MakotoKumon,IkUroMizumoto,Zentalwai GraduateSChoolofScienceandTbchnO1ogyl

ShapeMemoryAIloyActuatorwitllSimpleAdaptiveControl

MakotoKumon,IkUroMizumoto,Zentalwai GraduateSChoolofScienceandTbchnO1ogyl

KumamotoUniversity

2-39-1,Kurokami,Kumamoto,860-8555,Japan kumon＠gpo・kumamoto-u,acjp

‘AkifUmilndou

VehicleControlGro叩No.1,ＥＥ＆VehicleControlDept.,IsuzuMotorLtd、

８，Tsuchidana,Filjisawa-shi,Kanagawa-ken,252-8501,Japan

AlKifUmi工ndou＠notes・isuzu､cojp

Abstract

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1.Intmduction

ActuatorsaredevicesWhiChconvertenergyintopower efficiently・Forexample,motorsareconⅢnonlyusedfOr

soon,UndertheneedsOfefficiencybactuatorsarereqUired tobcsmaU,lightandpowcrinLBesidcs,itiSsignificantly

ationofactuatorS，specifications,whichisusUallyimplc- mentedaslocalfeedbackcontroUers・Smartactuatorsare candidatesinordertoachievethis,whiChcontainnotonly actuationpartsbutalsosensmgandcontrolhgsystemsin- sidesincethewholesystemutilizmgtheactuatorsbecomes simple・ThisreqUlrementconductstheneedofanghtand powerfillactuatingmaterialWhichhasanabintytosense itsstatusbyitselfAshnpleandrobustcontrolschemeis alsonecessarywhichiseasytOimPlementevenonaMicro ControlUnit(MCU)．

ShapeMemQXyAUoy[1],whichisdenotedasSMAbe-

1owEenerateslaｴgefOmeperweightandrecovprsitsmem‐

orizedshapebythephasetransition．Whenthealloyisin austenitephase,thematerialdefOnnedbyastressisableto

iscalledsuperelasticityThestiffnessofthealloyalsovanes dependingonitsphaseThephaseoftheaUoycanbeesti- matedbymeasuringitselectIicresistance、

Thephasetransitionwhichisthemajorfactortocon‐

trO1theallOycanbetriggeredbychangmgthetemperature・

HoweventhetemPeratureofthematerialisdifficulttocon‐

trolsinceitisstronglyeffectedbythetemperatuｴｅａ[ound thealloywhichcanvarymrealappncations、Inorderto

thestiffilessbysensingitselectricresistanceThisapproach

trollerpammeters・Selden[3]givesanotherapproachbased onOIWＯＦＦｃｏｎｔｒｏｌｏｆｓｍａｌｌＳＭＡｓｅｇｍｅntsinorderto

reducethelatencyofheatingprocess・Thisapproachisro‐

bUst,however,thetotalcontrolsysteI、becomescomplex asthenulnberofsegmentstocontrolbecomeslaIge・Both methodrequireadditionalsensorstorealizepositioncon‐

troL

Thepresentpaperismtendedtoproposeasimpleandro‐

bUstcontrolfbrSMAactuatorbyadoptingadaptivecontrol techniqUetooveIcometheuncertaintybnledevelopedac- tuatorutinzesacoUpleofaSMAandapasslvespringasan actuatortorealizebidirectionalmotionThepassiveSpnng isalsoutiUzedtomeasurethepositiontogetridofextemal

Inthenextsection(Sec2),characteristicsoftheSMA usedinthepresentpaperareshown,andthemodelofthe

systemiSalsoderivedSection3prOposesthecontrollerb TheeffectivenessoftheprOposedmethodisvalidatedby

2･ShapeMemoryAIloyACtuator

TheSMAｕｓｅｄｉｎｔｈｉsresearchwasBioMetalHe‐

Ux(BMX)fiomTbkiCorpOrationwhichwasaheUxcoilof Ni-THwireCharacteristicsaresunnaｴizedin[4]．

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FigureaRelation

内andthelengthof onantfrequency FigureloRelationbetweenelectricresistanceand

temperatureqeft)andstiffiness(right)Iheleftfigure showsaroughsketchoftheprOpertyb

2.3．PositionSensor

A1thoughthestifEnessoftheSMAcanbecontroＵｅｄｂｙ ｔｈｅＳＭＡｄＵｓｉｖｅｒａｎｄＭＣＵｕｎｉｔ,thepositionoftheactua‐

torisstiUneededtobemeaSuredbyothersensorslbthis

end,thespringoftheactuatorunitisutilizedtomeasurethe position

SpringsofconductivematerialsareablｅｔｏｐｅrfOrmas

sO1enoids・Theirmductance,WhichisdenotedasL,ismod‐

eledas咋旦ﾋﾟﾑ等{:趣,whereK,似ハjVbandJcrepre-

sentNagaokaCoefficient,penneabiUtyうmeanradiusofthe

6oil,numberofturnsandlengthrespectivelyandjVbiscon‐

stant､Ifthestiffnessofthespringisappropriatelychosen，

itispossibletoassume似,rcandKbecdhstant・Then，

LcanberewmittenasL＝砦,WhereOci…onstamt・

WhenthesolenoidisusedasapartOfLCRresonatonthe resonantfrequencyofthecircuitdenotedasハisgivenas

バー歳宕＝亘;F夛晨でniSimplieMhatihelengihof

theSpringlccanbeestimatedbymeasuringtheresonant fiequency（.Iflc＜1,thelinearizedversionoftheabove modelisappncable、

Actualmeasu１℃。resultofpositionsensorisshownin

Fig3・Theverticalandhorizontalaxisesshowthefie-

thefigure,theUnearmodelハー(0.03383Jc＋2.98)×106,

2.4．DynamicalModel

Thephasetransitionoftheactuatoristriggeredbyheat‐

mgtheaUoyanditsbehaviorissignificanUyeEfeCtedbythe

icalmodelofthesystemisdenved・

ＬｅｔＭｚ，Ｃ’んsandLorepresentmassofthetar‐

get,displacement,fiictioncoefficient,elasticcoefficientof thespringandthelengthbetweentheendoftｈｅＳＭＡ ａｎｄｔｈｅｏｔｈｅｒｅｎｄＯｆｔｈｅｓｐｒｉｎｇrespectivelybasShownin

Fi9.2(right)Denotethenormalizedelectricresistanceas入，

thestiffnessoftheSMArepresentedbyh(入)canbemod‐

eledbyaUnearmodelasshownabovea､。

【ＤｎＩｌ【］【Ｉ

Figure2･Schematicofthedevelopedactuator(1eft）

anditsdynamicalmodel(right）｝

２．１.EIectricResistanCe9StiflhlessａｎｄＰｈａｓｅ

ＴｈｅＳＭＡｏｆ２７５[nⅢ､]wasUsedasanactuatorfbrthis

sitetoaustenite・Sincethetemperatulesstartingandfinish- ingthesephasesaredifferent,theresistanceshowsahys‐

tereSisdUringheatingandcoolingprocess・Leftofthefig- urelshowsaroughsketchofthispropOrtybOntheother ha､｡,thereisahearrelationshiPbetwee、theresistance andthestiffneSsoftheaUoyasshownmtherightfigure ofFig､LHerenormalizedresistancerepresentslherateof

theresistancefromitsminimnnlvaluetothemaximumone・

Aslkuta[1Jreported,itisenoUghtocontroltheelectlicre‐

sistancewhentheSMAisutiUzedasanactuatorsincethe

stiffnessisequivalenttothegeneratedfOrce、

２．２．BidirectionalActuatoZ

TheshapememOryeffectoftheSMAistheunidi1℃c‐

tionalaction,anditgeneratespUlUngfOrceonly8Additional

actuatorssuchastheothｅｒＳＭＡareneededtorealizethe

bidirectionalactuatorBInthepresentpapenapassivespnng

isutiUzedbecauseitdosenotreqUireanyenergytoactu‐

ateitatall､TheleftfigureofFig､ZshowstheactUatorunit wmchcontainstheSMAandthespring、Oneendsofthe SMAandthespringareiixedtothebase,andtheotherends aretiedtoeachothenThisconnectedPomtisthetarget parttocontroLTheSMAisdrivenbysupplymganelectric

currentfromthedrivercircuitwhichgeneratesheat・The

ofthｅＳＭＡａｎｄ,hence,thestiffnessoftheSMAcanbe

controlled．

(1)

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凸づ〆 〆色

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〆^P〆 ,〆^〆

〆

Ｐ 〆

● 〆〆

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〆 ケゴ〆

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whereαandβareconstantsByusingthisstiffilessmodel，

ｔｈｅｎeutralpointofthemassdenotedasz汎pisgivenasa

fUnctionof入ａｓ

ThecontrolobjectiveisorganizedbythefOUowingtwo stepFirsUybthestiffilessoftheanoyisconnoUedwhich

positionoftheactuatorziscontroUedbythesecondSAC controUelbThefOnnercorreSpondstothefbrcecontroland thelatterachievesthepositioncontroLB1ockdiagramof

361．StiffhlessControl

ContrO1inputfbrthisstepisum(5)andtheoutputis theelectricresistance7whichcanbecomputedfiomthe nonnalizedresistance入givenin(4)ByUnearizing(4),the

、。＝ｚｏ＋－ １－入。

（６）

(5)and(6)givesthecOntrolinpUtfbrthesteadystate,which isdenotedasuo,asfbUows

uO＝Ｈ１(zd-Zb)入。_{Ｒ２Ｅ２＋Ｒ３Ａｄ．}

^（７）

(7)corTespondsto``Model入"inFigUre4・Then,thecontrol

mpuMiSdcfinedasu＝ｕｏ＋ｕ,,whereu1representsthe

bye北conve【getoOulisdesignedbySACtechniquｅａｓ

Ｕ，＝－ん入e＠Ａ，ｅ･入＝e入＋Ｐ〃入[u,］（８）

lJA＝Ｔ入e:ﾊｰｸﾞ入ハル

whereアヂ℃ArepresentsParaUelFeedfOrwardCompen‐

sator(PFC)inordertoassurethatthesystemsatisfiescon‐

ditionsrequiredmapplyingSAC.ｒ入ａｎｄぴ入representthe adaptivegainandtheparameterofグーmodificationrespec-

3．２．PositionControl

SincetheabovecontroUerperfbrmsthestiffnesscon‐

trol,thestiffnessisconsideredastheinputfOrtheposition controlsystem・Definethepositionerrordenotedaｓｅｚｂｙ

》･薑:(等-β-恥）（，）

(9)correSpondstothe"Modelz，，mFigure4・ThCfeedback signalisalsodefinedbyusingSACtechniqUeasaboveand

生十孟亀+坐i=二三･謎=一等人Ⅱ10）

A1thoughthelefthandsideof(10)containsthecontrolm-

ＡＤｓＬｏ

ｚｉｚｐい)＝ん(入)＋ｈ８．

^（２）

Summarizingabove,thedynanlicsofmechanicalpartare

delivedasfbUows：

Ｍ２(ｔ)＋c2＋(んい)＋ｈｓ)(z(t)－znp(入))＝Ｏ（３）

Sincethetemperatu1℃ofSMAplaysanimportantrole

ered・AssumethatthehysteresisshowninFig.１isnegli‐

gible・ThenthenonnalizedelectricresistanceoftheSMA

canbemodeledasafUnctionofitstemperaturewhichis

入＝１－tanh(ｑ(ｚ－ｚｏ))， ⁽⁴⁾

whereqandzoareconstant､cuorepresentsthemeantem‐

peratureofphasetransitionandmo＝３２６５[Iqinthiscase・

Quantityofheatsuppliedbythedrivercircuitcanbegiven

as雲wh・Mandrr聯senttheinputvoltageandthe

electricresistanceoftheSMArespectively，ｒｃａｎｂｅｎｎ‐

earlytransfbnnedinto入ａ､｡,hence,thedynamicsofthe

‘(艦)－ＭＭ)+(R,二十R･川(，）

whereRmR2andR3representconstantsandZbshowsthe

temperaturearoundtheSMA､zushowsthecontrolinputto

ModUlatio､(ＰＷＭ)isutinzedandthedurationrateofthe activestateisconsideredasthecontrolinputu・Thisleads

Sunmarizing(1),(2),(3),(4)and(5),anddiscretized thedynamicsbytakingtheeffectofPWMintoaccount,the discretetimedynanncalmodeloftheactuatorisderived、

３.Contml

Undertheexistenceofuncertaintyanddisturbance,the

contronershouldberObustbyutiUzingfeedbacksignals・

Addingtothis,thecontrolalgorithmmuStbesosimpleto

searchistodevelOpasmallacmatorunit､SimpleAdaptive Control(SAC)[2]whichisadOptedmthepresentpaperis oneofthecandidates・SAChasarObuStpropertyonthe uncertaintyoftheplant,ａｎｄthestructureofthecontroUer

AulhorIzedIicenSBdusellmltedt。:KumamotoUnlverB1tyTnalUser・DownloadedonJ0u｣gust6,２００９ａｔＯ４:４９fmmIEEEXplore、RestrIcUonsapply．

E1ectricresistance Model入

Actuator

臘iWlFT息

Model二 Ｍｏ 韮一十

十

十’

＋ MechnnicR1

Dvnamics

ulLllThel･ｍａｌlhermnI Dvnamics

5，

"

Ａ ,IC

Dvnamics Dvnamlcs

PFC入 PＦＣｚ

Displacement

Figure4｡Blockdiagramoftheproposedsystem

4oExPeriment0.1693,β＝0.0833.ThelengthofSMAcouldvaryfirom

275[1ｍ､]to343[mｍ］

Themethodproposedabovewasevaluatedbyexperl- RightofFig・Sshowstheresultwhenthedesなeddis- mentswithadevelopedacmatorandthecontrolalgorithm placementwas3ZO[ｍⅡ小Themeasureddisplacementby

driverwasreauzedbyMOSFETswitchingcircuitswith

ｃｕ江entmeasurementresisters、

thelaserdisplacementsensorwasaround313hnm]atwhere ４．１．StiffirIGRsControl（hespringsensorshowedawidevariation・A1thoughittook

FirstlyithestiffnesscontrolisevaluatedTheeffective expected,thetargetconvergedtothedesireddisplacement rangeoftheelectricresistanceoftheSMAsegmentused anditstayedforabout200[s］

fbrtheexpenmentwaSfrom55[Q]to７７[Q］

SoCondiuHRiIm

RightofFig5showstheresultwhenthedes並eddis- placementwas3ZO[mn4Themeasureddisplacementby

thelaserdisplacementsensorwasaround313hnm]atwhere thesplmgsensorshowedawidevariation・A1thoughittook

expected,thetargetconvergedtothedesireddisplacemem anditstayedforabout200[s］

5.Conclusion

ThepresentpaperpropoｓｅｄａｓｍａＵＳＭＡａｃｍａｔｏｒｕｎｉｔ ｗｈｉｃｈｃｏｕldsenseitsdisplacementandstiffilessandacon-

devicewasalsodevelopedtoevaluatetheproposedmethod 1hroughexperiments・Themethodsucceededmcomoning stiffnesswelLThepositioncouldbecon亡ouedtocon- vergethedesireddisplacement,althoughthepelfbnnance wasstinｎｅｅｄｅｄｔｏｂｅimprovedThemprovementcould bederivedbyassigningSMAanoysmparaUelmorderto producelargerfbrce・Coonngdevicessuchasfmsorpiezo‐

electlicmaterialswillalsohelptoimprovethepeIfOnnance．

０５０５０５８７７６６５

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Ｗ什砧ｒｒ諦fw際fwl…｢…’

｜ｌｌｌｌｌｌｌｌｌ

Ｏ１００２００３００４００５００…ｏｍｏ２ｍ３ｍ４ｏｏ

入`＝5866Positlali1Con杜ol

SMA・Theverticalandholizontalaxisesrepresentthe elechicresistance[Q]andthetime[s］

Thedevicewastestedtocontroltheresistanceto55.00, 58.66,6232,65.98,69.64ａｎｄ73.30[QlForsmallresis- tancecommands,５５．００ａｎｄ62.32,1heresistancewaswell contronedtocollvergeveryclosetothedesiredvalueAs thereferenceresistancegotlarger,theoutputovershotand itoscinateｄｆｏｒ６Ｚ３２ｃａｓｅ・Atthelargestcase,73.30,a smalloffsetenForexistedAsitisｓｈｏｗｎｉｎＦｉｇｕｒｅｌ，the resistanceissmallwhenthetemperatureishighA1though

matedbytheradiationoftheheatmtothesurroundingair・

Thisimpneslhattheperformancewinbebetterifthetem- peratureisorderedtobehigh，ortheresistanceissmalL However,theperfOm1ancewasstiUmtheacceptablerange anditcanbeconcludedthatthestiffnesscon位ollerprovided goodperfbmlances､LeftofFig5showstimeresponsesof

theresistanceof5866case，

４．２．PositionControl

Next，thepositioncontrolperformancewasevaluated TbtallengthoftheacmａｔｏｒＬｏｗａｓ３８３[mｍ］ａｎｄα＝

３ｍ

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[Z］ZIwaiandl`Mizumoto・RobustandSimpleAdaptiveCon- rolSystems、nzreMario"αノルＭｍａＪｑｆＣｏ"ｵﾉＤＪ,５５(6):1453- 1470,1992．

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hﾋﾋｐ:／/www・ｔｏｋｉ・ｃｏｄｐ/BioMeta1/、

Aulho｢izedⅡcenseduselimⅡedto:KumamotoUnive｢ｓｌｌｙＴ｢lalUser･DownloadedonAugust6p200gatO4:49fromlEEEXplore,RestrlctiDnsapply, I-L『

鐸 》）