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ACLOSEDLOOPFEEDBACKMETHODFORAMANUALBARSTRAIGHTENERROBERTJMIKLOSOVIC,ZHIQIANGGAODEPARTMENTOFELECTRICALANDCOMPUTERENGINEERINGCLEVELANDSTATEUNIVERSITYCLEVELAND,OHIO,USAABSTRACTAUTOMATIONOFAUNIQUEMANUALLYCONTROLLEDINDUSTRIALBARSTRAIGHTENERISPROPOSEDACONTINUOUSTIMECLOSEDLOOPMODELISCONSTRUCTEDINSIMULINKFORANEVENTDRIVENPROCESSTHROUGHTHEUSEOFASYNCHRONOUSTIMERSTHESYSTEMISSIMULATEDWITHLINEARANDNONLINEARPDCONTROLLERSANONLINEARFILTER,CALLEDTHETRACKINGDIFFERENTIATOR,ISINTRODUCEDASANALTERNATIVETOALINEARAPPROXIMATEMEANSOFPROVIDINGACCURATEDERIVATIVEFEEDBACKINTHEPRESENCEOFNOISEINBOTHCASES,THENONLINEARTECHNIQUESOUTPERFORMEDTHEIRLINEARCOUNTERPARTSWHILERETAININGTUNINGSIMPLICITYIBACKGROUNDPRECISIONSTRAIGHTENINGOFACYLINDRICALMETALBARISLARGELYBASEDONTHEABILITYTOPRECISELYMEASUREITSGEOMETRYAFEWFUNDAMENTALMEASUREMENTSANDHOWEACHINFLUENCESTHETOLERANCESPECIFICATIONONSTRAIGHTNESSSHOULDFIRSTBEUNDERSTOODMETHODSFORMEASURINGROUNDNESSANDSTRAIGHTNESSARECOVEREDTOLAYTHEGROUNDWORKFORTHEPROBLEMFORMULATIONTHEBASICOPERATIONOFTHEMACHINEISOUTLINEDINSECTIONII,ANDITSFUNDAMENTALLIMITATIONSANDNEEDFORAUTOMATIONAREDISCUSSEDSECTIONIIIADDRESSESTHETASKOFCLOSINGTHELOOPTHROUGHBLOCKDIAGRAMSANDTHEROLEOFNEWHARDWAREINTHEPROCESSSECTIONIVCONTAINSDESCRIPTIONSOFALLOFTHEBLOCKSTHATAREMODELEDINSIMULINKTHELINEARANDNONLINEARCONTROLLERDESIGNSAREDISCUSSEDINSECTIONV,THESYSTEMISSIMULATEDINSECTIONVI,ANDCONCLUDINGREMARKSAREMADEINSECTIONVIIAMEASURINGROUNDNESSROUNDNESSISAQUANTITYDERIVEDFROMCOMPARINGTHESHAPEOFACROSSSECTIONALAREAATONEDISTINCTPOINTALONGACYLINDERSLENGTHAGAINSTACIRCLEAROUNDMETALBARTHATISARBITRARILYLONGWITHRESPECTTOITSDIAMETERHASTOBECHECKEDFORROUNDNESSINMANYLOCATIONSLENGTHWISEANDAVERAGEDTOINSUREOVERALLCONSISTENCYROUNDNESSISAPPROXIMATEDBYROTATINGTHEWORKPIECEONEREVOLUTIONINAVEEBLOCKWHILEMEASURINGTHESURFACEWITHANINDICATORTAKINGTHEDIFFERENCEBETWEENTHEMINIMUMANDMAXIMUMINDICATORREADINGSINTHISCASEISREFERREDTOASTHETOTALINDICATORREADINGTIR1BMEASURINGSTRAIGHTNESSSTRAIGHTNESSISAQUANTITYDERIVEDFROMCOMPARINGTHEAXIALCENTERLINEOFASPECIFICSECTIONOFACYLINDERSLENGTHAGAINSTASTRAIGHTLINEASIMPLEMETHODFORAPPROXIMATINGSTRAIGHTNESSISBYROTATINGTHEBARONEREVOLUTIONBETWEENTWOVEEBLOCKSTHATAREAFIXEDDISTANCEDAPART,WHILEMEASURINGINTHECENTERWITHANINDICATORTHEDISTANCETHATTHEAXIALCENTERLINEOFTHEPARTDEVIATESFROMATHEORETICALLYSTRAIGHTCENTERLINEDIRECTLYBELOWTHEINDICATOREQUALSTHEEXTENTTOWHICHTHEPARTISBOWED,ORWARPED,OVERLENGTHDTHEMAXIMUMANDMINIMUMINDICATORREADINGSIXANDINAREPHYSICALLYREPRESENTEDINFIG1FROMTHIS,TIRISDERIVEDASTIRIXINR|BOW|R|BOW|2|BOW|1DEVIATIONSINROUNDNESS,OUTSIDEDIAMETERODSIZE,ANDFINISHCANADVERSELYAFFECTTHEMEASUREMENTFIGURE1MAXANDMININDICATORREADINGSOFABOWEDPARTCSTRAIGHTENINGTHESTRAIGHTENINGPROCESS,WHICHCANBEBROKENINTOSTEPS,SIMPLYINVOLVESCORRECTINGANYERRORWHILECHECKINGFORSTRAIGHTNESSFIRST,THEPARTISMEASUREDFORSTRAIGHTNESSTHEN,ITISROTATEDSOTHATTHEBOWISORIENTED180DEGREESAWAYFROMTHEVEEBLOCKSWITHTHEMAXIMUMINDICATORREADINGFACINGUPWARDSFINALLY,ACOUNTERBENDINGFORCEREPLACESTHEINDICATORANDSTRAIGHTENSTHEWORKPIECEAGAINSTTHEVEEBLOCKSIIMACHINEOPERATIONTHESTRAIGHTENERTOBEAUTOMATEDUSESANONCONTACTULTRASONICSENSORINPLACEOFTHEINDICATORANDROLLERSINPLACEOFTHEVEEBLOCKSINANEFFORTTOMINIMIZECONTACTWEARTHEPARTSLOWLYSPIRALSTHROUGHTHEMACHINETHEINDICATORREADINGBECOMESACONTINUOUSSINUSOIDATTHESENSORSOUTPUT,HAVINGAPEAKTOPEAKVALUEEQUALTOTHETIREACHREVOLUTIONTIRISSAMPLEDFROMTHESENSOROUTPUTANDCALCULATEDEACHREVOLUTION,MAKINGTHESAMPLEPERIODOFONEREVOLUTIONTHEMINIMUMTIMEBETWEENCONSECUTIVEBENDSYSPTIRISTHEPLANTOUTPUTYTOBECONTROLLEDWHENTHEPARTISSTRAIGHTENED,THEMACHINESTOPSROTATIONWITHTHEBOWFACINGUPWARDS,BUTTHEPARTCONTINUESTOFEEDLENGTHWISEWHILEANAIRCYLINDERCOUNTERBENDSTHEPARTOVERAPERIODOFTIMETHISBENDTIMEBTISTHECONTROLVARIABLEUFIG2ILLUSTRATESTHISOPERATIONFIGURE2THESTRAIGHTENERTOBEAUTOMATEDAPROCESSLIMITATIONSTHEREAREASPECTSOFTHEPROCESSTHATCANLIMITTHECONTROLLERSPERFORMANCEANDSLOWITDOWNBYEXTENDINGYSPEACHISOBSERVEDANDTAKENINTOCONSIDERATIONWHENPRODUCINGANACCURATESIMULATIONMODEL1THEULTRASONICSENSORINTRODUCESRFINOISEINTOITSTHEUSEOFAFEEDBACKFILTERISESSENTIAL2AROUGHPARTSURFACEFINISHADDSDISTORTIONTOTHESENSOROUTPUT3ANOUTOFROUNDPARTSUPERIMPOSESHARMONICSONTHESENSOROUTPUTSINUSOID,PLACINGABOUNDONTHEMINIMUMSTEADYSTATEERRORTHATISACHIEVABLE4INCONSISTENTMATERIALDENSITYPRODUCESFALSEMEASUREMENTSTHEMEASUREDFOCALLENGTHOFATRANSDUCERISDEPENDENTONTHEDENSITYOFTHEMATERIALTHATISBEINGMEASURED2THEUNITCANNOTMEASUREACCURATELYINTHEPRESENCEOFATIMEVARIANTMATERIALDENSITYIEHARDSPOTSALTHOUGHUNAVOIDABLE,ITCANBEDETECTED,SINCETIRCHANGESMONOTONICALLY5ANINCONSISTENTODCAUSESVERTICALSHIFTSINTHESENSOROUTPUTADIFFERENTIALTIRMEASUREMENTCANCELSTHESEAFFECTS6ATWISTEDPARTCONDITIONISDETECTEDWHENTHEANGULARPOSITIONOFTHEMAXIMUMINDICATORREADINGSLOWLYMOVESWITHEACHREVOLUTIONTHISCONDITIONISCREATEDWHENTHEPARTISNOTSTRAIGHTENEDATTHEPRECISEANGULARLOCATIONANDOCCURSBECAUSEOFTHEQUANTIZATIONAFFECTOFTHEDIGITALREADOUTUSEDBYTHEOPERATORTHENEWCONTROLLERWILLUSEACONTINUOUSSIGNALANDTHEPARTCANBESTRAIGHTENED30TO45DEGREESAHEADOFTHETWISTWHENENCOUNTEREDBTHENEEDFORAUTOMATIONREPLACEMENTOFTHEOPERATORWITHELECTRONICHARDWAREISBENEFICIALINSEVERALWAYSTHECOSTOFTHEELECTRONICSISMUCHLESSTHANTHEONGOINGHOURLYWAGEANDSCHEDULEOFANOPERATORTHELIMITATIONSASSOCIATEDWITHTHEDIGITALREADOUTAREELIMINATED,WHICHHELPSTHEMACHINETOSTRAIGHTENFASTERWITHMOREPRECISIONTHEPROCESSCANBEDRASTICALLYSPEDUPTOPRODUCEMORETHOUGHTHEMINIMUMSAMPLETIMEISONEREVOLUTION,ITDOESNOTNEEDTOBESLOWENOUGHFORHUMANCOMPREHENSIONAPROGRAMMABLELOGICCONTROLLERPLCCANMAKESEVERALCALCULATIONSANDTESTTHERESULTAGAINSTASETOFRULESMANYTIMESFASTERTHANAHUMANBEINGCRESEARCHMETHODOLOGYTHEFOCUSISSPLITBETWEENMODELINGANDCONTROLDESIGN,SINCETHISISANEWCONTROLPROBLEMTHEPROCESSISMANUALLYCONTROLLEDRATHERTHANBEINGSTRICTLYMANUALINOPERATION,MEANINGTHEMACHINENEEDSONLYANEWCONTROLLERTHEREISNONEEDFORACOMPLETEMECHANICALOVERHAUL,SOTHEBESTMETHODOFSTRAIGHTENINGISNOTRESEARCHEDTYPICALOFASMALLCOMPANY,TIMEANDMONEYARELIMITEDGAOANDHUANG3PRESENTEDANEWERRORBASEDCONTROLDESIGNFRAMEWORKINCLUDINGSUCHINNOVATIONSASANONLINEARTRACKINGDIFFERENTIATORANDANONLINEARPROPORTIONALINTEGRALDERIVATIVENPIDCONTROLMETHODTHESEMETHODSPROVETOBEPOWERFULANDSIMPLETOTUNE,WHICHMAKETHEMIDEALFORUSEINANINDUSTRIALENVIRONMENTIIIACLOSEDLOOPSOLUTIONTHETASKOFAUTOMATIONCANBEGINONCETHEPROCESSISWELLDEFINEDASTRAIGHTFORWARDSYSTEMBLOCKDIAGRAMISDEVELOPED,ANDEACHBLOCKISMODELEDINSIMULINKASPECTSOFTHEHARDWARECONFIGURATIONARECAREFULLYCONSIDEREDAFROMOPENLOOPTOCLOSEDLOOPTHEOPENLOOPMULTIINPUTMULTIOUTPUTMIMOBLOCKDIAGRAM,INFIG3,REPRESENTSTHEMANUALLYCONTROLLEDPROCESSTHEOPERATORCALCULATESTIRANDMONITORSTHEANGULARPOSITIONPOFTHEBOWWITHEACHREVOLUTIONWHENYAPPROACHESASPECIFIEDLIMIT,THEOPERATORSETSBTPROPORTIONALTOYANDITSRATE,ANDTHENPUSHESABUTTONBPTOSTRAIGHTENTHEPARTTHEBENDTIMERCREATESAPULSETRIGGEREDBYBPTHATCOUNTERBENDSTHEPARTFORBTMINUTESTHISEVENTFORCESTHEPARTTOHAVEASPECIFICRATEFORAPERIODOFTIMEAFTERTHEEVENT,THEPARTTAKESONANEWRATEANDTHEPROCESSPERPETUATESTHEREFORE,YISAPIECEWISECONTINUOUSFUNCTIONOFTIMETHEOPERATORSINVOLVEMENTINTHEPROCESSISREPRESENTEDASABLOCKINFIG4FIGURE3OPENLOOPBLOCKDIAGRAMFIGURE4OPERATORBLOCKREARRANGINGTHEBLOCKSANDBREAKINGEACHFUNCTIONDOWNINTOSMALLERMOREMANAGEABLEBLOCKSREDUCESTHEREPRESENTATIONTOAUSABLECLOSEDLOOP,SINGLEINPUTSINGLEOUTPUTSISOFORMFIG5SHOWSHOWASISOPLANTISOBTAINEDBYCOMBININGTHEPROCESSWITHTHETASKOFSAMPLINGTHETIR,SINCEITCANBECONSISTENTLYCOMPUTEDFIGURE5SISOPLANTBLOCKTHEPLANTHASAVARIABLEWIDTHPULSEASTHEINPUTUANDTHESAMPLEDTIRYASTHEOUTPUTTOBECONTROLLEDTHEINCOMINGCHANGINGPOSITIONOFTHEWORKPIECEISMODELEDASANUNKNOWNRATEDISTURBANCEDTHECLOSEDLOOPSISOBLOCKDIAGRAMISSHOWNINFIG6FIGURE6CLOSEDLOOPBLOCKDIAGRAMBHARDWARECONFIGURATIONDEPICTEDINFIG7,ANENCODERANDAPLCARETHEONLYHARDWARENEEDEDFORAUTOMATIONTHEENCODERFEEDSTHEANGULARPOSITIONOFTHEPARTBACKTOTHECONTROLLER,ANDTHEPLCHANDLESALLOFCLOSEDLOOPFUNCTIONSOUTSIDEOFTHEPROCESSFIGURE7HARDWARECONFIGURATIONFIG8DEPICTSTHEHARDWARELAYOUTFORPLANTDATAACQUISITIONDURINGMANUALOPERATIONTHEPLCISALSOUSEDTOCALIBRATEASTRIPCHARTRECORDER,SHOWNINFIG9,WHICHSIMPLIFIESCALIBRATIONFORTHEOPERATORANDREMOVESROOMFORERRORDURINGDATAACQUISITIONUSINGTHEPLCFORBOTHDATAACQUISITIONANDCONTROLKEEPSCOSTSLOWERFIGURE8OPENLOOPDATAACQUISITIONCONFIGURATIONFIGURE9CHARTRECORDERSETTINGSFORA006”TIRSIGNALIVMODELINGSIMULATIONMODELINGINVOLVESTHECONSTRUCTIONOFSIMULINKBLOCKSFOREACHOFTHEBLOCKSINTHESISODIAGRAMTHREEMODULARBLOCKSAREFIRSTDESIGNEDTOACCOMMODATETHEPRESENCEOFANEVENTDRIVENPLANTINACONTINUOUSTIMEENVIRONMENTWHERETHECONTROLVARIABLEISANASYNCHRONOUSPULSEWIDTHTHEYAREALLBASEDONCREATINGASYNCHRONOUSTIMERSINSIMULINKBYINTEGRATINGACONSTANTUNTILITREACHESAPRESETVALUE,THENSHUTTINGITOFFBYFEEDINGTHEINPUTWITHAZEROEQUATION2WILLREACHAVALUEOFONEINTHETIMEINTERVALEQUALTOTHEAVERAGEOFUTOVERITTHEACCURACYINCREASESIFTHEINTERVALISVERYSMALLORUTISACONSTANTFUNCTIONASUITABLEDIFFERENCEEQUATIONISGIVENIN3ATRIGGEREDSAMPLEANDHOLDTSHBLOCKTHEOUTPUTANDRATEOFTHEPLANTIMMEDIATELYAFTERTHEPARTHASBEENSTRAIGHTENEDAREDEPENDENTONBT,ANDTHEPREVIOUSYANDY,ALLOFWHICHOCCUROVERDIFFERENTTIMEINTERVALSTHEFUNCTIONOFTHETSHBLOCKISTOSAMPLEAVALUEATONEPOINTINTIMESOTHATITCANBEUSEDATANOTHERTIMESHOWNINFIG10,THEBLOCKBASICALLYSAMPLESTHEINPUTFORASMALLPERIODOFTIMEONTHERISINGEDGEOFANENABLINGPULSE,ANDTHENHOLDSTHATVALUECONSTANTATTHEOUTPUTUNTILTHEBLOCKISREENABLEDINSIMULINK,ACONSTANTVALUECANBEMAINTAINEDFORANARBITRARYPERIODOFTIMEBYBUILDINGTHEOUTPUTOFANINTEGRATORTOADESIREDVALUEATSECONDTIMERISCREATEDBYINTEGRATING1/TUNTILITEQUALSONEITISUSEDTOCONTROLTHESMALLTIMEINTERVALIN4WHICHTAKESATIMEAVERAGEOFTHEINPUTFIGURE10TSHSIMULINKBLOCKBPULSEBLOCKTHEBENDTIMERMUSTBEABLETOCONVERTBTFROMAVALUEINTOTHETIMEDPULSE,UTHEPULSEBLOCK,ILLUSTRATEDINFIG11,WASDESIGNEDFORTHISPURPOSEBYINCORPORATING2,ITCREATESAPULSETHATHASAMAGNITUDEEQUALTOTHESIGNOFTHEINPUTANDAPULSEWIDTHEQUALTOTHEINPUTSABSOLUTEVALUEFIGURE11PULSESIMULINKBLOCKTHEHEARTOFTHEPULSEBLOCKISTHEPULSESUBSYSTEMBLOCK,SHOWNINFIG12THERECIPROCALBLOCKGENERATESADIVIDEBYZEROERRORWHENEVERITSINPUTISZEROCONSEQUENTLY,THERECIPROCALBLOCKNEEDSTOBEISOLATEDINASUBSYSTEMTHATISONLYENABLEDWHENSUPPLIEDWITHAVALUETHATISLARGERTHANAUSERDEFINEDCONSTANTVCONTROLDESIGNTHEREARECURRENTLYMANYDIFFERENTCONTROLSTRUCTURESAVAILABLE,THESIMPLESTOFWHICHISTHEPIDCONTROLLERDESIGNFORTHISREASON,APDCONTROLLERISFIRSTAPPLIEDTOTHECLOSEDLOOPMODELTOVERIFYITSRESPONSEANDSTABILITYITISUSEDASABENCHMARKFOROTHERCONTROLLERSNEXT,ANONLINEARPDNPDCONTROLSCHEMEISINTRODUCEDITRETAINSTHETUNINGEASEOFTHEPDCONTROLLERWHILEIMPROVINGPERFORMANCELAST,ANONLINEARFILTER,CALLEDTHETRACKINGDIFFERENTIATORTD,ISINTRODUCEDASANALTERNATEMEANSOFPROVIDINGANACCURATEDERIVATIVEFEEDBACKTOTHECONTROLLERINTHEPRESENCEOFNOISE,THUSIMPROVINGPERFORMANCEALINEARPIDCONTROLFORMANYREASONS,PIDCONTROLISSTILLUSEDIN90OFINDUSTRIALAPPLICATIONS3THEREAREONLYTHREETUNINGPARAMETERS,EACHHAVINGDIRECTPHYSICALSIGNIFICANCETOTHEERRORSIGNAL,NOTTHEMODELTHISMAKESFOREASYTUNING,WITHOUTHAVINGTOSPENDCONSIDERABLERESOURCESONTHECONSTRUCTIONOFALINEARMODELLINEARMODELSAREOFTENINACCURATEANDREQUIRERETUNINGWHENTHEREALWORLDPLANTSTHEYREPRESENTARENONLINEARANDTIMEVARYINGACONTROLSTRUCTURETHATISERRORBASED,ANDNOTMODELBASED,ISMORERESILIENTTOMODELUNCERTAINTIES3THEPIDCONTROLLAWIN6REPRESENTSTHEDIRECTPHYSICALMEANINGSOFTHETHREEPARAMETERS,WHEREEISTHEERRORSIGNAL,KPISTHEPROPORTIONALGAIN,KIISTHEINTEGRALGAIN,ANDKDISTHEDERIVATIVEGAINKEKEDTKPI_D6VISIMULATIONTHEPDCONTROLLERANDTHENPDCONTROLLERARESIMULATEDINSIMULINKONTHECLOSEDLOOPMODELTHESIGNIFICANCEOFPRACTICALINITIALCONDITIONSANDDISTURBANCESARECONSIDEREDSIMULATIONRESULTSFROMTHETWOCASESAREPRESENTEDANDDISCUSSEDNEXT,THESTEADYSTATEERRORISCOMPAREDUNDERVARIOUSNOISEANDDISTURBANCECONDITIONSFINALLY,ASECONDORDERAPPROXIMATIONANDATDAREIMPLEMENTEDINTHEFEEDBACKLOOPANDSIMULATEDWITHHEAVYFEEDBACKNOISEFORBOTHCONTROLLERSATRANSIENTPERFORMANCESIMULATINGTHESYSTEMANDINDIVIDUALLYADJUSTINGPLANTPARAMETERSTOEMULATEVARIOUSREALWORLDCONDITIONSVERIFIEDTHEDESIGNFIG19GRAPHSTHEOUTPUTANDRATERESPONSEFORTHEPDCONTR