Sensorless Control of Induction Machines―With or W

IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.53,NO.1,FEBRUARY20067SensorlessControlofInductionMachines—WithorWithoutSignalInjection?JoachimHoltz,Fellow,IEEEAbstract—Controlledinductionmotordriveswithoutmechan-icalspeedsensorsatthemotorshafthavetheattractionsoflowcostandhighreliability.Toreplacethesensor,informationontherotorspeedisextractedfrommeasuredstatorcurrentsandfromvoltagesatmotorterminals.Vector-controlleddrivesrequireestimatingthemagnitudeandspatialorientationofthefundamen-talmagneticfluxwavesinthestatororintherotor.Open-loopestimatorsorclosed-loopobserversareusedforthispurpose.Theydifferwithrespecttoaccuracy,robustness,andsensitivityagainstmodelparametervariations.Dynamicperformanceandsteady-statespeedaccuracyaroundzerospeedrangeareachievedbysignalinjection,exploitingtheanisotropicpropertiesofthemachine.Theoverviewinthispaperusessignalflowgraphsofcomplexspacevectorquantitiestoprovideaninsightfuldescrip-tionofthesystemsusedinsensorlesscontrolofinductionmotors.IndexTerms—Adaptivetuning,identification,inductionmotor,modeling,observers,sensorlesspositioncontrol,sensorlessspeedcontrol,signalinjection,vectorcontrol.I.INTRODUCTIONCONTROLLEDinductionmotordriveswithoutspeedsen-sorhaveemergedasamaturetechnologyinthepastdecade[1],[2].Theadvantagesofsensorlesscontrolarere-ducedhardwarecomplexityandlowercost,reducedsizeofthedrivemachine,eliminationofthesensorcable,betternoiseimmunity,increasedreliability,andlessmaintenancerequire-ments.Amotorwithoutspeedsensorisindicatedforoperationinhostileenvironments.Notwithstandingtherapidprogressatwhichthenewtechnologieshaveemerged,therequirementofoperatingasensorlessdriveatverylowspeedconstitutesapersistingchallenge.Fig.1givesaschematicoverviewofthemethodologiesappliedtosensorlessspeedcontrol.Afirstcategorycomprisesthemethodsthatmodeltheinductionmotorbyitsstateequa-tions.Asinusoidalfluxdensitydistributionintheairgapisthenassumed,neglectingspaceharmonicsandothersecondaryeffects.Theapproachdefinestheclassoffundamentalmodels.Theyareeitherimplementedasopen-loopstructures,likethestatormodel,orasclosed-loopobservers.Thelattermakeuseoferrorsignalsbetweenmeasuredandestimatedquantitiesthatarefedbacktotheobserversinordertoincreasetheirrobustnessandimprovetheirdynamics.Fundamentalmodelshavetheirlimitsatzerostatorfrequency.Therotor-inducedManuscriptreceivedJanuary21,2004;revisedAugust3,2005.AbstractpublishedontheInternetNovember25,2005.TheauthoriswiththeElectricalMachinesandDrivesGroup,UniversityofWuppertal,Wuppertal42097,Germany.DigitalObjectIdentifier10.1109/TIE.2005.862324Fig.1.Methodsofsensorlessspeedcontrol.voltageisthenzero,whichrenderstheinductionmotoranunobservablesystem.Itisparticularlythelowspeedrangewhereanisotropicprop-ertiesofthemachinecanprovideadditionalinformationonthefieldangleorthepositionoftherotor.Voltagesinducedinthestatorwindingsbyspatialrotorslotharmonicscanbeutilizedtodetermineaccuratespeedsignals.Transientexcitationsbyinjectedsignalshavingotherfrequenciesthanthefundamental,ortransientscausedbyinverterswitching,servetodetectthespatialorientationsofexistinganisotropies.Theresponseofthemotorisusedtoidentifyeitherthefieldangle,ortherotorpositionangle.Boththefundamentalmodelmethodsandthesignalinjectiontechniquesarecompetingtoimprovethelowspeedperfor-manceofsensorlessdrives.Thisoverviewpapercharacterizesthemajorrepresentativesofeitherclass.Itvisualizestheirfunctionalitiesbycomplexsignalflowgraphsanddiscussestheirmeritsandshortcomings.II.OPEN-LOOPMODELSA.StatorModelThestatormodelisderivedbyintegratingthestator-inducedvoltageui=us−rsis,whichyieldsˆψs=
(ˆus−ˆrsis)dτ,ˆψr=1kr(ˆψs−σˆlsis)(1)whereσlsisthetotalleakageinductance,σ=1−l2m/lslristhetotalleakagefactor,andkr=lm/lristhecouplingfactoroftherotor.TheresultingstatorfluxlinkagevectorˆψsisthenusedtodeterminethestatorfieldangleˆδS=arg(ˆψs),0278-0046/$20.00©2006IEEE8IEEETRANSACTIONSONINDUSTRIALELECTRONICS,VOL.53,NO.1,FEBRUARY2006Fig.2.Statormodel.Theidealintegratorisapproximatedbyalow-passfilter.(a)Signalflowgraph.(b)Bodediagram.or,consideringtheleakagefluxvectorσˆlsis,therotorfieldangleˆδR=arg(ψr).Equation(1)isvisualizedbythesignalflowdiagraminFig.2(a)[3].Notethattimeisnormalizedasτ=ωsRt,whereωsRistheratedstatorfrequency.Thestatormodelasdefinedby(1)isdifficulttoapplyinpracticesinceunavoidabledisturbancesuzandiz,invariablysuperimposedtotheacquiredsignalsusandisinFig.2(a),impedeachievingtherequiredaccuracy.Itisparticularlytheoffsetanddrifteffectsthatarisefromanaloguesignalmeasure-ment.TheyaccumulateattheintegratoroutputinFig.2(a).Theresultingrunawayoftheoutputsignalisafundamentalproblemofanopenintegration.Anegativelow-gainfeedbackisthereforeaddedthatstabilizestheintegratorandpreventsitsoutputfromincreasingwithoutbounds.Thefeedbacksignalconvertstheintegratortoafirst-orderdelay,designedtohavealowcornerfrequency1/τ1.Thestatormodel(1)thusbecomesτ1dˆψsdτ+ˆψs=τ1(ˆus−ˆrsis).(2)TheBodediagraminFig.2(b)showsthatthefirst-orderdelay,orlow-passfilter,behavesasanintegratorforfrequenciesmuchhigherthanthecornerfrequency.Itisobviousthatthemodelbecomesinaccura