A Nonlinear Model Reference Adaptive Control for a Universal Motor using Backstepping Approach

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Bartholomew Atkins
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1 SI ranacton on Advanc n Spac Rarc & Eart Exploraton ASREE Vol. o. May 04 A onlnar Modl Rrnc Adaptv Control or a Unvral Motor ng actppng Approac Srar Ma* Arvnd Dand** & Aya Man*** *M. c Scolar Dpartnt o Elctrcal Engnrng Vrata jaba cnologcal Inttt Mba Maaratra IDIA. E-Mal: r6a{at}gal{dot}co **M. c Scolar Dpartnt o Elctrcal Engnrng Vrata jaba cnologcal Inttt Mba Maaratra IDIA. E-Mal: arvnddand{at}gal{dot}co ***M. c Scolar Dpartnt o Elctrcal Engnrng Vrata jaba cnologcal Inttt Mba Maaratra IDIA. E-Mal: ayaan0{at}gal{dot}co Abtract Or a to dgn a nonlnar controllr or t gvn Unvral otor. In ordr to attan g proranc pd tracng t adaptv bactppng control tcnq appld. A lnar rrnc odl dgnd to acv t pd tracng o t otor. o rglat t dynac o t otor t propod controllr dgnd to trac t lnar rrnc odl. Condrng t paratr ncrtant adaptv control tod d. ctvn o t controllr vrd ng t laton rlt. laton rlt ow tat t otor pd rpon gly robt dpt t ncrtant and load torq varaton and t otor alo cclly trac t pcd rrnc odl. Kyword Modl Rrnc Adaptv actppng Control; Spd Control; Unvral Motor UM. Abbrvaton ac Elctrootv Forc EMF; Modl Rrnc Adaptv actppng MRA; Unvral Motor UM. I. IRODUCIO HE poplarty and applcaton o t Unvral Motor UM a grown rapdly ovr t yar pccally n dotc. Ho applanc c a vac clanr xr drll aw tc. UM a vry powrl otor copard to t. It a any advantag l g tartng and rnnng torq nxpnv to anactr varabl pd tat can b rglatd tc. Dpt any advantag t a ortr pan o l copard to otr otor and rqr g antnanc [Grgor Papa 00]. Fdbac lnaraton control [Albrto Idor 995] a bn torogly tdd n t lat 0 yar by wc t orgnal nonlnar odl can b tranord nto a lnar odl trog propr coordnat tranoraton. alot all t wll-dvlopd lnar control tcnq gt b appld. t wn paratr ncrtant and nnown dtrbanc ar tan nto accont t approac ay not b applcabl bca t bad on t xact cancllaton o t nonlnarty. actppng control a nwly dvlopd tcnq to t control o ncrtan nonlnar yt partclarly to yt tat do not aty atcng condton [Krtc t al. 995]. ot ngagng pont o t to t vrtal control varabl to a t orgnal g ordr yt to b pl nog t t nal control otpt can b drvd tp by tp trog tabl yapnov ncton. A nonlnar torq controllr or an ndcton otor wa dgnd bad on adaptv bactppng approac n wc ovr paratraton ay occr [S & Sy 999]. In tat papr tr ar only two ncrtant owvr n t adaptaton law tr ar totally 5 ncrtanty paratr. t probl o ovr paratraton appnd. A pd controllr wa bad on bactppng wa dvlopd or ndcton otor bt tr wa a pobl nglarty probl [an & Cang 999]. A rrnc odl d to gv t drd trannt proranc n ordr to gt t rror odl and t a t drvaton o t control c aly. Fnally nonlnar adaptv pd controllr bad on nonlnar adaptv bactppng control tcnq drvd tp by tp. It a no nglarty and ovr paratraton [ango Zo & Yoy Wang 005]. rltd control c can trac t rrnc gnal qt wll ndr paratr ncrtant and load torq dtrbanc. papr propo a novl tratgy or provng tady proranc n a Unvral otor drv ng t odl rrnc adaptv bactppng MRA control [Ha ISS: Pbld by Standard Intrnatonal ornal SI

2 SI ranacton on Advanc n Spac Rarc & Eart Exploraton ASREE Vol. o. May 04 n 009]. Snc t MRA tod a t robtn proprt o t atcd ncrtant and dtrbanc t drv wt MRA controllr acv t qcly and tady dynac proranc. laton rlt ow tat t propod tod a a c bttr pd tracng proranc accratly wl png a good dynac proranc. Matcd ncrtant and dtrbanc t drv wt MRA controllr acv t qcly and tady dynac. II. MODE OF UIVERSA MOOR drntal qaton o t nvral otor av bn drvd ro t qvalnt odl. nvral otor bacally a r wond acn wt ld wndng connctd n r wt t rotor wndng [Panaj Sa 0]. yt qaton can b wrttn a ollow d v t R Ra t a t dt Wr t t t t lctrocancal part o t odlng. R a t aratr rtanc R t ld rtanc. a and ar t aratr and ld ndctanc rpctvly. t t bac and t bac contant. cancal part o t odlng xpland blow. d dt Wr t 4 t lctroagntc torq prodcd by t otor t load torq t rcton cocnt and t otor nrta. III. MODE REFERECE ADAPIVE ACKSEPPIG CORO In t tradtonal crrnt control c o Unvral otor t voltag qaton o t Unvral otor rwrttn by R R E 5 Wr and a a ar t control voltag and aratr crrnt rpctvly. lctroagntc torq or two pa cobnd can b xprd a 6 Wr = t wc t ont cocnt o t otor and ang R a =R =R and a = =. Condrng t qaton 4-6 t atatcal odl o t otor can b wrttn a R E 7 w Wl dvlopng t adaptaton law t ad tat tator rtanc t rcton cocnt and t load torq ar t nnown bt contant paratr n control yt t ollowng varabl ar dnd R R R 8 Wr t nonal val o t tator rtanc t rcton cocnt and t load torq ar R and and ΔR Δ and Δ ar t rror btwn t ral val and t nonal val o t tator rtanc t rcton cocnt and t load torq. Condrng t ncrtant n 8 t yt can b dcrbd a x x x g x 9 Wr R x x * R x g x 0 yt controllr objctv dnd a x 0 x Wr t notaton d or Drvatv o a tat ncton x: R n R along t drcton o a ld x [Haan K Kall 00]. n x = x x x And larly x x. Fro 9-0 t ollowng dynac can b obtand or t yt own n 7 x ωθ θ x g x x ncrtan paratr ar ad to b R Fro 7- t tat pac odl o t otor gvn a x ωθ θ 4 x Wr x g ISS: Pbld by Standard Intrnatonal ornal SI

3 SI ranacton on Advanc n Spac Rarc & Eart Exploraton ASREE Vol. o. May 04 ISS: Pbld by Standard Intrnatonal ornal SI 4 abov yt a nonlnar yt to agn t drd otpt rpon o t yt 4 a lnar rrnc odl dgnd a 5 Wr and ar t rrnc tat and ar t drd gan ω* t rrnc pd coand. Frtror t tracng rror btwn t dynac yt 4 and t rrnc odl 5 a 6 Accordng to 4-6 t tat qaton n tr o rror varabl ar gvn by x 7 Wr W now tat paratr ncrtant xt n t yt condrng t n t dgnd controllr w dn 8 Wr and ar t taton o and and ar t taton rror. n dn t nw rror varabl a 9 Wr α a tablng ncton or. at cantably convrg to α wc can b condrd a t control or t rt qaton o 7. tablng control ncton dnd a 0 Wr a potv contant. ang t drvatv o 9 wt rpct to t and tn btttng 7 and 0 nto t drvatv t nw rror dynac gvn by x o dgn t bactppng control yt t paratr ncrtant ar ad to b bondd and dn t ollowng yapnov ncton V Wr and ar adaptaton gan. Ung 0 and t drvatv o t yapnov ncton can b drvd a V V o nr t global ayptotcal tablty w t atd t ollowng nqalty 0 V 4 Accordng to and 4 a bactppng control can b dgnd a blow 5 Paratr adaptaton law or and ar dgnd a 6 IV. SIMUAIO RESUS o nvtgat t ctvn o t propod adaptv bactppng control yt or t otor a laton odl plntd n Matlab. yt drv tartd at no load and ncrad to 5 at t=. pd rrnc cangd ro 0 to 500rad at t=0. n at t=5 t rrnc pd ncrad to 000rad. tator rtanc and vco cocnt o t otor ar gvn wt t nonal val.. R = R n and = n. In ordr to vry t robtn to t cang o t yt paratr t tator rtanc and vco cocnt ar ncrad to R = R n and = n. Condrng t dynac rpon o t rrnc odl and yt odl t paratr o t rrnc odl 5 ar con to b l = 55 and = 0 t paratr o t propod controllr 5 ar con a l = 00 and = 0 and t adaptv gan n 6 ar gvn a γ = γ = and γ = [Ha n 009].

4 SI ranacton on Advanc n Spac Rarc & Eart Exploraton ASREE Vol. o. May 04 o dontrat t dynac proranc o t nvral otor wt t propod control c w dgn a ln odl n atlab wt t lp o t qaton prntd abov. g -6 ow t laton rlt o t gvn otor. Intally w apply drd tp npt avng a agntd o 500 nt wc t pd coand. Atr 5 w add anotr tp npt avng t a agntd. rrnc odl dgnd n t prvo cton vntally ttl at t qlbr pont.. ω * pd coand wc an tat t rrnc gnal convrg at t npt coand. Hnc t gr cont o t rpon o t rrnc odl and t actal pd rpon o t otor. a o t otor to trac t gvn rrnc gnal. W and concld tat t proranc o t controllr arly good a t cclly tracng t coand. Fgr : Motor Spd v Fgr ow t pd rror.. gr ow t rror n pd o t otor.. drnc btwn t actal pd and t rrnc gnal. W tat t pd rror arond rp tll 5 and rp atr addng anotr tp coand. Fgr 4: Etatd Paratr v Or cond tatd paratr load torq and t paratr a convrgd to a tabl val. Evn atr dtrbanc at 5 t antan t tady val. Fgr 5: Etatd Paratr v Or trd tatd paratr rtanc R and t paratr a convrgd to a tabl val. Evn atr dtrbanc at 5 t antan t tady val. Fgr 6: Etatd Paratr v Fgr ow t trajctory o tatd paratr tatd paratr and tatd paratr R. V. COCUSIO A nonlnar pd control c or nvral otor a bn propod n t papr. An adaptv bactppng controllr dgnd to rglat t pd and acv qcly and accratly pd tracng proranc by t dnton o a lnar rrnc odl. laton rlt ow t provnt wt rgard to t robtn o paratr ncrtant and load dtrbanc n t propod c. W tat t controllr proranc a bn vry good vn tog t load torq varyng and t paratr o t yt ar nnown. Morovr t torq rppl drng t cotaton on o t ot crtcal probl to b olvd by tr actvt. REFERECES [] Albrto Idor 995 onlnar Control Syt rln Hdlbrg w Yor: Sprngr-Vrlag. [] M. Krtc I. Kanllaopolo & P. Kootovc 995 onlnar and Adaptv Control Dgn w Yor: Wly. [] H.. an &. Cang 999 Fld Orntaton and Adaptv actppng or Indcton Motor Indtry Applcaton Conrnc 4t IAC Mtng Vol. 4 Pp [4] H.. S & K.K. Sy 999 onlnar Sldng Mod orq Control wt Adaptv actppng Approac or Indcton Motor Drv IEEE ranacton on Indtral Elctronc Vol. 46 o. Pp [5] Haan K Kall 00 onlnar Syt Uppr Saddl Rvr : Prntc Hall. [6] Grgor Papa 00 Unvral Motor Ecncy Iprovnt ng Evoltonary Optaton IEEE ranacton on Indtral Elctronc Vol. 50 o.. [7] ango Zo & Yoy Wang 005 Ral- onlnar Adaptv actppng Spd Control or a PM Syncrono Motor Control Engnrng Practc Vol. Pp [8] Ha n 009 Robt onlnar Spd Control or a rl DC Motor ng Modl Rrnc Adaptv actppng Approac IEEE Intrnatonal Conrnc on Mcatronc and Atoaton Cangcn Cna. ISS: Pbld by Standard Intrnatonal ornal SI 5

May 04 [9] Panaj Sa 0 Modlng Opn and Clod oop Rpon o Unvral Motor

5 SI ranacton on Advanc n Spac Rarc & Eart Exploraton ASREE Vol. o. May 04 [9] Panaj Sa 0 Modlng Opn and Clod oop Rpon o Unvral Motor ng PID Controllr VSRD Intrnatonal ornal o Elctrcal Elctronc & Concaton Engnrng Vol. o. 5. Srar Ma. M. c Elctrcal Engnrng wt pcalaton n Control Syt ro VI Mba. Major ara o rarc Adaptv Control. Arvnd Dand. M. c Elctrcal Engnrng wt pcalaton n Control Syt ro VI Mba. Aya Man. M. c Elctrcal Engnrng wt pcalaton n Control Syt ro VI Mba. Major ara o rarc robotc. ISS: Pbld by Standard Intrnatonal ornal SI 6

Exercises for lectures 7 Steady state, tracking and disturbance rejection

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