Practical Pinch Torque Detection Algorithm for Anti-Pinch Window Control System Application

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1 un -5, IEX, Gyonggi-Do, ora Praial Pinh orqu Dion Algorih for Ani-Pinh Windo Conrol Sys Aliaion Hy-in L*, Won-Sang Ra**, a-sung oon*** and in-a Park * * Darn of Elrial and Elronis Enginring, onsi Unirsiy, Soul, ora (l : ; E-ail: aslhj@onrol.yonsi.a.kr) **Guidan and Conrol Darn, Agny for Dfns Dlon, ajon, ora (l : ; E-ail: onsang@ail.o) ***Darn of Elrial Enginring, Changon aional Unirsiy, Changon, ora (l: ; E-ail: syoon@hangon.a.kr) Absra: A raial inh orqu siaor basd on h alan filr is roosd for lo-os ani-inh indo onrol syss. o obain h aura angular loiy fro Hall-ff snsor asurns, h angular loiy alulaion algorih is xud ih addiional rodurs for roing h asurn noiss. Aar fro h rious orks using h angular loiy sias and orqu sias for ding h inhd ondiion, h orqu ra is augnd o h sys odl and h roosd inh siaor is drid by alying h sady-sa alan filr rursion o h odl. h oiaion of his aroah os fro h ida ha h bias rrors in orqu sias du o h oor arar unrainis an b alos liinad by inroduing h orqu ra sa. For ding h inhd ondiion, a sysai ay o drin h hrshold ll of h orqu ra sias is also suggsd ia h drinisi siaion rror analysis. Siulaion rsuls ar gin o rify h inh dion rforan of h roosd algorih and is robusnss agains h oor arar unrainis. yords: orqu Esiaion, Pinh Dion, Ani-Pinh Windo Conrol Sys, alan Filr. IRODUCIO An ani-inh indo onrol sys assoiad ih a oor hil is inndd for rning injuris hn an obsal is arlssly inhd bn h losing indo and h sash of a oor hil. Ding a inhd obsal, h indo is onrolld o h rdrind osiion. hrfor, h sys rforan dnds on h rliabiliy of h inh dision algorih. h blok diagra of h ani-inh indo onrol sys is did in h Fig.. h sys undr onsidraion has a DC oor for indo lif hanis and on Hall-ff snsor ound a h nd of h oor shaf. h angular loiy of h oor shaf is alulad using h uls rain asurd by h Hall-snsor and fd bak ino h onrollr []. h onnional hods o d h inhd ondiion ar gnrally lassifid ino o agoris: h diffrnial y inh siaor is basd on h assuions ha h indo os ih onsan loiy undr h unobsrud oraing ondiion and h abru dro of loiy is ourrd in h inhd ondiion []. Hor, his algorih ould b inadqua in ral siuaions baus h friional orqu of indo fra has h norally arying hararisis hrough h full rang of hil losur anl [3]. his inh siaor rquirs sall aoun of ouaion bu is rforan ould b dgradd in h rsn of asurn noiss []. On h ohr hand, h absolu y inh siaor aks adanag of h fas rsons i by using h hangs of oor onrol urrn o onsa h V θ + Fig.. lok diagra of ani-inh indo onrol sys inh orqu as ll as h angular loiy [4-5]. I rognizs h inhd ondiion hn h urrn xds a rsribd hrshold. Hor, i anno guaran h robusnss agains h abnoral ibraions undr h ral driing ondiions. Moror, his hod rquirs an addiional urrn snsor o aoid fals alar [-5], and ould no b a gnral soluion baus h dion of inh ondiion oally dnds on h urrn lii drind by nginr s hurisi [-3]. In his ar, h lo-os ani-inh indo onrol sys, hih roids only h oor angular loiy asurns fro Hall-snsor, is undr onsidraion. Firs, o iro h qualiy of asurns, a n angular loiy alulaion algorih is roosd. h iulsi nois rjion algorih is dlod o ak u h ak oins in h onnional loiy alulaion hod. hn, using h angular loiy asurn, a n inh dion algorih basd on h sady-sa alan filr is roosd o oro h liiaions of h onnional inh orqu

2 siaors. h ibraion orqu aording o road ondiions, h ibraions of rfrn olag and h asurn noiss ar rgardd as disurbans and odld by hi noiss. Esially, o rfl h i-arying naur of h friional orqu hih is roorional o indo rals, an augnd oor odl ih h orqu ra sa is suggsd. Sin h orqu ra sia is lss snsii o h oor arar unrainis, h inh dion algorih using h orqu ra an aooda h high fidliy. In addiion, by analyzing h influn of h oor arar unrainis on h siaion rrors, a sysai ay o drin h hrshold ll of orqu ra a inhd ondiion is inrodud. Siulaion rsuls sho h inh dion rforan and robusnss of h roosd hod. un -5, IEX, Gyonggi-Do, ora Fig.. Hall-ff snsor asurns. AGULAR VELOCI CALCULAIO ALGORIHM FROM HALL-SESOR OUPUS h angular loiy of h DC oor an b alulad fro ouu of Hall-snsor, hih rodus h uls rain ih so noiss. h ouu of Hall-snsor is did in Fig.. On uls ans ha on of h agns insalld a h oor shaf ih onsan dislan is assd. In ordr o obain h angular loiy auraly, h loiy alulaion algorih is abl o surss so noiss if ossibl. h nir flo har of h angular loiy alulaion algorih is suarizd in Fig. 3. h daild dsriion of ah s is gin blo; h ouu olag of Hall-snsor and h aquisiion i a h asurd insan ar obaind and all arars ar iniializd. aus h angular loiy o b oud is an inu of inh orqu siaor, i is yildd a ry saling i of h siaor. Wihin h riod of siaor, h urrn angular loiy is alulad by using h auulad nubr of dgs during h filr saling riod as = π dg is a urrn angular loiy and () is h i inral bn h firs and final dgs. and ar h nubr of agns a h oor shaf and dgs of Hall-snsor ouu, rsily. h dg nubr an b obaind by ouning h rossing rfrn ouu olag of Hall-snsor,. V rf ( Vk Vrf ) ( Vk Vrf ) dg dg < 0 () A his oin, h rliabiliy of dg ouning is insigad. If only h urrn i inral bn h os rn o dgs is or han h /3 is of h rious inral, an dg ourrn is onfird and h nubr of dg is inrasd. Gnrally, h rang of angular loiy is boundd. Hn, by onsidring h oraion rang of h oor, on should Fig. 3. Flo har of angular loiy alulaion algorih hk hhr or no h insananous loiy and is ariaion saisfy h oraion rangs. ax &. (3) is h diffrn bn h rious and urrn loiy. ax, ax ar h rdrind axiu lii of loiy diffrn and axiu lii of loiy, rsily. If h alulad angular loiy is byond h noinal rang, i is disardd and h ouu loiy is ainaind as h rious alu. h aragd angular loiy is obaind using h 3-oin oing arag filr [6]. And hn, o liina h iulsi noiss, h 7-oin dian filr is alid. h rsul assd hrough h o filrs bos h final ouu of h angular loiy alulaion algorih. 3. ALMA FILER ASED PICH ORQUE ESIMAIO 3. Sa-sa odl for inh orqu siaor As shon in h Fig. 4, h DC oor sys o dri indo an b linarizd by ngling h nonlinar hararisis suh as baklash, sl-ra, oulob friion, ax

3 un -5, IEX, Gyonggi-Do, ora V + Ls + R I + d s+ s θ Fig. 4. Linarizd oor odl. h nonlaur lis of h linarizd oor odl is gin blo: θ V I L d R angular loiy (sd) angular osiion driing olag (onrolld olag) araur urrn roaional orqu disurban orqu araur induan araur rsisan on inria isous friion offiin bak looi for (f) offiin orqu offiin h ransfr funion fro h roaional orqu of DC oor o h angular loiy in Fig. 4 is gin by () s () = s s+ h roaional orqu is lassifid ino h onrol orqu, h ibraion orqu orqu (4) du o h road ondiion, h inh by h obsal and h load orqu indo igh. by h = d = (5) Sin h ibraion orqu aris along h road ondiion, h loiy ariaion du o h ibraion orqu is assud as zro an hi nois squn ihou loss of gnraliy. Fro (4) and (5), h oor sd an b rrin as = + ( + ) + u (6) h arian of is dfind by. u Using h fa ha h lrial dynais of h oor is gnrally fasr han h hanial on, h oor onrol orqu an b aroxiad as follo: Subsiuing (7) for (6) yilds u q Fig. 5. Pinh orqu and indo load orqu aars abruly a h inhd on and h inh orqu rofil an b hangd by h y of inhd obsals. h yial indo load and inh orqu ar shon in Fig. 5. Unforunaly, sin h agniud of h inh orqu is sallr han h indo load orqu a h nd of indo arur, i is ry diffiul o harariz h naur of h xognous orqu using h angular loiy asurn only. hrfor, i is or ffi o odl hs orqus as a singl sa ariabl for h inh siaor dsign. = + (9) h xognous orqu (9) hih is losly rlad o h inhd ondiion is onsidrd as a drinisi inu o b siad. As shon in Fig. 5, boh of xognous orqus and, ould b aroxiad as ra funions ih ror slos. In his as, on of sils ays o d h inh ondiion is o onior h slo of xognous orqu. Sin h oor arari unrainy auss h bias rror in h filrd orqu sia [4], h rious rsuls using h orqu sia only is no suiabl o h raial aliaions. o sol h robl, h orqu ra is augnd as an addiional sa and odld as h rando alk. = u d (0) is zro an hi nois ih h arian. u d o, fro (8), (9) and (0), on an ha h sa-sa odl for h dsign of inh siaor. x = Fx + GV + Gu () y = Hx+ ( V ) (7) R x =, u = u ud ( ) = u + V R R (8) + 0 R R 0 F = 0 0, G = 0, G = 0 0 h agniud of indo load orqu is roorional o 0 0 h indo osiion. On h onrary, h inh orqu and q d

4 h oarian aris of h ross and asurn noiss u and ar gin by q 0 o u, u = Q =, o, R = 0 qd 3. Pinh siaor using h alan filr Alying h sa ransiion quaion o h oninuous sys odl (), on gs h disr-i sa-sa quaion of h for. xk+ =Φ xk +Γ V + u k y = Hx + k k k () h aris ar dfind by using h saling i of h filr s. In h roding filr odl (), h fluuaion of driing olag is ngld and h olag inu is assud as onsan ihou loss of gnraliy. hn h inh siaor an b dsignd by alying h disr alan filr rursion o h sys quaion (). ( ) xk =Φ xk +Γ V + f, k yk HΦxk = PH R, R = HPH + R (3) f, k k k k, k, k P =ΦPΦ ΦPH R HPΦ + Q k+ k k, k k f, k is h alan filr gain and P k is a riori siaion rror oarian arix. aking ino aoun h ral-i ilnaion issu, h sady-sa alan filr gain is usd. PH HPH R f = ( + ) h rror oarian arix d (4) a sady-sa holds h folloing disr-i algbrai Riai quaion. 0 =Φ Φ Φ ( + ) Φ+Γ Γ P P P H HP H R HP Q 4. DECISIO OF PICH CODIIO 4. Sady-sa siaion rror analysis In his sion, h siaion rror du o h arar unrainis in h oor odl is analyzd. h rsuls gi us n insigh ino h alidiy of h orqu ra sias for inh dion. h unrainis of oor arars ar abl o gnra h biasd orqu sias. o failia h rror analysis, h nois sours ar ngld and h sady-sa alan filr for h oninuous i oor sys () is onsidrd. x = ( F H) x+ + GV (5) P f f 0 R R F = 0 0, G = 0, f = In h abo quaion, X ans h unrain arix un -5, IEX, Gyonggi-Do, ora orrsonding o h noinal arix X. Fro (8) and (5), h siaion rror sys an b obaind as h augnd sa quaions, z = Az+ u = = Cz R A = 0, R R 0 V 0 = 0, z =, u, C R = = (6) h driing olag is assud as s inu. h indo load orqu and inh orqu ar rgardd as h ra inus for alulaing h orqu ra siaion rror, sin h s inus rsul in h zro sady-sa siaion rror. On h ohr hand, hy ar onsidrd as h s inus o obain h sady-sa orqu siaion rror baus h ra inus ak h rror dirg. hn, aording o h final alu hor, h sady-sa siaion rrors an b radily drid. R( + R) r r ( ) ( ) = a + R( + R) a (7) R( + R) ( ) = + R( + R) s s ( a a ) ( + R) + R R( + R) is h agniud of oor driing olag, and is h inhd on. inus and r a, a r (8) ar h slos of h ra s s a, a ar h agniud of h s inus for h indo and inh orqu, rsily. 4. Dision of h hrshold ll Fro (7) and (8), i is obious ha arari unrainis dirly aff o h orqu and orqu ra sias. Hor, i auss largr bias rrors o h orqu sias han h orqu ra sias as shon in Fig. 9. hus, i is br hoi o us h orqu ra sia in h inh dion algorih. o, h raining robl in h dlon of inh dion algorih is o sablish h sysai annr for drining h rsribd hrshold ll of h orqu ra sias. for h filr onrgs,

5 < s, h iniial hrshold ll is drind as h axiu slo of dabl disurban orqu sifid in h indusrial sandards. Afr h filr onrgs, >, h hrshold ll is rdfind fro h rsul of sady-sa siaion rror analysis using h urrn orqu ra sia. In gnral, h DC oor anufaurr ainains h arar ariaions ihin ±0% of h noinal alus. Fro his fa, h boundary of orqu ra sia an b obaind fro (7), , 0 (9) Roughly saking, (9) ans ha h rasonabl hrshold alu o d h inhd ondiion is drind as 74% of h arag slo of dabl disurban orqu. ha is, h rsulan hrshold ll is s by ( s) ( ) + in 0.74 (0) s un -5, IEX, Gyonggi-Do, ora abl. oinal alus of h oor arars oor arar araur induan araur rsisan orqu onsan bak EMF onsan isous friion of. oor inria driing olag 3 L alu 3. 0 [H] R 3.53 [ Ω] V 60 [ /A] 0.09 [V/(rad/s)].46 [kg / s] [kg ] [V] 5. SIMULAIO RESULS h rforan of h sady-sa alan filr basd inh dion algorih has bn sd by siulaion on a DC oor hih has h arars in abl. In h siulaion, i is assud ha h asurn uda i is 0.05 sond and an obsal is aard a.5 sond afr indo lifing. h xognous orqu rofils did in Fig. 5 ar also alid. Fig. 6 shos h siaion rsuls of h roosd inh siaor for a s inh orqu undr h noinal ondiion. h siad sd, orqu and orqu ra abruly hang a h inhd on. h roosd siaor rfors ry ll n in h rsn of ra y inh orqu as in h Fig. 7. In noinal ass, h onnional disurban orqu siaor using h angular osiion and loiy asurns also roids good siaion rforans siilar o h roosd sh [], [5], [8]. Fig. 8 (a) indias h siulaion rsuls for h rious orqu siaor [] using angular osiion in h noinal as. h rforan oarison bn h rious hod [] and h roosd sh is don for h unrain as. o obsr h influn for h unrain as, h unrainy in h orqu onsan is assud as 0% of is noinal alu. As shon in Fig. 8 (b) and Fig. 9 (a), h orqu sias of boh filrs onain bias rrors as xd in his as. hs rsuls rrsn ha h inh dion hod basd on h orqu sias only is no rliabl and i ay roid inorr inh alar. A his oin, i is orh noing ha h orqu ra sias of h roosd filr ar fr fro bias rror and alays xd h rdrind hrshold ll for diding h inhd ondiion in Fig. 9 (b). Consqunly, n in h unrain ass, h roosd algorih shos rlaily robus inh dion rforan. Fig. 6. Esiaion rsul for a s inh orqu Fig. 7. Esiaion rsul for a ra inh orqu Fig. 8. Esiaion rsul for h rious orqu siaor []

6 un -5, IEX, Gyonggi-Do, ora 996. [] Robr P. Grbz, Mhod of Consaing for Abru Load Changs in an Ani-Pinh Windo Conrol Sys, US Pan, US00/ A, 00. [3] X. d Fruos, Ani-Pinh Windo Dri Cirui, US Pan, US003/03765 A, 003. [4] G. S. uja, R. Mnis and M. I. Valla, Disurban orqu Esiaion in a Snsorlss DC Dri, IEEE rans. Ind. Elron., Vol. 4, o. 4, , 995. [5]. Syd-Ahad and F. M. Wlls, orqu Esiaion and Consaion for Sd Conrol of A DC Moor Using an Adai Aroah, Pro. of h 36 h MWSCAS, Vol.,. 68-7, 993. [6] V. Lyandrs and S. riskin, On So Effiin Algorih for Moing-Arag Filring, Pro. of h 35 h MWSCAS, Vol., , 99. [7] M. uhola,. aajainn and. Raia, Coarison of Algorihs for Sandard Mdian Filring, IEEE rans. Signal Pro., Vol. 39, o., , 99. [8] L. Salaor and S. Sasi, LF asd Robus Conrol of Elrial Srodris, IEE Pro.-Elr. Por Al., Vol. 4, o. 3,. 6-68, 995. Fig. 9. Esiaion rsul and rror analysis in unrain as 6. COCLUSIO In his ar, h inh orqu dion algorih basd on h alan filr has bn roosd. h angular loiy as ouu of Hall-snsor and asurn for h filr ould b auraly alulad by inoling h n hods for h nois liinaion. Moror, by onsidring h orqu ra as an addiional sa ariabl, h roosd algorih ould iro h rliabiliy for h inh dion n in h rsn of h arar unrainis. Our aroah as oiad fro h obsraion ha h rious hods using h angular loiy or orqu sia ofn roids fals inh alar. In addiion, h rsuls of siaion rror analysis r gin o dri h hrshold ll of orqu ra sias a inhd ondiion. hrfor, i an b said ha h roosd sh gis h sysai ay o sol h inh dion robl. h roosd algorih is rfrrd for ral-i ilnaion by using h sady-sa alan filr gain. Siulaion rsuls ha shon ha h roosd algorih guarans h robus inh dion rforans. hus, i ill b a raial soluion for h dsign of lo-os ani-inh indo onrol sys. REFERECES [] H. W. i and S.. Sul, A Moor Sd Esiaor Using alan Filr in Lo-Sd Rang, IEEE rans. Ind. Elron., Vol. 43, o. 4, ,