外文翻译原文 虚拟数控系统 第一部分系统结构

BRITISH200ACCEPTED29SEPTEMBERAREALISTICANDCUBICMODULETHECONTROLLAWSCANBESELECTEDRANGINGFROMASIMPLEPIDTOCOMPLEXPOLEPLACEMENT,GENERALIZEDPREDICTIVECONTROLORSLIDINGMODECONTROLLERWITHFRICTIONCOMPENSATIONWHENTHEVIRTUALCNCISASSEMBLED,ITSPERFORMANCECANBETESTEDUSINGFREQUENCYANDTIMEWHICHLEADSTOPOORTRACKINGHIGHFREQUENCYCONTENTININTERNATIONALJOURNALOFMACHINETOOLSCNCMODELINGCONTROLSINTERPOLATION1INTRODUCTIONTHEOBJECTIVEOFTHEVIRTUALMANUFACTURINGTECHNOLOGYISTODESIGNACOMPLETELYDIGITALFACTORYWHERETHEPARTISMODELED,MACHINEDWITHOPTIMIZEDPROCESSPARAMETERS,ANDRESULTINGERRORSAREPREDICTEDWITHCORRECTIVEACTIONSBEINGTAKENINACOMPUTERSIMULATIONENVIRONMENTTHISPAPERPRESENTSAVIRTUALMODELOFACNCSYSTEMFORMACHINETOOLSTHECNCSYSTEMCONSISTSOFMECHANICALFEEDDRIVES,MOTORS,AMPLIFIERS,POSITIONVELOCITYACCELERATIONSENSORS,ANDREALTIMECOMPUTERALGORITHMSWHICHGENERATETIMESTAMPEDPOSITIONCOMMANDSTHROUGHTRAJECTORYGENERATIONANDCLOSETHEAXISSERVOLOOPS1THEVIRTUALCNCREQUIRESAREALISTICMATHEMATICALMODELOFEACHCNCCOMPONENTANDTHEIRLOGICALINTERCONNECTIONTHEREHASBEENSIGNIFICANTRESEARCHREPORTEDINMODELINGVARIOUSTRAJECTORYGENERATIONALGORITHMS24,CONTROLLAWS59,ANDPHYSICALCOMPONENTSOFTHEDRIVESSUCHASMOTORS,AMPLIFIERS,BALLSCREWANDLINEARDRIVESWITHVARIOUSFRICTIONCHARACTERISTICS1013THEMAJORITYOFTHEPASTRESEARCHFOCUSEDONTRAJECTORYGENERATION,MODELINGANDIDENTIFICATIONOFFEEDDRIVEDYNAMICS,ANDCONTROLLAWDEVELOPMENTWHENTHETRAJECTORYGENERATIONLEADSTODISCONTINUOUSPOSITIONCOMMANDS,THEIRFIRSTVELOCITY,SECONDACCELERATIONANDTHIRDJERKDERIVATIVESCONTAINFLUCTUATIONANDSUDDENCHANGESHIGHFLUCTUATIONINTHEVELOCITYRESULTSINPOORFEEDSASWELLASHIGHFREQUENCYCONTENTBEYONDTHEBANDWIDTHOFTHECLOSEDLOOPSYSTEM,VIRTUALCNCSYSTEMPARTCHIHOYEUNGA,YUSUFALTINTASAMANUFACTURINGAUTOMATIONLABORATORYUNIVERSITYOF2324MAINMALL,VANCOUVER,BDEPARTMENTOFMECHANICALENGINEERING,UNIVERSITYOFWATERLOO,RECEIVED8JULY2005AVAILABLEONLINEABSTRACTTHEPAPERPRESENTSACOMPREHENSIVEVIRTUALSIMULATIONMODELOFREPRESENTSANACTUALCNC,BUTWITHMODULARFEEDDRIVES,SENSORS,MOTORS,TRAJECTORYINTERPOLATIONANDAXISCONTROLLAWSCONSTANT,TRAPEZOIDALISYSTEMARCHITECTUREA,KAANERKORKMAZB,COLUMBIA,DEPARTMENTOFMECHANICALENGINEERING,BC,CANADAV6T1Z4UNIVERSITYAVENUEWEST,WATERLOO,ONT,CANADAN2L3G14AUGUST20052005ANDMODULARCNCSYSTEMTHEVIRTUALCNCARCHITECTUREANDAMPLIFIERSTHECNCSOFTWARELIBRARYINCLUDESAVARIETYOFACCELERATIONPROFILESCANBESELECTEDASATRAJECTORYGENERATIONMANUFACTURE46200611071123WWWELSEVIERCOM/LOCATE/IJMACTOOLTHESEPROBLEMS,PRITSCHOW14RECOMMENDEDJERKLIMITEDTRAJECTORIESWITHTRAPEZOIDALORSINESQUAREACCELERATIONPROFILES,FAVORINGTHELATTERFORBETTERCONTINUITYCHENANDTLUSTY2ALSOUSEDTHEJERKLIMITEDTRAJECTORIESWITHTRAPEZOIDALACCELERATIONPROFILESINTHEIRFEEDDRIVE08906955/SEEFRONTMATTERQ2005ELSEVIERLTDALLRIGHTSRESERVEDDOI101016/JIJMACHTOOLS200508002EMAILADDRESSESCYEUNGMECHUBCCACHYEUNG,ALTINTASMECHUBCCAYALTINTAS,KAANEMECHENG1UWATERLOOCAACCELERATIONANDLARGEJERKCOMMANDSMAYEXCITESTRUCTURALMODESOFTHEMACHINE,WHICHARENOTDESIRABLETODEALWITHCORRESPONDINGAUTHORTELC151988512115214FARICTIONANDLEADSCREWBACKLASHTHEAXISCANBECONFIGUREDTOHAVEACCELERATION,VELOCITYANDPOSITIONSENSORSWITHDEVELOPMENTWORKLATER,ERKORKMAZANDALTINTAS4DEVELOPEDATRAJECTORYGENERATIONWITHCUBICACCELERATIONPROFILESFORHIGHSPEEDMILLINGOPERATIONSTYPICALLY,THEPOSITIONERRORSORIGINATINGFROMTHECNCAREDEPENDENTONTHEROBUSTNESSANDTRACKINGABILITYOFTHEAXISCONTROLLAWSPRITSCHOW8NOTEDTHEIMPORTANCEOFACHIEVINGHIGHSERVOBANDWIDTH,INORDERTOBEABLETOTRACKSUDDENCHANGESINTHEMOTIONCOMMANDSACCURATELY,WHILEREJECTINGDISTURBANCESORIGINATINGFROMAXISFRICTIONANDCUTTINGFORCESTOMIZUKA9DEVELOPEDTHEZEROPHASEERRORTRACKINGCONTROLLERZPETC,WHICHPROVIDESAWIDEBANDWIDTHWITHZEROPHASEDELAYTHISDESIGNPHILOSOPHYISBASEDONTHECANCELLATIONOFSTABLECOMPONENTSOFTHECLOSEDLOOPSERVODYNAMICSINAFEEDFORWARDFASHIONBOUCHERETAL6USEDCASCADEDGENERALIZEDPREDICTIVECONTROLGPCFORACCURATETRACKINGOFVELOCITYANDPOSITIONCOMMANDSERKORKMAZANDALTINTAS5,12APPLIEDTHESLIDINGMODECONTROLSMCTECHNIQUEFORTHECONTROLOFHIGHSPEEDFEEDDRIVESTHEYFIRSTDESIGNEDASMCBASEDONTHERIGIDBODYDYNAMICSALONELATER,THEYIMPROVEDTHEIRCONTROLMETHODOLOGYTOACTIVELYCOMPENSATETHEEFFECTOFTHESTRUCTURALFLEXIBILITIESOFBALLSCREWDRIVESNUMEROUSPUBLICATIONSHAVEDEALTWITHTHEMODELINGANDIDENTIFICATIONOFTHEDYNAMICSOFTHEMACHINETOOLSFEEDDRIVESYSTEMKOREN15USEDASIMPLEFIRSTORDERLINEARMODELFORIDENTIFYINGTHEDYNAMICSOFCLASSICALFEEDDRIVESINALEADSCREWDRIVENMECHANISM,NONLINEARGUIDEWAYFRICTIONBECOMESASIGNIFICANTFACTORINDEGRADINGTHETRACKINGANDCONTOURINGACCURACY,ESPECIALLYATMOTIONREVERSALSINSHARPCORNERSANDCIRCULARARCQUADRANTSARMSTRONGETAL10PRESENTEDANEXCELLENTSURVEYONTHEPHYSICSBEHINDTHEFRICTIONPHENOMENONTHEYPOINTEDOUTTHATTHETYPICALFRICTIONCHARACTERISTICSFORLUBRICATEDMETALLICSURFACESINCONTACTCOULDBEDESCRIBEDBYTHESTRIBECKCURVEBACKLASHISALSORESPONSIBLEFORTHEMOTIONACCURACYLIMITATIONOFCNCMACHINETOOLSKAOETAL13REPORTEDANANALYTICALMETHODTOOBSERVEANDMODELTHEBACKLASHBEHAVIORONTHEMOTIONACCURACYOFCNCLATHESTUNINGPLAYSANIMPORTANTROLEINCONTROLLERDESIGNOVERTHELASTTWODECADES,THEUSEOFFUZZYLOGICCONTROLHASBEENWIDELYPROPOSEDINLITERATUREFORAUTOTUNINGCONTROLPARAMETERSDESILVAANDMACFARLANE16CONDUCTEDRESEARCHONAUTOTUNINGSERVOCONTROLLERSTHROUGHAHIERARCHICAL,MULTILEVELSYSTEMTHATCOULDBEAPPLIEDINTHECONTROLSTRUCTUREOFINDUSTRIALROBOTICMANIPULATORSWICKRAMARACHCHIANDDESILVA17,18APPLIEDAKNOWLEDGEBASEDHIERARCHICALCONTROLSYSTEMFORFISHPROCESSINGAPPLICATIONSLATER,DESILVA19INVESTIGATEDANANALYTICALFRAMEWORKFORKNOWLEDGEBASEDTUNINGOFSERVOCONTROLLERSHEPOINTEDOUTTHATASUBSTANTIALREDUCTIONINCOMPUTATIONALEFFORTCOULDBEACHIEVEDTHROUGHTHEAPPLICATIONOFTHEANALYTICALFRAMEWORKGOULETETAL20HASALSOUSEDAHIERARCHICALCONTROLSTRUCTUREFORADEPLOYABLEORBITINGMANIPULATORTHEYADDRESSEDTHEADVANTAGESOFCOMBININGCHYEUNGETAL/INTERNATIONALJOURNALOFMACHINE1108CRISPCONVENTIONALCONTROLWITHKNOWLEDGEBASEDFUZZYDEFINEDACCURACYANDNOISEPARAMETERSTHEPOSITIONERROROFEACHAXISISEVALUATEDINTHEFEEDBACKLOOPANDCOMBINEDTOPREDICTTHECONTOURINGERRORATEACHCONTROLINTERVALTHEUSERCANSELECTANYCONTROLLAW,LEADSCREWORLINEARDRIVEPARAMETERS,ASWELLASAMPLIFIER,MOTOR,FRICTIONFIELDANDSENSORSOTHATMOSTMACHINETOOLSCANBERECONFIGUREDAUTOMATICALLYBYTHEUSER,WHOCANADDNEWMODULESORMODIFYTHEEXISTINGALGORITHMSWHICHARECREATEDINMATLABENVIRONMENTTHEVIRTUALCNCSYSTEMCONSISTSOFTHREEMAINMODULESFEEDDRIVE,TRAJECTORYGENERATION,ANDAXISTRACKINGCONTROLLOGICCONTROLFORSTABILIZINGASPACEBASEDMANIPULATORWITHFLEXIBLEDEPLOYABLEANDSLEWINGLINKSHENCEFORTH,THEPAPERISORGANIZEDASFOLLOWSTHEARCHITECTUREOFTHEVIRTUALCNCSYSTEMISPRESENTEDINSECTION2,WHICHINCLUDESTHEMATHEMATICALMODELINGOFACTUATORS,FRICTION,TRAJECTORYGENERATIONANDCONTROLLAWSFUZZYLOGICAUTOTUNINGOFTHEAXISCONTROLLAWISSHOWNINSECTION3THEVIRTUALCNCISEXPERIMENTALLYVERIFIEDINCONTOURINGSTANDARDDIAMONDANDCIRCULARPATHSINSECTION4,ANDTHEPAPERISCONCLUDEDINSECTION52VIRTUALCNCARCHITECTURETHEVIRTUALCNCSYSTEMMUSTBEABLETOPREDICTTHEPERFORMANCEOFAREALCNCSYSTEMDURINGPARTMACHININGTHEMATHEMATICALMODELSOFALLWORKINGMODULESOFAREALCNCMUSTBEIDENTIFIEDANDINTEGRATEDASINAREALCNCSYSTEMFORACCURATEPREDICTIONOFPARTMACHININGPERFORMANCETHEARCHITECTUREOFTHEDEVELOPEDVIRTUALCNCSYSTEMISILLUSTRATEDINFIG1,WHICHRESEMBLESTHEREAL,RECONFIGURABLEANDOPENCNCDEVELOPEDINTHEMANUFACTURINGAUTOMATIONLABORATORY,UBC21THEVIRTUALCNCSYSTEMACCEPTSREFERENCETOOLPATHGENERATEDONCAD/CAMSYSTEMSINTHEFORMOFINDUSTRYSTANDARDCUTTERLOCATIONCLFORMATEACHBLOCKINTHECLFILECONTAINSNCBLOCKNUMBERS,TOOLPATHSINTHEFORMOFLINEAR,CIRCULARANDSPLINESEGMENTS,THECUTTERDIMENSIONS,TOOLCENTERCOORDINATES,ANDFEEDSPEEDFORMACHININGAPARTICULARPARTONACNCMACHINETOOLEACHTOOLPATHSEGMENT,SUCHASLINEAR,CIRCULARORSPLINEPATH,ISPASSEDTHROUGHTHETRAJECTORYGENERATIONALGORITHMWHICHCREATESDISPLACEMENT,FEED,ACCELERATIONANDJERKEXPRESSIONATDIVIDEDSEGMENTS1TRAJECTORYGENERATIONSETSUPTHEREALTIMEINTERPOLATIONPARAMETERSSUCHASDISCRETEDISPLACEMENTALONGTHEPATHANDITSFREQUENCYTHEINTERPOLATORGENERATESDISCRETEDISPLACEMENTCOMMANDSFOREACHAXISATEVERYCONTROLINTERVALTHEAXISCOMMANDSAREPASSEDONTOTHECONTROLLAW,WHICHSHAPESTHEOVERALLRESPONSEOFTHEFEEDDRIVETRANSFERFUNCTION,CONSISTINGOFDIGITALTOANALOGD/ACONVERTER,AMPLIFIER,SERVOMOTOR,INERTIA,VISCOUSDAMPING,GUIDEWAYTOOLSKDU2UCDU20OTHERWISE7THEVARIANCERUOFUISCOMPUTEDAS,RUZEUKEU2C1380ASEUZ02CN2CDU212CHYEUNGETAL/INTERNATIONALJOURNALOFMACHINETOOLSUSKUMINUSKUMINUSKUMAXUMAXUSKOUMAX84WHEREUSISTHECURRENTIETORQUECOMMANDGENERATEDBYTHECONTROLLAWANDUAISTHEACTUALCONTROLSIGNALPASSEDTOTHEAMPLIFIERUMINANDUMAXARETHELOWERANDUPPERSATURATIONLIMITS,WHICHAREIDENTIFIEDFROMTORQUELIMITSOFTHEMOTORTMIN/MAXAS,UMINMAXZ1KAKTTMINMAX5IIIQUANTIZATIONERRORANDMEASUREMENTNOISETHEDIGITALCONTROLCOMMANDISCONVERTEDINTOVOLTAGEFORANALOGDRIVESTHROUGHTHEDIGITALTOANALOGCONVERTERCIRCUITDACTHEDACQUANTIZATIONERRORUISASSUMEDTOBEPRESENTINTHECONTROLSIGNALAFTERBEINGQUANTIZEDBYTHEDAC,WHICHHASARESOLUTIONOFDUUSKZUCKCUK0UKZUSKKUCK6WHEREUCISTHECOMMANDCONTROLSIGNALGENERATEDBYTHEMOTIONCONTROLLERTHEQUANTIZATIONERRORUHASAUNIFORMPROBABILITYDISTRIBUTIONWITHZEROMEANANDISBOUNDEDBYFIG4QUANTIZATIONERROROFDACABLOCKDIAGRAMOFDACQUANTIZATIORRUZEUC138ZKNPUUDUZKDU2DUUDUZDU2128THEPOSITIONMEASUREMENTNOISEXISDEFINEDAS,XMKZXAKCXK0XKZXMKKXAK9WHEREXAANDXMARETHEACTUALANDMEASUREDAXISPOSITIONRESPECTIVELYSIMILARLY,XISASSUMEDTOHAVEAUNIFORMDISTRIBUTIONBETWEENKDX/2ANDCDX/2WITHAZEROMEANANDAVARIANCEOF,RXZDX21210WHEREDXISENCODERRESOLUTIONTHETACHOMETERMEASUREMENTNOISEUISDEFINEDASUMKZUKCUK0UKZUKZUMKKUK11WHEREUANDUMARETHEACTUALANDMEASUREDANGULARVELOCITYRESPECTIVELYTHEPROFILEOFTHETACHOMETERMEASUREMENTNOISEISREASONABLYASSUMEDTOHAVEANORMALDISTRIBUTIONWITHZEROMEANANDVARIANCEOFRUTHEVARIANCEOFTHETACHOMETERMEASUREMENTNOISEISOBTAINEDEITHERFROMTHECATALOG,ORBYMONITORINGTHENOISEINTHETACHOMETERSIGNALWHENCNCISPOWERED,BUTTHEAXISISATRESTIVGUIDEWAYFRICTIONTHEDISTURBANCETORQUETDCONSISTSOFNONLINEARGUIDEWAYFRICTIONTFANDCUTTINGFORCESTCREFLECTEDTOTHEMOTORSHAFTAS,TDKZTFKCTCK12THEDOMINANTNONLINEARAXISFRICTIONREFLECTEDONTHEMOTORSHAFTISCONSIDEREDASTHETYPICALFRICTIONCHARACTERISTICFORLUBRICATEDMETALLICSURFACESINCONTACT,WHICHCANBEN,BUNIFORMPROBABILITYDISTRIBUTIONFUNCTIONFIG5STRIBECKFRICTIONCURVEFORTWOLUBRICATEDMETALLICSURFACESINCONTACTDESCRIBEDBYTHESTRIBECKCURVE,ASSHOWNINFIG5THESTRIBECKCURVECONSISTSOFFOURDIFFERENTREGIONSSTATICFRICTIONZONE,BOUNDARYLUBRICATIONZONE,PARTIALLUBRICATIONZONE,ANDFULLFLUIDLUBRICATIONZONE10TSTRIBECKCANBECHARACTERIZEDANALYTICALLYWITHSUFFICIENTCLOSENESSASTGSTRIBECKUZTGSTATEKUUG1CTGCOUNL1KEKUUG2CTVISEU13WHERETSTATANDTCOULARETHESTATICFRICTIONANDTHECOULOMBFRICTIONTORQUERESPECTIVELYTVISCISTHEVISCOUSDAMPINGCOEFFICIENTTHATCORRESPONDSTOBINEQ1U1DETERMINESTHESPACINGBETWEENTHEBOUNDARYLUBRICATIONANDPARTIALFLUIDLUBRICATIONZONESU2DETERMINESTHESPACINGBETWEENTHEPARTIALLUBRICATIONANDFULLFLUIDLUBRICATIONREGIONSTHESUPERSCRIPTG“CORRESPONDSTOPOSITIVEANDNEGATIVECHYEUNGETAL/INTERNATIONALJOURNALOFMACHINEDIRECTIONSOFMOTIONTHEPARAMETERSOFTHESTRIBECKFRICTIONCURVECANBEENTEREDINTHEDRIVEMODELTHECHARACTERISTICSOFGUIDEWAYFRICTIONTORQUETFINDISCRETETIMEDOMAINCANBESUMMARIZEDASFOLLOWS,TFKZ0UKZ0ANDTAKZ0TAKUKZ0ANDTKSTATTAKTCSTATTCSTATUKZ0ANDTAKRTCSTATO0TKSTATUKZ0ANDTAKTKSTAT0TCSTRIBECKUKUKO0TKSTRIBECKUKUK0814XAKZXAKK1DKEXLKDCEXLKKDB2XLKRDCE0SETDKEZXLKKDBANDXLKCDB2XLKDKE0SETDKEZXLKANDDCE8WHERETAKZTMKKTCKTMKZKAKTUAK15SINCETHEEFFECTOFVISCOUSDAMPINGISINCLUDEDINTHEMODELOFRIGIDBODYDYNAMICS,THEFRICTIONTORQUEEXPRESSIONINEQ13ISREWRITTEN,NEGLECTINGVISCOUSDAMPINGCOMPONENTAS,TGSTRIBECKUKZTGSTATEKUKUG1CTGCOUNL1KEKUKUG216VBACKLASHTHESPACINGORDEADZONEBETWEENTHESCREWANDNUTCREATESTHEBACKLASH,WHICHISMODELEDBYADISENGAGEDZONE,ENGAGEMENTINTHEPOSITIVEDIRECTION,ANDENGAGEMENTINTHENEGATIVEDIRECTION,ASSHOWNINFIG6THEANALYTICALEXPRESSIONSFORTHEBACKLASHMODELARESUMMARIZEDASFOLLOWS,TOOLSJEZJKAKTRGANDBEZBKAKTRG21FIG10AXISCONTROLLAWINASTANDARDFORMFIG11HIERARCHICALSTRUCTUREOFAUTOTUNINGSTRATEGYCHYEUNGETAL/INTERNATIONALJOURNALOFMACHINETOOLSSTRENGTHOFTHEUNWANTEDJITTERCANBEEVALUATEDBYCONSIDERINGTHEFOURIERSPECTRUMOFTHECONTROLCOMMANDS,SEEFIG12THEINDEXOFDEVIATIONCORRESPONDINGTOTHEOSCILLATIONLEVELOFTHECONTROLSIGNAL,OSCINDEX,ISDEFINEDAS,OSCINDEXZSCHMAXKHMEANLMAXKLMEANWHERELOWFREQUENCYRANGE00FFTHRESHHIGHFREQUENCYRANGE0FTHRESHFFNYQUIST922FTHRESHISINTRODUCEDASATHRESHOLDVALUETODISTINGUISHBETWEENLOWANDHIGHFREQUENCYREGIONSFNYQUISTCORRESPONDSTOTHENYQUISTFREQUENCY,ORTHEHALFOFTHECONTROLSAMPLINGFREQUENCYLMAXANDHMAXARETHEMAXIMUMPOWERSPECTRUMMAGNITUDESOFTHEDOMINANTFREQUENCIESINTHELOWANDHIGHFREQUENCYRANGES,RESPECTIVELYSIMILARLY,LMEANANDHMEANARETHEAVERAGESOFMAGNITUDESCORRESPONDINGTOTHELOWANDHIGHFREQUENCYRANGESINTHEPOWERSPECTRUMTABLE1PRIMARYFUZZYSETSFORPERFORMANCEATTRIBUTESOFOSC,PHM,ANDTREPERFORMANCEATTRIBUTESDISCRETEPERFORMANCEINDEXINDEXOFDEVIATIONIODFOROSC,PHM,TREOSCANDPHMTREHIUNEL1THRESHOLD1IODLIUNLA2THRESHOLD2IODTHRESHOLD1ACCPME3THRESHOLD3IODTHRESHOLD2LIOQSM4THRESHOLD4IODTHRESHOLD3HIOQOK5THRESHOLD5IODTHRESHOLD4FOROSCANDPHMHIOQ,OVERQUALIFIEDLIOQ,LITTLEQUALIFIEDACCP,ACCEPTABLELIUN,LITTLEUNSATISFACTORYHIUN,HIGHLYUNSATISFACTORYFORTREOK,OKAYSM,SMALLME,MEDIUMLA,LARGEEL,EXTREMELYLARGECHYEUNGETAL/INTERNATIONALJOURNALOFMACHINETOOLS0TTEND24WHERETENDISTHETOTALDURATIONNEEDEDFORONECYCLEOFKSOSCILLATIONOFCONTROLSIGNALOSCDECREASESYSTEMSTABILITYPHMDECREASETRACKINGACCURACYTRENOCHANGEORSLIGHTLYBACKANDFORTHMOTIONONCETHESYSTEMPERFORMANCEATTRIBUTESCORRESPONDINGTOTHEOSCILLATIONLEVELOFCONTROLSIGNALOSC,THESYSTEMSTABILITYPHM,ANDTRACKINGACCURACYTREAREEVALUATED,THEYAREMAPPEDINTODISCRETEPERFORMANCEINDICESCORRESPONDINGTOSELECTEDPRIMARYFUZZYSETSASSHOWNINTABLES1AND2TABLE6LINGUISTICRULESFORTUNINGSMCPERFORMANCEATTRIBUTESTUNINGIFOSCZHIUNTHENDORIFOSCZLIUNTHENDORIFOSCZACCPTHENDORIFOSCZLIOQTHENDORIFOSCZHIOQTHENDIFPHMZHIUNTHENDORIFPHMZLIUNTHENDORIFPHMZACCPTHENDORIFPHMZLIOQTHENDORIFPHMZHIOQTHENDIFTREZELTHENDORIFTREZLATHENDORIFTREZMETHENDORIFTREZSMTHENDORIFTREZOKTHEND33DEVELOPMENTOFFUZZYDECISIONTABLEAFUZZYDECISIONTABLE,WHICHISUSEDTOTUNETHECONTROLLAWPARAMETERSINREALTIME,ISFIRSTPREPAREDOFFLINEASFOLLOWSIMEMBERSHIPFUNCTIONSINDEVELOPMENTOFTHEFUZZYDECISIONTABLE,THESYSTEMPERFORMANCEATTRIBUTESANDTHECORRESPONDINGTUNINGACTIONSMUSTBEFUZZIFIEDINTOPREDEFINEDMEMBERSHIPFUNCTIONSINAUTOTUNINGOFSMC,THEFUZZYINPUTVARIABLESARETHESYSTEMPERFORMANCEATTRIBUTESRNOCHANGEORSLIGHTLYDECREASEDECREASEINCREASEDECREASEIFSYSTEMISUNSTABLEBASEDONTHEEVALUATIONOFOSC,PHM,ANDTRETHEFUZZYOUTPUTVARIABLESCORRESPONDTOTHETUNINGACTIONSTHATAREDEFINEDASFOLLOWSDKSANDDRDENOTETHECHANGESINKSANDR,RESPECTIVELYTHEMEMBERSHIPFUNCTIONFOREACHFUZZYINPUTOROUTPUTSETISDESIGNEDINADISCRETETABULARFORM,BYAPPLYINGATRIANGULARSHAPEDFUNCTIONWITHAFULLACTIONKSZNLANDDRZNSKSZNMANDDRZZRKSZZRANDDRZZRKSZPSANDDRZZRKSZPMANDDRZPSKSZNMANDDRZNMKSZNSANDDRZNMKSZZRANDDRZZRKSZZRANDDRZPSKSZPSANDDRZPMKSZNSANDDRZNLKSZZRANDDRZNMKSZPSANDDRZPLKSZPSANDDRZPSKSZZRANDDRZZRMEMBERSHIPGRADEIEUNITYASSIGNEDATITSNORMALIZEDREPRESENTATIVEVALUEIEDIAGONALELEMENTSINTHEMEMBERSHIPFUNCTIONTABLESTHEOFFDIAGONALTERMSREPRESENTTHEREDUCINGWEIGHTTOMODELTHEDEGREEOFFUZZINESSASINDICATEDINTABLES3AND4IIFUZZYLINGUISTICRULESEXPERTKNOWLEDGEONTUNINGAND6FOREXAMPLE,THEFIRSTROWOFTHETABLE6ISINTERPRETEDASFOLLOWSIFTHEOSCILLATIONLEVELOFTHECONTROLSIGNALISHIGHLYUNSATISFACTORYIFOSCZHIUN,THENTHEFEEDBACKGAINKSMUSTBELARGELYDECREASEDANDDISTURBANCEESTIMATORGAINRMUSTBESLIGHTLYDECREASEDTHENDKSZNLANDDRZNSIIIFUZZYCOMPOSITERELATIONTABLETHEPERFORMANCEATTRIBUTESOFTHECONTROLLER,THETUNINGACTIONS,ANDTHERULESOFTUNINGMUSTBERELATEDTOEACHOTHERUSINGFUZZYCOMPOSITERELATIONSHIPFUNCTIONS24THROUGHFUZZYIMPLICATIONIFTHEN,THEFUZZYRELATIONMRIFORTHEITHINDIVIDUALRULERIDEFINEDINTABLE6ISDEVELOPEDAS,MRIOSCPHMTREDKSDRC12C12C12C12C12ZMINMINPUTIOSCPHMTREMOUTPUTIDKSDRC2C325WHEREMINPUT,FORMEDASA51COLUMNVECTOR,ISAMEMBERSHIPFUNCTIONOFTHEMEASUREDFUZZYSTATEFORTHEINPUTVARIABLESIEOSC,PHM,ANDTRELISTEDINTABLE3MOUTPUTDENOTESA17ROWVECTORWHICHRELATESTOMEMBERSHIPFUNCTIONSOFTHECORRESPONDINGFUZZYSTATEFORTHEOUTPUTVARIABLESIEDKSANDDRGIVENINTABLE4TABLE7FUZZYDECISIONTABLEFORSMCTUNINGPERFORMANCEATTRIBUTESINPUTTUNINGACTIONOUTPUTDKSDROSCHIUNK02545K01552LIUNK024560ACCP00LIOQ015520HIOQ0245601552PHMHIUNK02456K02456LIUNK01552K02456ACCP00LIOQ001552HIOQ0155202456TREELK01552K02545LA0K02456ME0155202545SM0155201552OK00CHYEUNGETAL/INTERNATIONALJOURNALOFMACHINETOOLSPHMTREMOUTPUTIDKSDRC138LEADSTOTHECOMPARISONOFEACHCORRESPONDINGELEMENTANDTHEMINOPERATIONENFORCESTHESELECTIONOFTHEELEMENTWHICHHASTHEMINIMUMVALUEEACHRESULTINGRULEMRIBECOMESA57MATRIX,ANDTHEREAREFIVERULESMAPPINGFROMEACHINPUTXAXISYAXIS64898757680476904769000777360009810900198110028438101015915159151616G10G103051810K43051810K4776110K9776110K9K5,C5K5,C512210K312210K31241810K71241810K7010K35010K326256,K1867227658,K2452021529,K1473025228,K23887388,K351237,K441420,K352301,K42000030003VARIABLETOEACHOUTPUTVARIABLE,TOTALING15SETSOFMATRICESFOREACHOFDKSANDDRASTHEINDIVIDUALRULESAREJOINEDTHROUGHTHEFUZZYCONNECTIVEOROPERATOR,THERESULTINGFUZZYRELATIONMATRIXBETWEENEACHOFTHEFUZZYINPUTANDOUTPUTVARIABLESISFORMEDAS,MROSCPHMTREDKSDRZMAX5IZ1MRIOSCPHMTREDKSDRC12C12C12C12C12“C12C12C12C12C1226BYCOMPARINGEACHELEMENTOFTHEFUZZYRELATIONTABLEFORINDIVIDUALRULES,THEMAXIMUMOFTHEMEMBERSHIPGRADESCORRESPONDINGTOEACHPAIROFINPUTOUTPUTSTATESISCHOSENCONSIDEREDINSMCTUNING,6RESULTINGFUZZYCOMPOSITERELATIONMATRICESORTABLESAREDEVELOPEDINTOTALIVFUZZYDECISIONTABLETHEFUZZYDECISIONTABLEISCALCULATEDBYMATCHINGTHESYSTEMPERFORMANCEATTRIBUTESTOTHECOMPOSITEFUZZYRELATIONTABLES,THROUGHTHEUSEOFTHECOMPOSITIONALRULEOFINFERENCEIESUPOFMINOPERATIONAS24,MCZSUPMINMINPUTOSCPHMTREMROSCPHMTREDKSDRC12C12C12C12C1227WHEREMINPUT,MR,ANDMCARETHEMEMBERSHIPFUNCTIONSOFTHEFUZZYINPUTVARIABLES,THERESULTINGFUZZYCOMPOSITERELATIONCALCULATEDUSINGEQ26,ANDTHECORRESPONDINGOUTPUTVARIABLES,RESPECTIVELYINTHEUSEOFASUPOFMINOPERATION,THEMEMBERSHIPFUNCTIONVECTOROFTHEINPUTVARIABLESISFIRSTCOMPAREDWITHEACHCOLUMNOFTHEFUZZYRELATIONTABLETHEN,THELOWERVALUEINEACHPAIROFCOMPAREDELEMENTSISTAKENFOREACHCOLUMN,THELARGESTVALUEINTHEVECTOROFELEMENTSISSELECTED,THUSRESULTINGINAROWVECTORINORDERTOOBTAINANUMERICALVALUE,C,THATDETERMINESTHEDEGREEOFTUNINGACTION,ADEFUZZIFICATIONISAPPLIEDUSINGTHEDISCRETECENTROIDMETHODAS,TABLE9SUMMARYOFFUZZYTUNINGFORTHREEDIFFERENTSCENARIOSRESULTSOFFUZZYTUNINGFORSMCCASE1CASE2CASE3PRESELECTEDLRAD/S200200200INITIAL/TUNEDKSV/MM/S1/0363001/031510/0269INITIAL/TUNEDRV/MM100/47161/391210,000/3716INITIAL/FINALMAXIMUMTRACKING