基于RBF神经网络辨识的直接甲醇燃料电池电堆非成性建模与自适应模糊控制-英文-

1、Article ID : 100726417 (2006) 0420346206Nonlinear modeling based on RBF neural net works identif ication and a da ptivef uzzy control of DMFC stackMIAO Qi n g ( 苗青) ,CAO Gu a n g2yi ( 曹广益) ,ZHU Xi n2j i a n ( 朱新坚)F uel Cell I ns t i t ute , S ha n gha i J i a ot o n g U n i ve rs i t y , S ha n gha

2、i 200030 , P. R. Chi n aAbstract The t e mp e rat ure models of a node a nd cat hode of direct met ha nol f uel cell ( DMFC) s t ac k w e re es t a blis he d by usi ng ra dial ba2sis f uncti on ( RB F) ne ural net w or ks i de ntificati on t ec hnique t o deal wit h t he modeli ng a nd c ont r ol p

3、r oble m of DMFC s t ac k . An a dap tive f uzzy ne ural net w or ks t e mp e rat ure c ont r olle r w as designe d bas e d on t he i de ntificati on models es t a blis he d , a nd p a ra met e rs of t he c on2 t r olle r w e re regulat e d by novel bac k p r op agati on ( B P) algorit hm . Si mulat

4、i on res ults s how t hat t he RB F ne ural net w or ks i de ntificati on modeli ng met hod is c orrect , eff ective a nd t he models es t a blis he d have good acc uracy . More ove r , p e rf or ma nce of t he a dap tive f uzzy ne ural net w or ks t e mp e rat ure c ont r olle r designe d is s up e

5、 ri or .Key words direct met ha nol f uel cell ( DMFC) s t ac k , ra dial basis f uncti on ( RB F) ne ural net w or ks , c ont r olle r .t he re a re ma ny f a ct ors aff e cti ng w or ki ng t e mp e rat ureof DM FC s t a c k , na mely , (1) t he f uel fl ow rat e of met ha n ol a n d air , ( 2) t h

6、e i nlet t e mp e rat ure of met ha 2 n ol a n d air , ( 3) f uel utilit y , ( 4) c urre nt de nsit y a n d p ola rizati o n c urve , etc . In t his p ap e r , t he i nfl ue nc e of diff e re nt f uel fl ow rat e of met ha n ol a n d air o n t he w or ki ng t e mp e rat ure of DM FC s t a c k is s t

7、 u die d . Thet es ti ng c o n diti o n of DM FC s t a c k is as f oll ows . The i n 2 let t e mp e rat ure of ai r is 40 C , t he i nlet t e mp e rat ure of met ha n ol 60 , ai r f uel utilit y 30 % , met ha n ol f uelutilit y 60 % , c urre nt de nsit y 100 mAc m2 , fl ow rat e of met ha n ol 5 - 5

8、0 mLmi n , a n d fl ow rat e of ai r 5 - 75 mLmi n . U n de r t his t es ti ng c o n diti o n , 1 200 gr o up s of w or ki ng t e mp e rat ure resp o ns e val ues u n de r diff e re ntf uel fl ow rat es of met ha n ol a n d air a re o bt ai ne d . Thes e a re us e d as t rai ni ng dat a f or RB F ne

9、 ural net w or ksi de ntific ati o n m o del a n d f uzzy c o nt r olle r of DM FCs t a c k .The res t of t his p ap e r is orga nize d as f oll ows . InSe cti o n 2 , a brief a nalysis of t he w or ki ng p ri ncip le a n dc ha ra ct e ris tics of DM FC s t a c k a re p res e nt e d . In Se c 2ti o

10、n 3 , w e des c ri be t he t e mp e rat ure m o deli ng p r oc ess i n det ail wit h RB F ne ural net w or k us e d t o s et up a n o nli ne a r t e mp e rat ure m o del of DM FC s t a c k . In Se c 2 ti o n 4 , a n o n2li ne n ovel a dap tive f uzzy ne ural net w or ksc o nt r olle r of DM FC s t a

11、 c k is designe d , a n d t he p a ra me 2t e rs of t he c o nt r olle r a re re gulat e d by n ovel B P algo 2rit h m . Fi nally , si m ulati o n res ults a re give n .1 IntroductionDire ct met ha n ol f uelc ell ( DM FC ) is desira ble t os e rve as t he p ow e r s ys t e m f or p ort a ble de vic

12、 es s uc h asc ell ula r p h o nes , p ort a ble c o mp ut e rs , etc . d ue t o t he t he oretic ally high e ne rgy de nsit y a n d t he liqui d f uel1 , 2us e d t hat c a n be s t ore d a n d t ra nsp ort e d s af ely .Pe rf or ma nc e a n d a vaila bilit y of DM FC s t a c k a re he a vily dep e

13、n de nt o n its op e rati ng t e mp e rat ure . The ra nge of t e mp e rat ure f or s t a ble op e rati ng of DM FCs t a c k is a b o ut 60 - 130 C , a n d t he n or mal op e rati ngt e mp e rat ure is a b o ut 80 C . Whe n op e rati ng t e mp e ra 2t ure is bel ow 60 C , p e rf or ma nc e of DM FC

14、s t a c k dr op ssignific a ntly . How e ve r , a highe r op e rati ng t e mp e rat ure is f a vora ble f or i mp r ovi ng t he p e rf or ma nc e of DM FC s t a c k . B ut , w he n t he op e rati ng t e mp e rat ure is highe rt ha n 130 C , me m bra ne dry a c c ele rat es , a n d ele ct r o 2lyt e

15、de c o mp ositi o n i nc re as es , w hic h i nc re as e t he ris k of s h ort2ci rc uit a n d s h ort e n t he s t a c k lif esp a n 2 25 . S o , c o nt r ol of t he op e rati ng t e mp e rat ure wit hi n a sp e cifie d ra nge a n d re d uci ng t e mp e rat ure fl uct uati o n a re i mp or 2t a nt

16、.Ac c or di ng t o e xp e ri me nt al a nalysis of DM FC s t a c k ,Receive d Oct . 29 , 2004 ; Revis e d Dec . 27 , 2004Pr oject s upp ort e d by Nati onal High2Tec hnol ogy Res ea rc h a nd De2vel op me nt Pr ogra m of Chi na ( Gra nt N o . 2003AA517020) MIAO Qi ng , Ph . D . Ca ndi dat e , E2mail

17、 : mia oqi ng sjt u . org ;CAO Gua ng2yi , Ph . D . , Pr of . , E2mail : gy2ca o sjt u . e du . c n Vol . 10 N o . 4 Aug . 2006 MIAO Q , et al . : N o nli ne a r m o deli ng bas e d o n RB F ne ural net w or ks . . . 347 Ac c or di ng t o DM FC s t a c k dyna mic c ha ra ct e ris tic , de 22 Descrip

18、tion and analysisstackThe s c he matic dia gra m of t he dire ct c ell a n d a p h ot o of DM FC si ngle c ellof DMFCTfi ni ng V ( t ) = va ( t ) , vc ( t ) , ( t ) = a ( t ) , ( t ) , ( t ) , ( t ) T , t he t e mp e rat ure m o del of DM2cebmet ha n ol f uela re s h ow n i nFC c a n be des c ri be

19、d asd( t )= f ( t ) , V ( t ) .( 1)Figs . 1 a n d 2 , resp e ctively . DM FC c o nsis ts of a n o de ,c at h o de , ele ct r olyt e me m bra ne , c at alys t la ye rs , diff u 2d tB as e d o n e xp e rie nc es , t he t e mp e rat ure of a n o de ,c at h o de , ele ct r olyt e la ye r a n d bip ola r

20、 p lat es mai nly dep e n d o n t hre e f a ct ors : he at e mitt e d by ele ct r o 2 c he mic al re a cti o n t hat i nc re as es t he t e mp e rat ure , c o n 2 ve cti o n he at of e x ha us t e d gas es a n d c o n d ucti o n he at oft he s t a c k ha r dw a re t hat l ow e r t he t e mp e rat ur

21、e . The f uel fl ow rat e of c at h o de a n d a n o de c a n i nfl ue nc e t he t e mp e rat ure of DM FC . Sl ow fl ow rat e of f uel le a ds t oa n a de quat e re a cti o n , les s he at l os t , a n d highe r t e m 2p e rat ure p r o d uc e d . O n t he ot he r ha n d , f as t fl ow of f uel res

22、 ults i n a n i na de quat e re a cti o n , wit h m uc h m ore he at fl owi ng a w a y wit h t he re m na nt f uel , le a di ng t ol ow e r t e mp e rat ure . Th us , s t e a dy t e mp e rat ure of t he s t a c k va ries wit h t he fl ow rat e of f e e di ng f uel of a n o de a n d c at h o de i n a

23、 c o mp le x ma n ne r . In ge ne ral , i n or de r t o c o ol t he s t a c k a n d e ns ure f ull us e of t he f uel , it is as s u me d t hat o xi da nt is e xc es sive a n d t he f uel s up p lyrat e is n ot be yo n d t he ma xi m u m re a cti o n rat e c ap a cit y6 , 7si o n la ye rs , fl ow c

24、ha n nels , a n d bip ola r p lat es .1 , 7 - Cat hode a nd a node fl ow c ha nnels ; 2 , 6 - Cat hode a nd a node diff usi on laye rs ; 3 , 5 - Cat hode a nd a node cat alys t laye rs ; 4 - Me mbra ne ;8 , 9 - Cat hode a nd a node bip ola r plat esFig. 1 A s c he matic diagra m of DMFC2 , 3of t he

25、s t a c k . To f a cilit at e m o deli ng a n d c o nt r ol de 2signi ng , t he ai m of m o del i de ntific ati o n is t hat t he es 2t a blis he d m o del c a n dyna micly si m ulat e t he va ryi ng t e mp e rat ure c urve of t he s t a c k bas e d o n diff e re nt f uel fl ow rat e . The f oll owi

26、 ng diff e re ntial e quati o n is us e d t o des c ri be t he t e mp e rat ure m o del of DM FC s t a c k .Fig. 2 Phot o of DMFC si ngle cell( k + 1) = f ( k) , V ( k) .(2)In a DM FC , t he f oll owi ng c at alytic ally a ctivat e d re 2a cti o ns t a ke p la c e .An o de re a cti o n :3Identif ica

27、tionstructure and DMFCstack algorithm ba sed on RBF neuralnet works3. 1Structure of RBF neural net worksRB F ne ural net w or ks ha ve go o d ap p r o xi mati o n a bili 2t y a n d high a c c ura c y i n c o nt ras t t o t he B P ne ural net 2+-CH3 O H + H2 O CO2 + 6 HCat h o de re a cti o n :+ 6e .

28、3 O+-+ 6 H + 6e3 H O .222Tot al re a cti o n :3CH3 O H + 2 O2 + H2 O CO2 + 3 H2 O .i2t h RB F ne ural net w or ks o utp ut c a n bew or ks . Therep res e nt e das a li ne a rly w eight e d s u m:Nof Nbasisby a ( t ) , t heele ct r olyt e la ye rThe a n o de t e mp e rat ure is de n ot e dc at h o de

29、 t e mp e rat ure by c ( t ) , t he2 , 3f u ncti o nst e mp e rat ure by e ( t ) a n d t he bip ola r p lat es t e mp e ra 2t ure by b ( t ) , resp e ctively . va ( t ) a n d vc ( t ) a re t he a n o de a n d t he c at h o de f uel fl ow rat e , resp e ctively .i ( )+ wX k, i = 1 , 2 ,j ij ( ) )( )Y

30、 k = w, m ,30 ij = 12 2X ( k) - Cj jj ( X ( k) ) = e xp,( 4) HYPERLINK :/www / 1994-2014 China Academic Journal Electronic Publishing House. All rights reserved. 348 J o u r n al of S h a n gh a i U n i ve r s i t y de n ot e w eights , j ( X ( k ) ) is aw he re a n dw j iw 0 i(7)(8) ( 9)F = f , f ,

31、 f, f ,12m - 1mNGa ussia n a ctivati o n f u ncti o n , Cj ( j = 1 , 2 , N ) RE = e , e , e, e ,12m - 1mis t he c e nt e r of t he j2t h hi d de n n o de , wit h t he s a medi me nsi o n as t he i np ut ve ct or X , j is t he wi dt h of t hej2t h hi d de n u nit .W = w 1 , w 2 , w m - 1 , w m , = (

32、)1 , 2 ,n - 1 ,n .10L et a n ort h ogo nal mat ri x be = BA .Furt he r defi neAW = Q .de c o mp ositi o noft here gres sive3 . 2Identif ication system and study algorithmof RBF neural net works( 11)In or de r t o i mp r ove ge ne ralizati o n a bilit y of net w or ka n d a voi d ove r2fitti ng p r o

33、 d uc e d by OLS algorit h m , ROLS algorit h m ref e rre d t o Ref . 8 - 10 is e xt e n de dt o a m ulti2i np ut a n d m ulti2o utp ut s ys t e m . This algo2rit h m is us e d t o es t a blis h a t e mp e rat ure m o del of DM 2FC s t a c k .A wi de class of n o nli ne a r s ys t e ms c a n be des

34、c ri be d by t he f oll owi ng n o nli ne a r a ut ore gres sive m o del wit h(12)( 6) c a n alt e r natively be e x2The RB F net w or k m o delp ress e d as :Y = BAW + E = B Q + E , w he re(13)8 210e x oge n o us i np uts .Y( k) = F ( Y( k - 1) ) ,(14)B = b1 , b2 , bm - 1 , bm , a 1 , m, Y( k - n y

35、 ) , U ( k - 1) ,10a 1 , 21, U ( k - n u ) ) + e ( k) ,(5)A =,(15)w he re Y ( k ) is a n o utp ut ve ct or , U ( k ) is a n i np utve ct or , n y a n d n u a re la gs of t he o utp ut a n d t he i np ut resp e ctively , F ( ) is a n o nli ne a r f u ncti o n , a n d e ( k)is w hit e n ois e ve ct or

36、 i n t he s ys t e m .0am - 1 , m01(16)W of RB F ( 12 ) . TheQ = q1 , q2 ,S o , k n owi ng, qm - 1 , qm .A a n d Q , t he w eights ve ct orTFor DM FC s t a c k , U ( k ) = va ( k) , vc ( k ) is t hei np ut ve ct or , na mely f uel fl ow rat e of a n o de a n d c a 2t h o de of t he di re ct met ha n

37、 ol f uel c ell s t a c k , resp e c 2ne ural net w or k m o del c a n be s olve d f r o m8 210ze r o ra n k re gula rize d e rr or c rit e ri o n is as f oll ows.TTT J R ( Q ,) = t ra c e ( E E + Q Qtively . Y( k) = a ( k) ,c ( k) ,e ( k) ,b ( k) is t heo utp ut ve ct or , na mely t he a n o de t e

38、 mp e rat ure , t he c a 2t h o de t e mp e rat ure , t he ele ct r olyt e la ye r t e mp e rat ure a n d t he bip ola r p lat es t e mp e rat ure , resp e ctively . The)= t ra c e ( YT Y - Q T ( B T B + ) Q ) ,( 17)w he re = 1 , 2 ,p a ra met e r ve ct or .,m - 1 ,m is t he re gula rizati o ns t r

39、uct ure s c he me of i de ntific ati o n s ys t e m bas e dRB F ne ural net w or k is s h ow n i n Fig . 3 .o n3 . 3 Modeling test procedureThe MA TLAB ne ural net w or k t o ol b o x is us e d t o p e r 2 f or m t he t rai ni ng a n d si m ulati o n . Fi rs t , 1 200 gr o up s of w or ki ng t e mp

40、e rat ure resp o ns e val ues a re s ele ct e d ase xp e ri me nt dat a u n de r diff e re nt t he f uel fl ow rat e ofa n o de a n d c at h o de . The op e rati ng c o n diti o n p a ra me 2t e rs a n d p hysics c ha ra ct e ris tic p a ra met e rs of DM FC s t a c k a re lis t e d i n Ta ble 1 . A

41、 p h ot o of c o nt r olli ng a n d t es ti ng s ys t e m of DM FC s t a c k is s h ow n i n Fig . 4 .Se c o n dly , i n or de r t o ma ke all i np ut a n d o utp utf alli ng i nt o ( 0 , 1 ) , t he f oll owi ng n or malizati o n isFig. 3 Ide ntificati on s t r uct ure of DMFC s t ac k bas e d onRB

42、F ne ural net w or ks2 , 3The m ulti2i np ut a n d m ulti2o utp utus e d:s ys t e mc a nbew ritt e n i n a li ne a r a ut ore gressive f or m asY = F + E = W + E , w he reX -Xmi n + d1(18)X=,Xma x - Xmi n + d2(6)w he re X is t he origi nal dat a , Xma x is t he ma xi m u m of HYPERLINK :/www / 1994-

43、2014 China Academic Journal Electronic Publishing House. All rights reserved. Vol . 10 N o . 4 Aug . 2006 MIAO Q , et al . : N o nli ne a r m o deli ng bas e d o n RB F ne ural net w or ks . . . 349 X , Xmi n is t he mi ni m u m of X , Xis t he res ult of n or2malizati o n . He re , 0 d1 d2 0 . 1 ,

44、c h o osi ng d1 =0 . 06 , d2 = 0 . 1 .p e rf or m dyna mic i de ntific ati o n si m ulati o n of t he DM FC s t a c k. U n de r va ri o us gas fl ow rat es , c o mp a ri ng t he dis c ret e t e mp e rat ure val ues c alc ulat e d by t he ne ural net w or ks wit h a ct ual s a mp le d t e mp e rat ur

45、e dat a o b 2t ai ne d f r o m t he e xp e ri me nt of DM FC s t a c k , t he si m u 2lati o n res ults a re s h ow n i n Fig . 5 . The si m ulati o n re 2s ults i n dic at e t hat t he RB F ne ural net w or ks m o del c a n i mit at e t he dyna mic t e mp e rat ure resp o ns e of a ct uals t a c k

46、, a n d t he ma xi mal e rr or is n ot be yo n d 2 C . Forsi mp licit y a n d ge ne ralit y , i n Fig . 5 , o nly t he c o mp a ri ngres ults of a n o de a n d c at h o de c e nt e rs t e mp e rat ures ofThe p urp os e of RB F ne ural net w or k t rai ni ng ist omi ni mize me a n s qua re e rr ors (

47、MS E) 2 , 3: 12EMS E = N ( yj ( k) -yj ( k) ) ,(19)j kof e xp e ri me nt al dat a , yj ( k )w he re N is t he n u m be ra n d yj ( k) a re t he desi re d o utp ut of DM FC s t a c k a n dt he o utp ut of net w or k m o del at t he k2t h s a mp le ti me .Ta ble 1 Physical c ha ract e ris tic p a ra m

48、et e rs a nd op e rati ng c ondi2ti on p a ra met e rs of DMFC s t ac kc o2fl ow t yp e DM FC s t a c k at f o ur diff e re nt gasrat es a re give n .fl owPa ra met e rsVal uesLe ngt h wi dt h t hic knessElect rolyt e me mbra neAnode cat alys t laye r30 mm 30 mm 1 . 5 mmNafi on 115PtC : 20 wt % , Ru

49、 : 10 wt %10 wt % Nafi on s ol uti on , ca rbon p ow de r10 wt %Nafi on s ol uti on , PtC10 wt % P TF E s ol uti on , ca rbon p ow de rGrap hit e plat e60 - 130 CAnode diff usi on laye rCat hode cat alys t laye rCat hode diff usi on laye rBip ola r mat e rialWork t e mp e rat ure of DMFC Work p ress

50、 ure of t he a node a ndcat hodeMet ha nol c once nt rati on( a ) Ide ntificati on res ults of a node t e mp e rat ure0 . 3 MPa1 . 0 molL5 - 50 mLmi n5 - 75 mLmi n- 1 . 5 - + 1 . 5 Cs80 CFl ow rat e of met ha nolFl ow rat e of airError c ha nge of t e mp e rat ureThe op ti mal t e mp e rat ure val u

51、e( b) Ide ntificati on res ults of cat hode t e mp e rat ureFig. 5 Ide ntificati on res ults unde r 4 diff e re nt f uel fl ow rat esAda ptive f uzzy neural net works con2trol of DMFC stackIn t his s e cti o n , a n i de ntific ati o n m o del is t rai ne d i n 2s t e a d of t he re al DM FC s t a c

52、 k , a n d a n o n2li ne a dap tive f uzzy ne ural net w or ks t e mp e rat ure c o nt r olle r designe d . The s c he me of a dap tive f uzzy ne ural net w or ks c o nt r ols ys t e m of DM FC s t a c k is s h ow n i n Fig . 6 .4Fig. 4 Phot o of c ont r olli ng a nd t es ti ng s ys t e m of DMFC s

53、t ac k3. 4Simulation resultsD uri ng RB F ne ural net w or kt rai ni ng , t he desi re dMS E is 1 C . To vali dat e t he fi nal RB F ne ural net w or ksm o del , t he ne ural net w or ks t rai ne d a b ove is us e d t o HYPERLINK :/www / 1994-2014 China Academic Journal Electronic Publishing House.

54、All rights reserved. 350 J o u r n al of S h a n gh a i U n i ve r s i t y i nt e grat es all a cti o ns re c o m 2a n d 4 a n d a cts a cle a re dLayer 5me n de d by op e rati o n .The n o deL a ye rs 3(4)a i(5) i (24)a=(3) .a iiFig. 6 Sc he me of a dap tive f uzzy ne ural net w or ksc ont r ol s y

55、s t e m of DMFC s t ac kThe e xp ressi o n of m i j a n d i j w hic h a re a dap tively re2gulat e d by B P algorit h m a re give n as f oll ows :Ac c or di ng t o t he e xp e ri me nts , w he n op e rati o n p res 2s ure a n d t e mp e rat ure of DM FC s t a c k a re 0 . 3 M Pa a n d80 C , resp e c

56、tively , t he c ha ra ct e ris tic of s t a c k is op ti 25 E(2)m(2)( t + 1) =( t ) - m i ji j(2)5 m i j(3)35 a k5 E5 ymal. Ch o os e T= 80 C ast he i de al t e mp e rat ure ofC as t he t e mp e rat ureC as t he ra nge of t e m 2(2)m( t ) - (25)=,i j5 y5 E(3)(2)5 a k 5 m i jkDM FC s t a c k , T = 50

57、 - 130 ra nge , T = - 1 . 5 - + 1 . 5(2)(2)( t + 1) = i j ( t ) - i j(2)5i jp e rat ure e rr or , resp e ctively . Furt he r m ore , s ele ctTa n d T as f uzzy va ria ble , w he n T is highe r t ha n T 3 ,i nc re as e t he fl ow rat e of f uel ; a n d w he n T is l ow e r5 a (3)5 E5 yk= (2)( t ) - ,

58、( 26)i j5 y5 a (3) 5(2)kk i j311 , 12t ha n T , l ow e r t he fl ow rat e of f uel .4 . 1 Structure and study algorithm of f uzzy neural net works controllerAn o n2li ne n ovel a dap tive f uzzy ne uralw he rea da ptive5 E5 y = y ( t ) -yi deal ( t ) ,(27)net w or ks(4) 5 y a k - y=,(28)c o nt r oll

59、e r ref e rre d t o Ref . 11 - 13 is de vel op e d , t hep a ra met e rs of t he a dap tive f uzzy ne ural net w or ks c o n 2t r olle r a re re gulat e d by a n ovel B P algorit h m . Thef u ncti o ns of t he n o des i n e a c h of t he five la ye rs of a da 2p tive f uzzy ne ural net w or ks a re

60、des c ri be d as f oll ows .5 a (3)(3)a iik2 ( xi -m i j ),(3)a5 a (3)k2ki j(29)=5 m (2)i j0 ,Layer 1Ea c h n o de o nly t ra ns mits i np ut val ues t o22 ( x i - m i j ) (3)5 a (3)a k,t he ne xt la ye r .3ki j(30)=(2)5i j(1) (1)a = u i = xi ,(20)0 .Simulation results( k)( k)w he re u a n d a de n