ứng dụng thụât toán gần đúng để đánh giá các thông số điều khiển trong quá trình làm việc động cơ xe ô tô

NGHIEN Cljru - TRAO DOI ufng dung thuat toan gan dung de danh gia cac thong so' dieu khien qua trinh lam viec dong ctfxe oto (*) TS LE HONG P H U O N G - (**) THS LE ANH SdN flat van de Trong gan thap ky qua, viec tff dpng dieu khien bffdc dau da va dang dffdc ap dung Hnh vffc cd gidi Mot nhffng hffdng di chinh la ffng diing phffdng phap dieu khien tdi ffu de giai quye't cac van de bffc xue cua nganh dat Do vay, viec xay dffng thuat loan de dieu khien tdi ffu cac phffdng tien cd gidi hoat dpng tren dffdng la he't sffc can thie't De cd ke't qua mong mudn qua trinh dieu khien can xay difng phffdng phap danh gia cac tri sd tin hieu dieu khien va dau cua dd'i tffdng dffdc dieu khien Dffdi day chung tdi gidi thieu mot phffdng phap ffng diing de xay dffng md hinh toan hpc va dieu khien tdi ifu dpng cd lap tren cac phffdng tien cd gidi chung hoat dpng tren dffdng theo thdi gian thifc Phi/ifng phap gan diing danh gia trj so cac thong so dieu l(hien De danh gia cac tri sd cac thdng so' dieu khien (tin hieu dau viio) cua dpng cd vdi cac ham sd tffdng thich theo mo hinh loan hpc cd quan diem: mdt la sff dung cac ham rieng biet mo ta cac gia tri de tai mdi diem lam viec bat ky thuoc trffdng che dp lam viec cua dpng cd (tffc cho td hdp bat ky cua cac thdng sd nhff md men xoan M^ va tde dp ciia dpng cd n), hai la sff dimg mot hain nha't cd tinh bao triim ca dai thdng sd Vi dii neu nhff ket qua cua cac thdng sd dau la mffc tieu hao nhien lieu hay Iffdng dpc td cd phan xa ciia ddng cd (nhff CO, CH va NOx) tai 10 diem lam viec (tffdng dffdng 10 cap gia tri cua md men xoan va tde dp ddng cd- n^) va ctia thdng sd dieu khien (bao gdm he so' dff Iffdng khdng a, Iffu Iffdng xa tuan hoan ngffdc-P^ va gdc danh Iffa sdm cua ddng cd 6; dd thdng sd dau va thff hai se dffdc tinh theo da thffc bac 4, cdn thdng sd thff ba theo da thffc bac (nghTa la gia tri khae cua mot thdng sd cac gia tri cua ta't ca cac thdng sd dieu khien cdn lai la khdng ddi), nhff vay tdng sd lan cua bat ky thdng sd dau nao tai mdi mdt thdi diem thuoc 10 diem lam viec cua cac td hdp khae deu se la 80 (4x4x5) Theo quan diem thff nhat de lam gan dung eac ket qua (xap xi CLic bp) tai mdi diem lam viec cua ddng cd can 10 ham sd cho mdi mdt td hdp gdm mot tin hieu dau Cling tin hieu dau vao bat ky a , va PW Theo quan diem thff hai (xap xi loan phan) cho bat ky mdt tin hieu dau chi can chpn mdt ham nha't cho nd bao kin het dai ciia ca tin hieu dau vao bao gdm a , 9, P^ , M, va n^, So sanh giffa each lam gan dung da neu thi xap xi toan phan td't hdn 10 xap xi ciic bd ke ca tinh thuan tien va ca kha nang dff bao phu hdp vdi cac ke't qua dau (vi du nhff mffc tieu hao nhien lieu hay Iffdng ddc to cd phan xa) tai cac diem lam viec khae dai che' dp boat ddng cd the cua ddng cd, ma khdng phai la 10 td hdp cua md men xoan va td'c dp ma chung ta dang tien hanh nghien cffu Tuy nhien cac gia tri ciia ham gan diing toan phan cd chat Iffdng tha'p hdn cac gia tri cua tap hdp cac ham cue bp ta sff dung da thffc cung bac, bdi vi ham toan phan can phai tinh hang loat nhdm sd lieu dd de cho cung cd ke't qua thi tap hdp cac ham cue bp chi can mot so cac bieu thffc tinh la du Dieu khang dinh tren cd the minh hoa bang md hinh ddn gian sau: cho ham so' Y vdi cac bien x, z ; ta't ca eac phep cac tap hdp khae cija x, y va z cd the, chia phan nhdm theo gia tri cua z ( nhdm mdt bao gdm ta't ca cac diem cd gia tri z=Z|; nhdm bao gdm ta't ca cac diem cdn lai vdi z=z, nhff md ta tren Hinh 1) Xtfp 3d cue b^ v6i c&c Xip xi t o ^ p h ^ Hinhl: Sd minh hoa xap xi cue bo va xap xi loan phan cac tri so tai cac diem lam viec qua trinh dieu khien tdi ifu dong CO dot Tren sd dd y la bien dpc lap, x la tin hieu dau vao thay ddi, cdn z la md men xoan ciia dpng cd can dieu khien De ddn gian hoa ta chi sff dung mdt tin hieu dau viio nhien sff so sanh giffa xap xi ctic bd va xap xi loan phan cd the md rdng cho so'Iffdng tin hieu dau vao y Trong dd thffa nhan cac mdi quan he cua y vdi x vii ciia y vdi z la tuyen (*) Vien Ky thuat Co gidi QS-BQP (**) Vien Ky Ihuat Co gii^i QS-BQP TAP CHi C d KHi VIET NAM • So 148 - Thang 11 nam 2009 C^ ^'^^l NGHIEN cufu- TRAO DOI tinh, vi mpi quan he phi tuyen deu cd the bien ddi tuyen tinh thdng qua phep chuyen ddi tffdng thich Cac dffdng thang A|B1 va AjB2 la eac ham xap xi cue bd dai dien cho nhdm sd lieu ( cac diem cd z=Z| va T=T.y Cac dffdng thang tren cd gdc nghieng tffdng ffng la a, va a, Khi dd ham xap xi toan phan cho ca nhdm sd lieu cd dang: (1) Y=a3X-Ha^z-i-a3, Gdc nghieng tffdng dd'i cua mat phang chffa dffdng A^B^ va A^B^ so vdi true z khae biet vdi cac gdc cua cac dffdng thang A|B| va A^B,, bdi vi nd dffdc xac dinh cho ta't ca cac phan dff chung cua ca hai nhdm sd heu dat gia tri nhd nha't Gdc nghieng se bang cac gdc cua A|B| va A^B^ a,=a2 Mat phang A^ Bj A^B^ dffdc xac dinh theo (1), eat cac mat z=Z| va z=z, theo cac dffdng Aj B, va A^B^ Dffdng thang A^ B^ cho chung ta ke't qua gan dung kem hdn cac diem lam viec vdi z=Zj, bdi vi dffdng thang A^B^ dffdc xac dinh theo phffdng phap binh phffdng nhd nha't, vay khdng the cd dffdng thang nao khae cho ta phan dff tha'p hdn nffa De chffng minh ta xet n tap hdp dffdi dang: (2) ((x,.,x,., x,.,y.);i=l,2, n), \ / \\ j,, 2i' kl ^ r ' Trong dd y la gia tri quan tr5c cua bien phu thudc, cdn xli, ,xki la cac gia tri cua k cac bien ddc lap d lan thff i Cho ta't ca cac lan ta cd phffdng trinh: (3) y,=b„-i-b,x,.-(- +b,x,.-i-e., ^ ^ ' -' ^ 111 k kl i' Ta't ca n lan thoa man phffdng trinh dang ma tran: (4) y = xb-i-e, Trong dd: (5)Y' = (y, y„),b,-(b, b^),E'(E, b„) b la cac he so danh gia ciia cac thdng sd, cdn la sd' hang dff d lan thff i, dffdc tinh bang gia tri dff bao Gia tri dff bao dffdc tinh nhff sau (6) r=(71,3^2 ãã>'ô> Hay dffdi mdt dang khae Y =xb, (7) Cac phan cua b dffdc xac dinh theo phffdng phap binh phffdng nhd nha't, nhd dd cac phan dff dat gia tri cifc tieu va chung dffdc xac dinh theo bieu thffc: Trong m, n la sd lan ciia nhdm so' lieu tffdng ffng vdi z=Z|, z=Zj Cac vec td bj va bj cae he so' hdi quy ciia eac nhdm sd heu dffdc xac dinh bang each thay (10) vao (9): (11) bl=(X/X,)-'(X,TY,)va (12) b2 = ( X / X ,)-'(X/Y , ) Viee lap cua cac ma tran X va Y cd the dffdc xac dinh qua vec td b ciia cac he sd hdi quy toan phan tap hdp cac so'lieu, bang each thay (10) va (11) vao (8): (13) ,=i I Thay (7) vao (8) va lay dao hao ham theo b, cho bieu thffc bang khdng, tff dd ta tim dffdc gia tri cudi cung cua bia: (9) b =(X'^X)-'(X^Y), Gia tri cac bien sd ciia cac ham xa'p xi cue bd va toan phan cd the xac dinh dffdc thdng qua cac bien tffdng ffng X va Y cac bieu thffc da md ta tren Cac ma tran X,, X,, Y^, Y, ctia cac nhdm sd lieu tffdng ffng vdi z=z z=z, se la: (10) ,v, gn TAP CHi Cd KHi VIET NAM X, Y= Y2 Tff dd ehung ta tim dffdc b theo bieu thffc: -1 (14) ixl xl) v^2y (y^ yl) Trong cac cdng thffc (13) va (14) eac dffdng thang ngang va dffng phan chia cac khd'i cae ma tran phan Bien ddi bieu thffc (14) ta tim dffdc b nhff sau: (15) b=(X/.X, +X/X,)-'(X,-^ Y, + X J ) , Sau thay the X,T.Y, tff (11) va X^^.Y^ tff (12) vao bieu thffc (14) ta dffdc: (16) b=(x,T.x, +X7x^)-'(x; Y,b, + x / x^b^), Tff (16)tacd nhan xet rang, gia tri cua cac thdng sd cua ham toan phan bang gia tri trung binh cac thdng sdciia cac ham cue bp bl va b2„ ma chung dffdc lay vdi trpng Iffdng tffdng ddi phu hdp Chi h=h^ thi b= b|=b2, dieu co nghia sff xap xi toan phan bang xap xi cue bp neu nhff tat ca xap xi cue bp la ddng nha't Chat Iffdng danh gia eac phep thong qua cac ham cue bp cd the so sanh dffdc nhffng gi ma ham toan phan dat dffdc Khi sff dung cac bieu thffc (5) he sd ddn dinh R2 dffde xac dinh nhff sau: (17) ' N I.(Y,-Yif R'=l- i=\ I^iY^-Yif 1=1 (8) min£^e; =min^(.v, - v,)' =vym{Y-YtY-Y)^ 1=1 X= e.e =1 Y.(Yi-Yd' /=i Trong dd Y dffdc chpn cho e.e'^ cd gia tri be nhat, tffdng dffdng vdi R^ dat gia tri ldn nhat Neu nhff sii dung eac gia tri Y khae vdi Y tinh theo bieu thffc (5), thi R- se cang nhd Nhff vay de kiem tra chat Iffdng xap xi tap hdp cac sd lieu cue bd se sii dung eac gia tri dff bao cua ham xap xi toan phan, dSn de'n eac phan dff thu dffdc cang ldn Chi trffdng hdp ma cae he so' hdi quy ciia cac nhdm sdlieu cue bp bang nhau, thi xap xi toan phan cd gia tri bang xap xi cue bp, trffdng hdp ngffdc lai ket qua se xau di Theo ke't qua tinh toan neu tren bang.l thi Iffdng sd hang cd qua trinh xap xi hdi quy tai mdt bac cho trffdc nao dd cua da thffc se tang vpt tang sd Iffdng cac bien dpc lap, bdi vi chung bao gdm ta't ca cac tich hdp cua cac tham sddd So 148 - Thang 11 nilm 2009 NGHIEN CQU- TRAO DOI 10 20 35 21 56 126 M ' • Bang 1: tu'dng sd hang cua da thffc bac N vdi M thong sd dpc lap Nhff vay dffdi mot va chi mdt Iffdng so' hang xac dinh thi bac ciia da thffc N se giam tang cac bien sd dpc lap M Tff sd lieu bang ta cd nhan xet rang, da thffc bac vdi bien ddc lap cd Iffdng so' hang nhd hdn da thffc bac vdi bien sd' Ne'u tri mot phffdng trinh vdi sd Iffdng sd hang nha't dinh cdn cac phffdng trinh cdn lai vdi Iffdng so' hang y se cho chung ta ket qua la viec giam bac da thffc cua ham xap xi cue bd anh hffdng trffc tiep de'n chat Iffdng cua ham xap xi toan phan Nhffng ket luan cd tinh chat ly thuyet da neu deu dffdc kiem chffng thdng qua viiec xap xi hoi quy cac ket qua thffc nghiem, tuan thii dung theo trinh tff cua vi du minh hoa Ket qua thffc nghiem cho tha'y rang, ham xap xi toan phan cho mffc tieu hao nhien lieu va Iffdng ddc tdcd phan xa ciia ddng cd cd the dffdc sff dung td't hdn de dff bao cac gia tri ciia cac thdng sd' dau vao ma cac tri so' ciia tai trpng va td'c dp dpng cd nam ngoai viing cac gia tri Tuy nhien, viec xap xi cue bp cd ket qua vffa chinh xac hdn vffa cd tri so' phan dff hdi quy nhd hdn, sff khae biet giffa cac tri sd thay ddi tff vai phan tram den hang chuc lan Cac phan tich ly thuyet va ket qua thffc nghiem da neu cho phep ta ket luan ve cac dac tinh ciia hai dang xap xi, cd the ffng diing chung de xay dffng md hinh toan hpc ciia dpng cd ddt thdng qua mdi tffdng quan cac tri so' cac tin hieu dau vao vil tin hieu dau Nghien cihi cai tien be tlii/ cdng suat theo huiofng so' hoa viec va chi thi • ket qua (*) HO HtfU HAI Gidi thieu B$ thff cdng suat dffdc sff dung d hau he't cac cd sd san xuat va sffa chffa ldn dpng cd, dtd Sau lap rap hay sufa chffa ldn, ddng cd, hop so', cau dffdc dffa len be thff de chay Ddng cd sau chay dffdc thii cdng sua't Cac cd sd san xua't va sufa chffa dtd cd quy md tffdng dd'i ldn d nffdc ta hien hau het deu sff dung be thff cdng sua't cua Lien X6 cu Hien cac be thff deu da cu, cac bd phan va hien thi ke't qua hau nhff da xudng cap va can dffde sffa chffa, cai tien Xua't phat tff nhffng ndi dung tren, bai bao se trinh bay ket qua cai tien be thff cdng sua't theo hffdng sd hda viec va chi thi ket qua tai Phan xffa cd - sffa chffa, Cdng ty than Quang Hanh thudc Tap doan Than - Khoang san Viet Nam Z Ba thiir cdng suat dpng cd Ket luan Tdm lai qua viec chffng minh loan hpc ta khang dinh dffdc chat Iffdng ciia dang ham sd danh gia cac ket qua cac thdng sd viec xay dffng md hinh loan hpc va sff dung chung de dieu khien qua trinh lam viec ciia ddng cd xe td chay tren dffdng Tff dd cd each lifa chpn phu hdp vdi mdi mot ddi tffdng nghien cffu cii the, de xay dffng dffdc mot md hinh toan hpc cua dpng cd hdp ly va dffdng nhien ke't qua dieu khien nd dat dffdc y dinh mong mudn • Tai li^u tham khao: [1 ]Ty3enKo A.M OCHOBW reopi^n aBTOMainiecKoro perynnpoBHua Bbicuiaa uiKona - M 1997 [2]l/lnMeB n.A EneKipoHn 33 aBT0MaTM4H0 ynpasneHne na aBTOMo6nnMTeflBuraTenn.TexHMKa Co(J)Mn1993 [3]flflbiKMH M.B OnTi/iManbHoe aflanrnBHoe ynpaBneHne HenpepbiBHWMM npotieccaMH.EHeproMSflaT - M 1995 [4] Rilling.J H Application of modem control theory to engine control Proceeding of IEEE conference on Decision and Control, 1999 [5] Prabhaker R Optimization of automotive engine fuel economy and emission SAE9.'J0095.1995 ^IZJ C3 Hinh 1: So be thiir eong sua't May dien pha, Hop so, Gia d9 dpng cO (chay r& hay thff), Dpng cO thff, CO cau noi tdi dong ho mo men Be thff cdng sua't la thie't bi dung de cdng sua't ciia dpng cd dd't Nd dffdc sff dung phd bien tai cac cd sd lap rap va sffa chffa ldn dpng cd, d td de chay dpng cd va cac cum may khae nhff hop so, cau chu ddng va de cdng sua't ciia ddng cd sau lap rap mdi hay sffa chffa ldn Ca'u tao cua be thff cdng suat tai Phan xffdng Cd - Sffa chffa thuoc Cong ty than Quang Hanh (dffdc the hien tren sd Hinh 1) gdm eac thie't bi chinh: may dien ba pha 1, hop sd 2, va gia dd dpng cd Ngoai cdn (*) Trffdng Dai hoc Bich Khoa Ha Noi TAP CHi Cd KHi VIET NAM • So l48 • Thiing 11 n;lni 2009 ... khae cho ta phan dff tha''p hdn nffa De chffng minh ta xet n tap hdp dffdi dang: (2) ((x,.,x,., x,.,y.);i=l,2, n), \ / \\ j,, 2i'' kl ^ r '' Trong dd y la gia tri quan tr5c cua bien phu thudc, cdn... +b,x,.-i-e., ^ ^ '' -'' ^ 111 k kl i'' Ta''t ca n lan thoa man phffdng trinh dang ma tran: (4) y = xb-i-e, Trong dd: (5)Y'' = (y, y„),b,-(b, b^),E''(E, b„) b la cac he so danh gia ciia cac thdng sd, cdn la... lan thff i, dffdc tinh bang gia tri dff bao Gia tri dff bao dffdc tinh nhff sau (6) r=(71,3^2 ãã> ''ô> Hay dffdi mdt dang khae Y =xb, (7) Cac phan cua b dffdc xac dinh theo phffdng phap binh phffdng