance,TsfornoiseattenuationandKsSstopenalizelargeinputs,respectively.TheoptimalcontrollerwasobtainedbysolvingtheproblemFig.7showsotherdesignparametersusedinthez-axiscontroldesignandthefinalsensitivityfunctionfromthecomputedcontroller.ThefinalsensitivityfunctionSsclearlyshowsthatthecontrollerhasdoubleintegralactioninlowfrequencyrangeasintendedwiththeshapeofThedesignedcontrollerwasconvertedtoadiscrete-timecontrollerKzfora2kHzsampleandholdrateandimplementedonaDSPboardfortests.ThefinalcontrollerKzwasa5thordercontroller.TheclassicalfeedbacksensitivityfunctionSsisthetransferfunctionfromthereferencesignalrttothecontrolerrorsignalet,i.e.etSs?rt.TocomparetrackingperformancebetweenthedesignedcontrollerandPIDcontroller,afixed-amplitudesinewaveofvaryingfrequencieswasinjectedasacommandsignalandthecorrespondingerrorsignalwasmeasuredandtheratiooftheirmagnitudeversusfrequencywasplottedinFig.8.Thusitisanempiricalsensitivityfunctionplotandwecanestimatetheleveloftrackingperformancefromthisplot.Thecontrollershows0.4%trackingerrorfor1Hzsinecommand,but10%fromPIDcontrollerinthisparticulardesign.Itisduetotheintendeddoubleintegralactionfromcontroldesign.Similarlyothercontrollersweredesignedforthex-andy-axesbutthetrackingperformancefromcontrolwassimilartothatfromPIDcontrolinthex-andy-axeswhichhavevoicecoilmotorsandLMguides.Acircularreferencetrajectoryof7.5mminradiusiny-zplanewasgiventothey-andz-axisservoasacommandwithafederateof25mm/secanditscontourerrorsarecomparedinFig.9.Notethatthecontourerrorsaredifferentfromthetrackingerrors.Atrackingcontrollerattemptstominimizethedifferencebetweenthereferencetrajectory,whichisspecifiedasafunctionoftime,andtheoutputofthecontrolledplant.Ontheotherhand,acontouringcontrollerattemptstominimizethedifferencebetweenthespatialtrajectoryofthereferenceandthespatialtrajectorytracedbytheoutputofthecontrolledplant.Thecontourerrorfromtwoaxesservomotiontakesintoaccountonlythespatialtrajectoriesandlargetrackingerrordoesnotnecessarilymeanlargecontourerror.Ifoneaxisisingreatsynchronizationwiththeotheraxisalthoughithaslargetrackingerrorduetotimedelay,thenthefinalcontourerrormaybesmallinthesensethattheoutputofthecontrolledplantmatcheswellthecommandedreferencetrajectorywithsameamountoftimedelayfrombothaxes.Iftwoaxeshavegoodtrackingperformancethentheywillshowgoodcontourerror.InFig.9,they-axisservomotionisdrawnhorizontallyandthez-axisservomotionisdrawnvertically.Thebluecircleinthemiddleofthefigurerepresentsthe0μmerrorline,i