FPGA-Based Implementation Sliding Mode Control and nonlinear Adaptive backstepping control of a Permanent Magnet Synchronous Machine Drive

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1 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou FPGA-Ba Imlmntaton Slng Mo ontol an nonlna Aatv bactng contol o a Pmannt Magnt Synchonou Machn Dv BADE BOSSOUFI, MOHAMMED KAIM, AHMED AGIOUI, aboatoy o Elctcal Engnng an Mantnanc. Hgh School o Tchnology-Ouja, Unvty o Mohamm I, Moocco. STI Tam, Faculty o Scnc Dha El Mahaz Fz, Moocco Ba_a@hotmal.com Abtact: In th a, th aatv an non-aatv nonlna Bactng contol aoach o a mannt magnt ynchonou moto v cu an analyz. W nt a Matlab&Smuln mulaton an xmntal ult om a bnchma ba on FPGA. Th gn o a contoll o a nonlna ytm wh th tat vcto mnon hgh, can otn b a cult ta, not mobl. Th Bactng tchnu ov a ytmatc mtho to a th ty o oblm. It combn th noton o yaunov uncton an a contoll ocu cuvly. Ft, th aatv an no aatv Bactng contol aoach utlz to obtan th obutn o mmatch aamt unctant. Th ovall tablty o th ytm hown ung yaunov tchnu. Th mulaton ult claly how that th oo chm can tac th nc. Sconly, om xmntal ult a montat to valat th oo contoll. Th xmntal ult ca om a ototyng latom a gvn to llutat th cncy an th bnt o th oo aoach an th vaou tag o mlmntaton o th tuctu n FPGA. Kywo: Not Aatv Bactng contol; Bactng Dgn Tchnu; FPGA; Pmannt Magnt Synchonou Machn PMSM; yaunov Stablty; obut Aatv ontol; Sytm Gnato; uablty.. Intoucton Th-ha Pmannt Magnt Synchonou Moto PMSM tongly u n nuty an conum mo than 70% o nutal lctcty. Th why conabl ot an nt ach a bng on to mov th omanc an th cncy. Th cncy o lctcal machn v gatly uc at lght loa, wh th lux magntu nc hl on t ntal valu. Th lo mnmzaton alz ung hgh-ualty matal an xcllnt gn ocu n th manuactung oc. Moov, xt contol algothm a mloy n o to mov machn omanc. In th a w a ntt n two mo contol o PMSM v, th not aatv bactng an nct lng mo contol ISMO. Th not aatv bactng aoach o a choc o gn tool o accommoaton o unctant nonlnat. An can avo watul cancllaton. Howv, th not aatv bactng aoach caabl o ng almot all th obutn ot o th mmatch unctant. Th not aatv bactng a goou an ocu gn mthoology o nonlna bac contol. Th ncal a o th aoach to cuvly gn contoll o machn tou contant unctanty ubytm n th tuctu an t bac th bac gnal towa th contol nut. Th aoach nt om th aoach o th convntonal bac lnazaton n that t can avo cancllaton o uul nonlnat n uung th objctv o tablzaton an tacng. A nonlna bactng contol gn chm vlo o th tacng contol o PMSM that ha xact mol nowlg. Th aymtotc tablty o th ultng clo loo ytm guaant accong to yaunov tablty thom. Th vaaton o th PMSM wly u n hgh-omanc alcaton. Th PMSM ha vy lag ow nty, hgh ow acto an hgh cncy. In a hgh-omanc contol o PMSM, th nomaton o oto oton an vy motant. In th contol loo, o th l ont contol, th coonat tanomaton ha n c oto oton. oto oton an can b mau by a hat nco o oth ty o no, n oth ca th mau wth an Enco olv connct to th PMSM machn v. Howv, th nc o uch no not acctabl o cot, mantnanc an lablty aon. Th conct o nol contol E-ISSN: olum 9, 04

2 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou wa oo n th 970 an ha bn contnually vlo o PMSM oto oton an tmaton. Th bac ncl o nol contol to uc th oto an oton ung vaou nomaton an man, nclung ct calculaton, aamt ntcaton, conton tmaton, nct maung an o on. Th tato cunt an voltag a gnally u to calculat th nomaton o an oto oton. Th FPGA tchnology now u by an ncang numb o gn n vaou l o alcaton uch a gnal ocng, tlcommuncaton, vo, mb contol ytm, an lctcal contol ytm. Th lat oman,.. th tu o contol o lctcal machn, wll b nt n th a []. In, th comonnt hav alay bn u wth ucc n many nt alcaton uch a Pul Wth Moulaton PWM, contol o nucton machn v an multmachn ytm contol. Th bcau th FPGA-ba mlmntaton o contoll can cntly anw cunt an utu challng o th l. onng th comlxty o th vty o th lctc contol vc o th machn, t cult to n wth unval mann a gnal tuctu o uch ytm. onng th comlxty o th vty o th lctc contol vc o th machn, t cult to n wth unval mann a gnal tuctu o uch ytm. Howv, by havng a lxon coma to th lmnt mot commonly ncount n th ytm, t obl to n a gnal tuctu o an lctc contol vc o machn whch how n Fg.: alzaton cally am o utu hgh omanc alcaton. In th aoach, not only th achtctu coonng to th contol algothm tu, but alo achtctu an th AD ntac, Enco ntac an S UAT achtctu [].. PMSM mol ytm In th a, w aly th nt algothm contol on a machn ty PMSM Pmannt Magnt Synchonou Moto [], whch cont o th tato wnng an a oto magnt. Th moto cb by th ollowng uaton oltag, Flux, Tou,. ω. t. ω. t.... t ω. Wh th otaton', th Numb o a o ol, th momnt o nta, th ocnt o vcou cton, th tv tou, th lux ouc by th mannt magnt, an th - ax tato nuctanc, an th - ax tato voltag, th tato wnng tanc an th lctomagntc tou.. Nonlna not aatv Bactng aoach Th chmatc agam o th contol ytm tuy wth alcaton o th nonlna Bactng contoll hown n Fg.. Th aamt o th ynchonou machn a gvn n th Anx. In th cton, w mloy th nonlna Bactng chm to gn th contoll o PMSM ytm wth angula vlocty maumnt. Fg.: Achtctu o th ontol Th a nt th alzaton o a latom o not aatv an aatv Bactng contol o PMSM ung FPGA ba contoll. Th E-ISSN: olum 9, 04

3 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou Fg.: Sytm conguaton o not-aatv Bactng ontol Th Not Aatv Bactng aoach algothm contol tchnu that can lnazng a nonlna ytm uch a th PMSM machn v n th nc o unctant. Unl oth bac lnazaton tchnu, aatv Bactng ha th lxblty o ng uul non lnaty ntact ung tablzaton. Th nc o Bactng th tablzaton o a vtual contol tat. Hnc, t gnat a coonng o vaabl whch can b tablz by caully lctng o contol nut. Th nut can b tmn om yaunov tablty analy [4]. It obvou that th ynamc mol o PMSM hghly nonlna bcau o th coulng btwn th an th tato cunt uaton. Accong to th vcto contol ncl, th ct ax cunt alway oc to b zo n o to ont all th lnag lux n th ax an achv maxmum tou am.. t. t t Th vcto [ ] [ ] T x choc a tat vcto jut by th act that cunt an a mauabl an that th contol o th ntantanou tou can b on comotabl va th cunt an/o. An tato voltag a contol vaabl u [ ] T. Th ncal objctv o th bactng contoll to gulat th o th PMSM v to t nc valu whatv xtnal tubanc. W aum that th ngn aamt a nown an nvaant... Bactng S ontoll Th t t n th tacng o: Th vatv o : t 4 W n th ollowng uaatc uncton: 5 It vatv along th oluton o 5, gvn by: 6 Ung th Bactng gn mtho, w con th - ax cunt comonnt an a ou vtual contol lmnt an cy t E-ISSN: olum 9, 04

4 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou bhavo, whch a call tablzng uncton n th bactng gn tmnology a ollow: Wth a otv contant Subttutng 7 n 6 th vatv o : Bactng unt ontoll W hav th aymtotc tablty o th ogn o th ytm. W n cunt ollowng o: wth 0 Th ynamc can b wttn: To analyz th tablty o th ytm w oo th ollowng yaunov uncton: 0 It vatv along th tajcto 8, 9 an 0 : [ ] [. ] Th xon oun abov u th ollowng contol law: Wth th choc th vatv o bcom: Smulaton an tt omanc In th cton, w how th gat movmnt o omanc PMSM machn, at t th ult o not aatv Bactng contol analyz. At, th omanc o th nct lng mo contol cu an coma to that bo.th chaacttc o th PMSM moto mulat n th xmnt a ollow: 0.4, 4, S,4 mh, S,8 mh, 0,00047 Kg,m, Fo a tajctoy 50 a/ at 0, 4.5A an 7N.m.th ollowng Fg. hown th omanc o th nut outut lnazaton contol. a b E-ISSN: olum 9, 04

5 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou c b c Fg.: a S on tajctoy, b Elctomagntc Tou, c - ax cunt wthout unctant, - ax Flux wthout unctant Follow o th tajctoy Fo tt th uth tajctoy, th nc wa ma vaabl. Th nc o th ct comonnt o cunt wa t to zo. Fo a tajctoy 00a/ at 0, 00a/ at t0., 50a/ at t0.6, th ollowng Fg.4 hown th omanc o th PMSM. a E-ISSN: olum 9, 04

6 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou Fg.: a S on tajctoy, b Eo S on, c abc Ax Stato unt, Ax Stato unt, - Ax Stato Flux, Elctomagntc Tou Dtubanc jcton tou loa Fo a tajctoy 50a/ at 0, 0a/ at t0.4 an 7 N.m at t0.4, th ollowng Fg.5 hown th omanc o th PMSM. c a b E-ISSN: olum 9, 04

7 Fg.5: a S on tajctoy, b Eo S on, c abc Ax Stato unt, Ax Stato unt, - Ax Stato Flux, Elctomagntc Tou 4. Nonlna aatv Bactng aoach ontol 4.. Pncl In th vou cton, th contol law a vlo un th aumton that th machn aamt a nown an nvaant. Th aumton not alway tu. In act, th low cat by th magnt va wth ncang tmatu an wth th l cat by th tato cunt. Stato tanc alo va wth tmatu. Alo, th chang n oatng conton mlctly loa tou an hnc th cocnt o cton an nta. Aatv Bactng von ta nto account th vaaton o th aamt. In uaton 7, w o not now xactly th valu o th loa tou, t wll b lac by t tmat Ĉ Fom an 5, w uc th ynamc o th o a ollow: t.. 6 Wth th o o th tmat loa tou. Th Dynamc o an ct cunt uaatc wt: t t 7 t t t. 8 To analyz th tablty o th ytm w oo th ollowng yaunov uncton: 9 It vatv along th tajcto 6, 7 an 8 : ]. [ 0 Th xon 6 oun abov u th ollowng contol law: Tho th ynamc o th yaunov uncton can b ml a ollow: WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou E-ISSN: olum 9, 04

8 Hnc th aataton law a ollow: 4 5 Wth th choc, th xon 9 bcom: 0 6 So th ytm globally aymtotcally tabl n th nc o aamtc unctant. 4.. Smulaton an tt omanc Fg.6: Sytm conguaton o aatv Bactng ontol Th ollowng ult a obtan by choong th ollowng valu: Gan o th contol law: 5 0., 0.0, Aataton gan: 5 0., 0 0., Follow o th tajctoy a WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou E-ISSN: olum 9, 04

9 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou b a c b Fg.7: Tt omanc o th aatv contoll o tajctoy tacng a S on tajctoy b Eo S on c - ax cunt wthout unctant abc ax cunt Dtubanc jcton c Fg.8: Tt omanc o th aatv contoll o jctng tubanc tou loa al at t 0.. a S on tajctoy b - ax cunt wthout unctant c Elctomagntc Tou E-ISSN: olum 9, 04

10 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou Paamtc unctant a Fg.9: Tt omanc o th aatv contoll ollowng a chang n a S on tajctoy b - ax cunt wthout unctant c Elctomagntc Tou cunt a b a c b Fg.0: Tt omanc o th aatv contoll ollowng a chang n a S on tajctoy b - ax cunt wthout unctant E-ISSN: olum 9, 04

WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou a b Fg.: Tt omanc o th aatv contoll ollowng a chang n an S on tajctoy b - ax cunt wthout unctant 5.

11 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou a b Fg.: Tt omanc o th aatv contoll ollowng a chang n an S on tajctoy b - ax cunt wthout unctant 5. FPGA-Ba Imlmntaton o an obut Bactng contol ytm 5.. Dvlomnt o th Imlmntaton Th a val manuactu o FPGA comonnt uch: Actl, Xlnx an Alta tc. Th manuactu u nt tchnolog o th mlmntaton o FPGA. Th tchnolog a attactv bcau thy ov conguabl tuctu that th mot nttng bcau thy allow gat lxblty n gn. Nowaay, FPGA o th oblty to u cat bloc uch a AM, multl w ntac PI an PU co. Th achtctu gnng wa on ung wth AD tool. Th cton ma gahcally o va a hawa cton languag hgh lvl, alo call HD Hawa Dcton anguag. I commonly u languag HD an log. Th two languag a tanaz an ov th cton wth nt lvl, an cally th avantag o bng otabl an comatbl wth all FPGA tchnolog vouly ntouc [7]. In th a an FPGA XS500E SatanE om Xlnx u. Th FPGA contan 400,000 logc gat an nclu an ntnal ocllato whch u a 50MHz uncy cloc. Th ma como om a matx o 576 lc ln togth by ogammabl conncton. Th mulaton ocu bgn by vyng th unctonalty o th contol algothm by talng a unctonal mol ung Smuln Sytm Gnato o Xlnx bloc. Fo th alcaton, th unctonal mol cont n a Smuln tm ct mol o th No aatv Bactng algothm aocat wth a voltag nvt an PMSM mol. Th Fg. ummaz th nt t o ogammng an FPGA. Th ynthz gnat wth AD tool t on Ntlt whch cb th connctvty o th achtctu. Thn th lacmnt-outng otmally lac comonnt an om all th outng btwn nt logc. Th two t a u to gnat a conguaton l to b ownloa nto th mmoy o th FPGA. Th l call bttam. It can b ctly loa nto FPGA om a hot comut. Fg.: Pogammng FPGA v In th wo an FPGA XS500E SatanE om Xlnx u. Th FPGA contan 400,000 logc gat an nclu an ntnal ocllato whch u a 50MHz uncy cloc. Th ma como om a matx o 576 lc ln togth by ogammabl conncton. E-ISSN: olum 9, 04

12 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou 5.. Smulaton Pocu Th mulaton ocu bgn by vyng th unctonalty o th contol algothm by talng a unctonal mol ung Smuln Sytm Gnato o Xlnx bloc. Fo th alcaton, th unctonal mol cont n a Smuln tm ct mol o th No aatv Bactng algothm aocat wth a voltag nvt an PMSM mol. Th Fg. how n tal th ogammng o th contol hown n Fg. n th SYSTEM GENEATO nvonmnt om Xlnx, w wll mlmnt t lat n th mmoy o th FPGA o th mulaton o PMSM. Fg.: Functonal Mol o No aatv Bactng ontoll om SYSTEM GENEATO Th unctonal mol o no aatv Bactng ontoll om SYSTEM GENEATO como th nt bloc: - Th bloc nco ntac I allow th aataton btwn th FPGA an th acuton boa to nuty th oto oton o th PMSM, - Th AD ntac allow th conncton btwn th FPGA an th analog-gtal convt ADS7476MSPS -bt A / D that wll b boun by th ollowng two Hall Ect tanuc o th acuton o th tato cunt machn, - Th bloc o coonat tanomaton: th tanomaton o Pa Inv abc-to-, - Th bloc o coonat tanomaton: th tanomaton o Pa -to-abc, - Th SW bloc th mot motant, bcau can ov contol ul to th IGBT voltag nvt n th ow cton om wll-gulat voltag, - Th bloc o th contoll no aatv Bactng whch gn to gulat th an tato cunt o th PMSM, - Bloc "Tmng" whch contol th bgnnng an th n o ach bloc, whch allow th h n th voltag nc 0, 0 an 0 at th bgnnng o ach amlng o, - Th S bloc allow gnal tmng an covy o gnal vw, cat by anoth ogam on Matlab & Smuln to vualz th outut gnal. E-ISSN: olum 9, 04

WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou Th con t o th mulaton th tmnaton o th utabl amlng

Fo xaml, w nt th contucton o Bloc la' Tanomaton n th ytm gnato nvonmnt om Xlnx, whch chaactz by th ollowng ytm 8: 0

Exmntal ult Th mlmntaton o th nct contol by lng mo on FPGA vc chaactz by a uc oaton tm. Th Fg.

All ult w xtact om th FPGA by th hsco tool o Xlnx. Fg.4: Pa Tanomaton Mol.

13 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou Th con t o th mulaton th tmnaton o th utabl amlng o an x ont omat. Th Fg.4 gv th ccaton mol o th abc-to- a tanomaton. Fo xaml, w nt th contucton o Bloc la' Tanomaton n th ytm gnato nvonmnt om Xlnx, whch chaactz by th ollowng ytm 8: 0 π 4π oθ o θ o θ 6 a 4π 4π Snθ Sn θ Sn θ b c PMSM OAD Fg.5: Pototyng latom contol 6. Exmntal ult Th mlmntaton o th nct contol by lng mo on FPGA vc chaactz by a uc oaton tm. Th Fg.6 hown th xmntal ult o Inct Slng Mo PMSM wth th FPGA latom a hown. Uat uncy o th mlmntaton 0 Hz. All ult w xtact om th FPGA by th hsco tool o Xlnx. Fg.4: Pa Tanomaton Mol. Th ccaton mol thn u o th nton o th coonng Data Flow Gah. Th Fg.4 how th DFG coonng to th Pa tanomaton moul. 5.. Pototyng latom To tt th FPGA ba contoll, a ototyng latom o th contol o a Pmannt magnt Synchonou Machn wa ambl Fg.5. FPGA Invt IGBT a b E-ISSN: olum 9, 04

14 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou c Fg.6: a Stato cunt locu o ISM, b abcax cunt n th PMSM, c -ax an -ax cunt n th PMSM In Fg.7.a th xmntal ult No Aatv Bactng ontol o PMSM wth th FPGA latom a how th voluton o th tato cunt whch how that th outut ollow th nc an. Th Fg.7.b how th tato cunt a an b. Uat uncy o th mlmntaton 0 Hz. a b Fg.6: a S omanc oto o PMSM, b Eo S omanc Th Exmntal ult how th omanc o PMSM machn, ung two aoach contol nonlna. Th two contol algothm how th obutn an cacté o th ytm. 7. oncluon In th a a obut contnuou aoach Nonlna not Aatv Bactng ontol an Aatv Bactng ontol tatgy o mannt-magnt ynchonou moto PMSM v ytm nt. Th FPGA ba mlmntaton tal, a bnch tt wa alz by a ototyng latom, th xmntal ult obtan how th ctvn an th bnt o ou contbuton an th nt t o mlmntaton o th contol FPGA. Acnowlgmnt W than all tho who contbut to ma th wo, nclung my tach n my hom laboatoy STI Tam an th nt o Molng an mulaton o th ytm, my w an all my n o th uot. Th wo wa om n th Monto Inttut, Unvty o g UG n Blgum. nc [] Mlco, ; Mn, MF; atalao, PS Molng, ontol an Smulaton o Full- Pow onvt Wn Tubn Eu wth Pmannt Magnt SynchonouGnato vol 5, g Ma - A 00. [].. hn an K. P. hn, "Automatc luxwanng contol o mannt magnt ynchonou moto ung a uc-o contoll," IEEE Tan. Pow Elcton., vol. 5, , St [] M. oc, K. zn, S Snol Slng Mo Tou ontol o Inucton Moto, IEEE Tan on. Inutal Elctonc, Fbuay 00. [4] Hn-ang Shh an Kuo-Ka Shyu, Non na Slng Mo Tou ontol Wth Aatv Bactng Aoach Fo Inucton Moto Dv, IEEE Tanacton on Inutal Elctonc, ol. 46, N, Al 999, [5] D. Zhang an H., A tochatc-ba FPGA contoll o an nucton moto v wth ntgat nual ntwo algothm, IEEE Tan. In. Elcton., vol. 55, no., , Fb E-ISSN: olum 9, 04

15 WSEAS TANSATIONS on SYSTEMS an ONTO Ba Boou, Mohamm Kam, Ahm agou [6]. F. ung an. S. hn, Wat bath tmatu contol by a cunt uzzy contoll an t FPGA mlmntaton, IEEE Tan. In. Elcton., vol. 5, no., , un [7] E. MONMASSON, an M. ta FPGA Dgn Mthoology o Inutal ontol Sytm A vw, IEEE Tan In. Elcton.., vol.54, no. 4,.84-84, Augut [8] B.BOSSOUFI, M.KAIM, S.IONITA, A.AGIOUI, ow-s Snol ontol o PMSM Moto v Ung a NONINEA Aoach Bactng ontol: FPGA-Ba Imlmntaton ounal o Thotcal an Al Inomaton Tchnology ATIT, 54-66, ol. 6 No., 9th Fbuay 0. [9] B.BOSSOUFI, M.KAIM, S.IONITA, A.AGIOUI, Nonlna Non Aatv Bactng wth Slng-Mo Tou ontol Aoach o PMSM Moto ounal o ounal o Elctcal Sytm ES, ol.8 No., un 0. [0] B.BOSSOUFI, M.KAIM, S.IONITA, A.AGIOUI, Inct Slng Mo ontol o a Pmannt Magnt Synchonou Machn: FPGA-Ba Imlmntaton wth Matlab & Smuln Smulaton ounal o Thotcal an Al Inomaton Tchnology ATIT, -4, ol. 9 No., 5 th uly 0. [] A. AGIOUI, H. MAHMOUDI, B.BOSSOUFI, Dct na Pctv ontol O Pmannt Magnt Synchonou Moto PMSM ounal o Thotcal an Al Inomaton Tchnology ATIT, - 8, ol. No., 5th Stmb 0. [] T.., K. T. Song,. H., an.. Tng, Tacng contol o uncycl-mol mobl obot ung a atuaton bac contoll, IEEE Tan. ontol Syt. Tchnol., vol. 9, no.,. 05 8, Ma. 00. [] T. H., S.. hang, an Y. X. hn, Imlmntaton o humanl vng ll by autonomou uzzy bhavo contol on an FPGA ba ca-l mobl obot, IEEE Tan. In. Elcton., vol. 50, no. 5, , Oct. 00. [4] S. S. Solano, A.. aba, I. Batuon, F.. Mono-lo, an M. Box, FPGA mlmntaton o mb uzzy contoll o obotc alcaton, IEEE Tan. In. Elcton., vol. 54, no. 4, , Aug [5] Z. P. ang an H. Njmj, Tacng contol o mobl obot: A ca tuy n bactng, Automatca, vol., no. 7,. 9 99, ul E-ISSN: olum 9, 04

Applications of Lagrange Equations

Applications of Lagrange Equations Applcaton of agang Euaton Ca Stuy : Elctc Ccut ng th agang uaton of oton, vlop th athatcal ol fo th ccut hown n Fgu.Sulat th ult by SIMI. Th ccuty paat a: 0.0 H, 0.00 H, 0.00 H, C 0.0 F, C 0. F, 0 Ω, Ω