Graphical Representation of Fuzzy State Space of a Boiler System
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1 EEN DNES in NEU NEWOKS UZZY SYSES & EOUIONY OPUIN il eeenion o uzzy Se Se o oile Syem NOO INY HISH ZIDH ISI 3 HI HD uly o omue nd emil Siene Unieiy enoloi 445 S lm Selno YSI 3 Demen o emi uly o Siene Unieii enoloi lyi83 Sudi Joo YSI iny@m.uim.edu.my zid@m.uim.edu.my 3 i@inuin.um.my : - il eeenion i ueul o illue omle uue in die o inuiie y. i ymoli o neo nd i onneiiy n e imliied e o lined noe. In een udie o omle onol yem dieed een inodued o deine nd inee e ineonneion uue undelyin e dynmi o e inein uyem. enelly e min omonen o oe ln e uine oile nd em uine. Ou inee in i udy i o eeen e oile yem uin il eeenion. e oile yem oni o uyem nmely une ueee dum ie nd eee. ee uyem ill e nomed ino eie nd ineonneion eeen uyem ill e oied i ede o e. Iniilly e inu-ouu ile e ideniied uin e e o. e il eeenion o oile yem n iniil e o ue eloion in liion o uzzy. Key-Wod: - uzzy omined yle Poe Pln Se Se odel uli-onneed Syem. Inoduion il eeenion i eemely ueul o illue omle uue in die nd inuiie y nd u ey e idely ued in mny ield. eoy oide memil modelin o udyin ineonneion mon elemen in nul nd mn-mde yem []. In een udie o omle onol yem dieed e een inodued o deine nd inee e ineonneion uue undelyin e dynmi o e inein uyem. Suyem ee oied i eie ile ineonneion i ede o e []. eoem nd loim o eoy eeen e eiol oeie o e yem e oeie o e eie o ede o e [3]. enelly e min omonen o omined yle o oe ln e uine oile nd em uine [4]. Ou inee in i udy i e oile yem. ie mo el lie oee oile dynmi e ily non-line nd indin n ue model i lmo imoile due o uneinie in e yem. e e e o i ed on ime domin nlyi nd ynei uin e ile. I i uniied meod o modelin nlyzin nd deinin ide ne o yem [5]. i o i ell udied nd i oide ood oimion in modelin enineein nd ioloil yem [6-9]. In ddiion e memil equion e eeened in mi le nd i ode dieenil equion. eoe only e ize o mi ne odin o e omleiie o e yem. oile Syem oile yem oni o ie min uyem nmely une ie dum eee nd ueee [4]. ed on e yil dum-ye oile e eede i ulied o e dum ee e e i eoed. e e lo ino donome en ene e ie. In e ie e e om e une i ued o inee e e emeue nd eenully o ue eoion. u e iulion o e em nd e nd em miue e le in e dum e donome nd e ie. Sem eneed in e ie i eed in e dum ee i lo ou e ueee on o e i eue uine. I my e eyled o e oile in e eee ee i eney onen i ineed. Deueein y e i inodued in e ueee o onol o min em emeue. o e omuion oe e ie o din e in e une. e o e lein e une ne e e y diion nd oneion o e ueee. e e en need y oneion o e eee nd e eonomize eoe eiin e oile i e. e une il i ued o ne diion e diiuion eeen e ISSN: ISN:
![ie nd e ueee. Semi dim o oile yem i on in i. [4]. i.. Semi Dim o oile Syem 3 il eeenion o oile Syem eoy i ueul eeenion eue e elemen o e n e deined o o e one o one oeondene i e elemen o mny ind o enineein yem [3].](/docs-images/75/71903341/images/2-0.jpg "In ddiion i ymoli o neo nd o i onneiiy i imlie n ion o e eliy n e imliied e o lined node []. dieed E oen eed i deined y e o node nd E o lin (o. e e o node nd ede n e onenienly leled y... j 3 nd.")
2 ie nd e ueee. Semi dim o oile yem i on in i. [4]. i.. Semi Dim o oile Syem 3 il eeenion o oile Syem eoy i ueul eeenion eue e elemen o e n e deined o o e one o one oeondene i e elemen o mny ind o enineein yem [3]. In ddiion i ymoli o neo nd o i onneiiy i imlie n ion o e eliy n e imliied e o lined node []. dieed E oen eed i deined y e o node nd E o lin (o. e e o node nd ede n e onenienly leled y... j 3 nd...e n e e e E 3 eeiely. e oile yem n e iulized in e om o on in i.. Iniilly e e e model i ued o deemine e inu nd ouu mee o e uyem on in le [8] []. e omlee nomenlue n e ound in [4]. le. Se Se eeenion o oile Syem Suyem ie nd in e e equion Se eo Inu-Ouu eo Sueee ( ( u ( y ie J J ( d i ( u y eee o i i i o ( i u ( o P y Dum do do e do D d m ( e ( u d y une l e e ( ( ( ( u e i i y EEN DNES in NEU NEWOKS UZZY SYSES & EOUIONY OPUIN ISSN: ISN:
3 EEN DNES in NEU NEWOKS UZZY SYSES & EOUIONY OPUIN e 4 e 5 e e 3 3 e 8 e e 6 6 e 9 e 7 e e 3 e 4 i.. il eeenion o oile Syem e onuion o e il eeenion o oile yem n e omlized y e olloin ooiion. Pooiion e oile yem o omined yle oe ln in Ody e. l 994 [4] n e eened y E: ee e ( o eie oeond o e uyem eled o e oile nd e E( o ede oeond o e inuouu ile oied i e omonen. Hoee e il eeenion o oile yem in i. i i. eoe moe omeenie il eeenion o e yem i needed i i oulined in e olloin eion 4 uzzy Se Se odel uzzy Se Se odel (SS o une inodued nd olloed y uzzy Se Se loim i e uoe o olin e inee olem ee e inu mee iee e deied ouome n e dedued []. In i loim e uneinie in e mee e eened y uzzy nume [3] i e ineed in e e e model o e yem. e uzzy loim een on o ie ood mee eimion o ueee yem [4].e deiniion o SS o muliile dynmi yem i ien ollo: Deiniion uzzy Se Se odel o muliile dynmi yem i deined ẋ u ~ e S : y~ 5 4 e ee u ~ denoe e uzziied inu eo u u...u n nd ~ y denoe e uzziied ouu eo y y...y m i iniil ondiion nd. e elemen o e mi inu mi n nd ouu mi m e non o eiied uy. e muli-onneed yem o SS n e ieed yem o SS S i i olleion o uyem S S S j... j. o e o S in mulionneed yem i n e nomed ino oin in e Euliden n-e ee e elemen o nd mie n e ien oodine o oin in inie dimenionl e. u SS n e emedded in Euliden e y uin e olloin nomion. eoem ien uzzy e e yem S j u m. m e nomion : n m n S j n i ijeie m. Poo (i e S S m E nm n...n m m n n m m n n m m m... In oe od S ee i union S n n ISSN: ISN:
4 EEN DNES in NEU NEWOKS UZZY SYSES & EOUIONY OPUIN (ii e S S eoe......n...m nd n n... n n n m n m n n m m n m (iii Pi ny oin nm en... n ee ij ij ij. onequenly S u n m S n i n m m m Sine i iy u i ono. m m eoe S S i one o one Suyem Ode o mie Sueee 3 4 le. SS o Euliden n-e ee S i in Euliden n-e S3 ie eee Dum S i S4 do do S5 e 5 une 9 5 S ISSN: ISN:
5 EEN DNES in NEU NEWOKS UZZY SYSES & EOUIONY OPUIN y uin i nomion e uzzy Se Se odel o e oile yem n e emedded in Euliden e. e deiled i on in le. e Euliden -e o e ee i deemined y e ol ize o nd mie in e uyem o SS. ee eie ill e emedded ino e me Euliden n-e. 5 i e mimum lue o i ill eeen e ize o e n-e. e min o SS o Euliden e ill e e iniil e o ue eloion ie o SS. 5 onluion e i il eeenion o e oile yem een ueully modeled uin e i eoeil one. We inlly oulined enel oedue in onuion o il eenion o uzzy Se Se odel o yem. mle onuion o oile yem i eened. i ne o ill imliy e emi dim o ineonneion o uyem in oile. u e il eeenion ill led o e deelomen o uzzy il eeenion o oile ee e enique o deemine e memei lue o e uyem ill e diued. eeene: [].Hy eoy. ddion Weley Puliin omny. lioni US 967. [] D.D.Silj Dynmi Nonline nlyi: Hiid Syem. ile in Pe. ://.ienedie.om. eieed uu 7. [3] O.Si & K.Pei eoy eeenion o enineein yem nd ei emedded nolede. iiil Inelliene in Enineein [4].W.Ody.W.Pie..Jonon.. Kei &.J.imle odellin nd Simulion o Poe eneion Pln. Sine-el ondon 994. [5] N.S. Nie onol Syem Enineein. ddion Weley. enlo P lioni 995. [6] I.D.J.Onen...Ye & J..lemmin e-nlyi o niml oemen uin Se- Se odel. Eoloy. 84( [7] W..eende.W.Heemin..n ee & J..eel Se Se odelin o We le luuion in Siin eime. Jounl o Hydoloy [8].Imil une odellin uin Se Se eeenion. Sienii ee Jounl 3( [9] W..eende.W.Heemin..n ee & J..eel non-line e e o o model ounde luuion. Jounl o Hydoloy. dne in We eoue [] S.u S.um &.md Eienlue o uzzy ye-3. Nionl Semin on uzzy eoy nd liion S lm lyi 8. [] N..Hi.Imil &.md odelin o Sueee Syem uin Se Se eeenion Po. o In. oneene on Siene & enoloy: liion in Induy & Eduion Penn-3 De 8. [].Imil.md.S.md & S.md Oiml Pmee Eimion o ISO Syem ed on uzzy Nume Junl enoloi lum nd Sin Kunii. 8( [3].Kumn &..u Inoduion o uzzy imei: eoy nd liion n Nond einold Ne Yo 985. [4] N..Hi.Imil &.md uzzy loimi o o eimin e inu mee o ueee yem. Nionl Semin on uzzy eoy nd liion. S lm lyi 8. Nomenlue e - i e - e 3 - e4 - e 5 - P e 6 - e 7 - P e 8 - Po e 3 - e e4 - d i e e 9 - i e - d e - e - - une S - Sueee S 3 - eee 4 - ie S - Dum S 5 S ISSN: ISN:
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