Sensorless Control of Surface-Mount Permanent-Magnet Synchro(2)

willconvergetothisdisk.

P2(Localstabilityunderpersistentexcitation):Thezeroequi-libriumof(10)isexponentiallystableifthereexistsconstantsT, >0suchthat

1

t+TTω2

(s)ds≥ .

tP3(Constantnonzerospeed):Ifthespeedisconstantandsatis es

|ω|>12

4

γψm

其他

292IEEETRANSACTIONSONPOWERELECTRONICS,VOL.25,NO.2,FEBRUARY

2010

Fig.2.

Speedobserverconstructionutilizingpositionestimate,θ

.thentheoriginistheuniqueequilibriumof(10)anditis

globallyasymptoticallystable.1

Remark1:Itisalsoprovenin[17]thatatzerospeed,thevectorxisnotobservable;hence,itisnotpossibletoreconstructthepositionwithanobserver;therefore,othertechniques,e.g.,signalinjection,shouldbetried.

Remark2:Itshouldbenotedthattheobserver(8)doesnotrequirespeedinformation,whichisastrongadvantage.Nor-mally,Luenberger-typeobserverscannotbeconstructedwithoutknowingω.Forexample,see[8]and[9].

Remark3:Asimilarnonlinearobserverwasutilizedin[20].However,thestatevariable,zdoesnotcontainanycurrentvari-able.Incontrast,itcontainsspeedω.Thus,themodelincludesthemechanicaldynamics,sothatitdependsontheloadcharac-teristics.Correspondingly,thefulldescriptionisquitecomplex.However,inthispaper,onlythemotormodelisdealt.Thestatevariable,xdoesnotcontainω.Hence,theoriginalmotordy-namics(2)aretransformedsuccinctlyintoasimpleform(5).

Ifthereisnoangleerror,thenψ2

= η( x)ψ2

η( x) 2isusedasthedrivingm

2.Thedifference,tom

termthatforcestheerrorvanish.B.SpeedObserver

Toconstructaspeedcontrollerortocompensatethecross-couplingvoltages,ωLidandωLiq,itisnecessarytoestimatethespeed.However,itisnotdesirabletoobtainaspeedestimatethroughnumericaldifferentiationofthepositionestimates.In-stead,weutilizeatracking-controller-typespeedestimatoroftheform[19]

z˙1=Kp(θ z1)+Kiz2(11)z˙2=θ

z1(12)ω =Kp(θ

z1)+Kiz2(13)

whereKpandKiareproportionalandintegralgains,respec-tively.ThespeedestimatorblockdiagramisshowninFig.2.The

loopbandwidthcanbemadeKpandKi.Then,z1tracksθ

widebyselectingproperPIgains,

,ifθ isnotchangingfastcomparedwiththeloopbandwidth.Sincez1≈θ

,thenodevaluepriortotheintegralblock,1/simpliesaspeedestimateω .ApplicationstudyofthesimilarPLL-typespeedestimatorwasshownin[22]and[23].

1Note

thepresenceofthefreeadaptationgainγonthelower

bound.

Fig.3.Overallsensorlesscontrolblockdiagramwiththenonlinearobserver

andthespeedestimator.

C.SensorlessControl

ThedynamicmodelofSPMSMinthesynchronousframeisgivenby

L˙ied= Rsied+ωLieq+ved

(14)L˙ieq= Rsieq ωLied ωψm+veq

(15)

wheresuperscript“e”signi esavariableinthesynchronousframe.ThesensorlesscontrolblockforanSPMSMthatincludesthenonlinearobserverisoutputsangleestimateθ

showninFig.3.Thenonlinearobserver

basedonwhichthe eldorientationcontrolisestablished.AconventionalPIcontrollerisutilizedford-andq-axiscurrentcontrolalongwiththedecouplingandtheback-EMFcompensation.Thespeedcontrollerutilizesω thatcomesoutfromthespeedestimator.

Janssonetal.[21]pointedthatinjectionofd-axiscurrenten-hancedtherobustnessofthesensorlesssystemagainstRsvaria-tion.Theyappliedd-axiscurrentinproportiontoq-axiscurrent.However,weinjectd-axiscurrentpulsesinalow-frequencyre-gion.Togeneratesuchcurrentpulses,weapplyavoltagepulsetrain,asshowninFig.3.Inthisexperiment,thepulsefrequencyis200Hz,thepeaklevelis50V,andthepulsedutyis0.2ms.Notethatnod-axiscurrentisinjectedif|ω|>100r/min.

III.SIMULATIONANDEXPERIMENTALRESULTS

SimulationwasperformedwiththeMATLABSimulinkusingthemotorparameterscommandω

listedinTableI.Fig.4(a)showsthespeed

andtheshaftspeedωr.Inthespeedcontrolblock,atorquelimitr

anda eldweakeningweresetup.Inadditiontotheinertialloadcausedbyspeedchanges,extraloadtorqueswereapplied,asshowninFig.4(b).Thespeedresponselookssatisfactoryevenundertheloadtorqueand(d)showsestimates,sinθ

stepchange.Fig.4(c)

,cosθ ,andθ inanexpandedtime

其他

LEEetal.:SENSORLESSCONTROLOFSPMSMsTABLE1

PARAMETERSOFSPMSMSFORSIMULATIONANDE

XPERIMENTS

Fig.4.Simulationresultsof(a)realspeedandtheestimatedspeed.(b)Load

torqueandthetorqueresponse.(c)Estimatedtrigonometricalfunctions,sinθ

andcosθ

.(d)Realpositionanditsestimates.scale.Agoodtrackingperformancewasshownafteratransientperiod.

ExperimentswasperformedwithadynamotestbenchthatwasmadefromtwoSPMSMs.Theshaftsofthetwomotorswereconnectedviaacoupler,asshowninFig.5(b).Allthenonlinearobserverandcontrolalgorithmswereimplemented

in

293

Fig.5.Photosoftheexperimentsetup.(a)Inverterforthetestmotor.(b)Dynamotest

bench.

parisonbetweentherealandtheestimatedpositiondataunderno-loadconditionat(a)80r/minand(b)300r/min.

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294IEEETRANSACTIONSONPOWERELECTRONICS,VOL.25,NO.2,FEBRUARY

2010

parisonbetweentherealandtheestimatedpositiondataunderafullsteploadat(a)100r/minand(b)600

r/min.

Fig.8.Speedresponseswithafullsteploadat(a)100r/minand(b)500

r/min.

Fig.9.Speedandthecorrespondingtorqueresponsesat1000r/minwhenafull-loadtorqueis(a)appliedand(b)

removed.

Fig.10.Speedcontrolresponsewithastepfull-loadtorque.

aTMS320vc33DSPboardshowninFig.5(a).Thepulsewidthmodulation(PWM)switchingfrequencywassettobe8kHzandthedeadtime2µs.Thedeadtimewascompensated,andvoltagecommandvalueswereusedforvαβinthenonlinearobserver(8).Thecurrentcontrolalgorithmwascarriedoutevery125µs,andthespeedcontrolFig.6showssinθ

loopwasactivatedevery1.25ms.

,cosθ ,andθ ,alongwithrealpositionθmeasuredbya6000pulsesperrevolutionencoderundernoloadwhen(a)ωr=80r/minand(b)300r/min,respectively.

其他

LEEetal.:SENSORLESSCONTROLOFSPMSMs

Fig.11.Experimentalresultat

start-up.

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