Neural Network Modeling and Nonlinear Predictive ...

7 downloads 0 Views 192KB Size Report
Abstract― Fed-batch fermentation processes are common methods of producing biological recombinant from different microorganisms. Model-based control of ...
 2009 IEEE International Conference on Control and Automation  Christchurch, New Zealand, December 9-11, 2009

 FrPT4.4

 1HXUDO1HWZRUN0RGHOLQJDQG1RQOLQHDU3UHGLFWLYH&RQWURORI D%LRWHFKQRORJLFDO)HGEDWFK3URFHVV  

$1LNIHWUDW$59DOL9%DEDHLSRXU  $EVWUDFW² )HGEDWFK IHUPHQWDWLRQ SURFHVVHV DUH FRPPRQ PHWKRGV RI SURGXFLQJ ELRORJLFDO UHFRPELQDQW IURP GLIIHUHQW PLFURRUJDQLVPV 0RGHOEDVHG FRQWURO RI ELRSURFHVVHV LV D GLIILFXOW WDVN GXH WR WKH FKDOOHQJHV DVVRFLDWHG ZLWK ELRSURFHVV PRGHOLQJ 7KH SDSHU GHDOV ZLWK WKH PXOWLOD\HU SHUFHSWURQ QHXUDO QHWZRUN PRGHOLQJ RI IHGEDWFK FXOWLYDWLRQ RI ( FROL %/ '(  >S(7DLIQȖ@ XQGHU PD[LPXP DWWDLQDEOH VSHFLILF JURZWKUDWHLQWKHZKROHRISURFHVVIRUSURGXFLQJȖ,QWHUIHURQ SURWHLQEDVHGRQH[SHULPHQWDOGDWD7KHQHXUDOQHWZRUNPRGHO EDVHG SUHGLFWLYH FRQWURO 1103&  VFKHPH LV GHVLJQHG IRU FRQWUROOLQJ WKH FRQFLGHUHG IHGEDWFK ELRWHFKQRORJLFDO SURFHVV 7KH QRQOLQHDU SUHGLFWLYH FRQWURO EDVHG RQ WKLV PRGHO VKRZ JRRGSHUIRUPDQFHIRUWUDFNLQJUHIHUHQFHWUDMHFWRULHV .H\ZRUGV²)HGEDWFK0/3QHXUDOQHWZRUN1103&

 ,

,1752'8&7,21

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

$KPDG 5H]D 9DOL LV ZLWK 'HSDUWPHQW RI &RQWURO (QJLQHHULQJ (OHFWULFDO (QJLQHHULQJ 5HVHDUFK &HQWHU 7HKUDQ ,UDQ HPDLO DUYDOL#JPDLOFRP 

1HXUDO QHWZRUNV KDYH WKH DGYDQWDJHV RI GLVWULEXWHG LQIRUPDWLRQ SURFHVVLQJ DQG WKH LQKHUHQW SRWHQWLDO IRU SDUDOOHOFRPSXWDWLRQ

9DOLROODK%DEDHLSRXULVZLWK'HSDUWPHQWRI%LRFKHPLFDO(QJLQHHULQJ %LRWHFKQRORJ\5HVHDUFK&HQWHU7HKUDQ,UDQ HPDLOEDED#VEPXDFLU 

,Q PDQ\ FDVHV ZKHQ VXIILFLHQWO\ ULFK GDWD DUH DYDLODEOH

978-1-4244-4707-7/09/$25.00 ©2009 IEEE

2366

 



WKH\ FDQ SURYLGH IDLUO\ DFFXUDWH PRGHOV IRU QRQOLQHDU FRQWUROV ZKHQ PRGHO HTXDWLRQV DUH QRW NQRZQ RU RQO\ SDUWLDO VWDWH LQIRUPDWLRQ LV DYDLODEOH 'XH WR WKHLU SDUDOOHO SURFHVVLQJFDSDELOLW\QRQOLQHDULW\LQQDWXUHDQGWKHLUDELOLW\ WR PRGHO ZLWKRXW D SULRUL NQRZOHGJH QHXUDO QHWZRUNV FDQ EH XVHG VXFFHVVIXOO\ WR FDSWXUH WKH G\QDPLFV RI QRQOLQHDU DQGFRPSOH[PXOWLYDULDEOHV\VWHPV

,QWKLVVWXG\WKHR[\JHQDQGSHULSKHUDOSDUDPHWHUVVXFKDV S+ DQG WHPSHUDWXUH DUH NHSW FRQVWDQW DQG WKH RQO\ FRQWURO YDULDEOHLVLQOHWIHHGUDWH 7KH PDWKHPDWLFDO PRGHO IRU WKH FRQVLGHUHG ( FROL IHG EDWFK FXOWLYDWLRQ EDVHG RQ PDVV EDODQFH FRPSRQHQW LV SUHVHQWHGE\WKHIROORZLQJGLIIHUHQWLDOHTXDWLRQV>@

G; GW G6 GW

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Ȗ,QWHUIHURQ SURWHLQ RI ( FROL %/ '( >S(7DLIQȖ@7KHIHHGLQJUDWHLVFRQWUROOHGE\ WXQLQJWKHIHHGLQJSXPSVSHHG 7KH S+ ZDV PDLQWDLQHG DW  E\ WKH DGGLWLRQ RI  ZY  1+2+ RU  0 +32 VROXWLRQV 'LVVROYHG 2[\JHQ ZDV PDLQWDLQHGDW“ YY RIDLUVDWXUDWLRQE\FRQWUROOLQJ RIERWKWKHLQOHWDLU ZKLFKZDVHQULFKHGZLWKSXUHR[\JHQ  DQGDJLWDWLRQUDWH>@

G$ GW G9 GW

P;  

 J/@)IHHGUDWH>/K@9ELRUHDFWRU YROXPH >/@ 6LQ JOXFRVH FRQFHQWUDWLRQ RI IHHG >J/@ — VSHFLILF JURZWK UDWH RI ELRPDVV >J J/@ JJ@ JJ@.6VDWXUDWLRQFRQVWDQW.LLQKLELWLRQFRQVWDQW DQG P P LVWKHPD[LPXPVSHFLILFJURZWK

,GHQWLILFDWLRQ RI WKH SURFHVV ZDV GRQH RIIOLQH E\ XWLOL]LQJ JHQHWLF DOJRULWKP DQG 362 E\ PHDQV RI H[SHULPHQWDO GDWD JDWKHUHGIURPSUHYLRXVUXQV>@ 3URFHVVLQSXWDQGRXWSXWVDUHFKRVHQDV

X >)@ \

ª; º «6 » ¬ ¼ ,, 1(85$/1(7:25.02'(/,1*

1HXUDOQHWZRUNVKDYHLPSRUWDQWSURSHUWLHVUHODWHGWRFRQWURO V\VWHPV7KHXVDJHRIQHXUDOQHWZRUNVLQQRQOLQHDUFRQWURO SUREOHPV DULVHV IURP LWV DELOLW\ WR DSSUR[LPDWH DUELWUDU\ FRQWLQXRXV QRQOLQHDU IXQFWLRQV LQ SDUWLFXODU PXOWLOD\HU SHUFHSWURQ QHWZRUNV 0/3  DUH RQH RI WKRVH QHWZRUNV ZKLFK DUH JRRG DSSUR[LPDWRUV DQG DUH XVHG LQ WKLV VWXG\ WRR,QRXUVWXG\0/3VHSDUDWHVWKHVSDFHRIIHDWXUHVZLWK OHVV XQLWV WKDQ WKH RWKHUV QHWZRUNV OLNH 5DGLDO %DVLV )XQFWLRQ1HXUDO1HWZRUNV SURYLGLQJDUHDVRQDEOHWUDGHRII EHWZHHQPRGHOFRPSOH[LW\DQGSHUIRUPDQFH 7KHFKRVHQ0/3QHWZRUNVWUXFWXUHLVD11$5;ZKHUHWKH UHJUHVVRUYHFWRUFDQEHH[SUHVVHGDV

2367

 



M W

> \ W    \ W  Q D X W  Q N 

X W  Q E  Q N   @7

   

:KHUHQDLVWKHQXPEHURISUHYLRXVV\VWHPRXWSXWVQEWKH QXPEHU RI SUHYLRXV LQSXWV DQG QN WKH GHOD\ DSSOLHG WR WKH LQSXWV7KHSUHGLFWRUFDQEHZULWWHQDV

\Ö W _ T

\Ö W _ W  T

J M W T   

:KHUH M W LV D YHFWRU FRQWDLQLQJ WKH UHJUHVVRUV T LV D YHFWRU FRQWDLQLQJ WKH QHWZRUN ZHLJKWV DQG J   LV WKH IXQFWLRQ UHSUHVHQWHG E\ WKH QHXUDO QHWZRUN :KHQ QR RU RQO\ YHU\ OLWWOH QRLVH LV SUHVHQW WKLV VWUXFWXUH LV SUHIHUUHG LQVWHDGRIUHFXUUHQWVWUXFWXUHV7KHQRWDWLRQ \Ö W _ T VWDQGV IRUWKHSUHGLFWLYHRXWSXW>@ 1HWZRUN WUDLQLQJ ZDV GRQH E\ /HYHQEHUJ0DUTXDUGW DOJRULWKP 7KH /HYHQEHUJ±0DUTXDUGW DOJRULWKP LV IDVWHU WKDQ WKH FODVVLFDO EDFNSURSDJDWLRQ DOJRULWKP 7KLV DOJRULWKPLVNQRZQWREHDUREXVWDQGIDVWJUDGLHQWPHWKRG EHFDXVH RI LWV VHFRQGRUGHU FRQYHUJLQJ VSHHG ZLWKRXW KDYLQJWRFRPSXWHWKH+HVVLDQPDWUL[>@

SDLUVRILQSXWRXWSXWVGDWDZHUHJDWKHUHGVDPSOHV DUH XVHG IRU LGHQWLILFDWLRQ DQG WKH UHVW DUH XVHG IRU YDOLGDWLRQ $ KLVWRJUDP VKRZLQJ WKH GLVWULEXWLRQ RI WKH SUHGLFWLRQ HUURUV RI ELRPDVV DQG JOXFRVH FRQFHQWUDWLRQ IRU YDOLGDWLRQ GDWDLVGHSLFWHGLQ)LJ 5HVXOWV VKRZ 0/3 QHWZRUN ZLWK /0 OHDUQLQJ DOJRULWKP JLYHV JRRG PRGHOLQJ SHUIRUPDQFH DQG WKH HUURUV OHVV WKDQ  7KHVH UHVXOWV MXVWLI\ WKDW WKLV PHWKRG SURYLGHV DQ HIILFLHQWDQGDFFXUDWHZD\IRUPRGHOLGHQWLILFDWLRQRI(FROL IHGEDWFKFXOWLYDWLRQSURFHVV 7KHUHIRUHWKLVWUDLQHGQHWZRUNLVDFFXUDWHDQGSURSHUIRUWKH XVHDVDPRGHOLQPRGHOSUHGLFWLYHFRQWUROOHU ,,, 1(85$/1(7:25.02'(/%$6('35(',&7,9(&21752/

7KH 1HXUDO 1HWZRUN 0RGHOEDVHG 3UHGLFWLYH &RQWUROOHU 1103& XVHVDQHXUDOQHWZRUNPRGHORIDQRQOLQHDUSODQW WR SUHGLFW IXWXUH SHUIRUPDQFH 7KH 1103& VWUDWHJ\ LV VKRZQLQ)LJ

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



+LVWRJUDPRIELRPDVVYDOLGDWLRQSUHGLFWLRQHUURU +LVWRJUDPRIELRPDVVYDOLGDWLRQSUHGLFWLRQHUURU

2QFH WKH QHXUDO QHWZRUN KDV EHHQ WUDLQHG DFFRUGLQJ WR SUHYLRXV VHFWLRQ WKH QHWZRUN FDQ EH XVHG DV DQ LQWHUQDO PRGHO RI D SUHGLFWLYH FRQWUROOHU 7KH 0/3 JHQHUDWHV SUHGLFWLRQRIIXWXUHSURFHVVRXWSXWVRYHUSUHGLFWLRQKRUL]RQ 7KH SUHGLFWLRQV DUH SDVVHG WR D QXPHULFDO RSWLPL]DWLRQ URXWLQHZKLFKDWWHPSWVWRPLQLPL]HDVSHFLILHGFRVWIXQFWLRQ   LQ VHDUFKLQJ DQ RSWLPDO FRQWURO VLJQDO X W  DW HDFK VDPSOHLQVWDQW





       





 )LJ7KHQHXUDOQHWZRUN0RGHOEDVHG3UHGLFWLYH&RQWUROOHUVWUXFWXUH



+LVWRJUDPRIJOXFRVHYDOLGDWLRQSUHGLFWLRQHUURU +LVWRJUDPRIJORFRVHYDOLGDWLRQSUHGLFWLRQHUURU

7KH FRVW IXQFWLRQ RI WKH SUHGLFWLYHFRQWUROVWUDWHJ\KDVWKH IRUPRIDVIROORZV -

1

¦ \Ö W  L  U W  L

L 1



 4

1X

 ¦ 'X W  M   M 

 5

  

7KHPRGLILFDWLRQRIWKHFRQWURODFWLRQLVRQO\OLPLWHGLQ1X VWHSVZKHUH1XLVFRQWUROKRUL]RQDQG1X1VR



X W1X X W1X « X W1   

  

,Q   \Ö W  L LVSUHGLFWHGRXWSXWVYHFWRUU WL LVUHIHUHQFH













)LJ+LVWRJUDPRISUHGLFWLRQHUURURIELRPDVVDQGJOXFRVH FRQFHQWUDWLRQ

VLJQDOVYHFWRUDQG 'X LVLQFUHPHQWRILQSXWYHFWRUV5DQG 4DUHZHLJKWLQJPDWUL[HVDQG 1DQG1DUHPLQLPXPDQG PD[LPXPSUHGLFWLRQKRUL]RQVDQG1XLVWKHFRQWUROKRUL]RQ

2368

 



7KHVHSDUDPHWHUVPXVWEHWXQHGDVFRQWUROOHUSDUDPHWHUV 7KH RSWLPL]DWLRQ VWUDWHJ\ ZKLFK LV XVHG LV 4XDVL1HZWRQ 4XDVL1HZWRQ PHWKRGV DUH SUREDEO\ WKH PRVW SRSXODU JHQHUDO SXUSRVH DOJRULWKPV IRU XQFRQVWUDLQHG RSWLPL]DWLRQ :H XVHG WKH %)*6 %UR\GHQ)OHWFKHU*ROGIDUE6KDQQR  DOJRULWKPIRUXSGDWLQJWKHLQYHUVH+HVVLDQ>@

1103& FRXOG WUDFN WKH UHIHUHQFH WUDMHFWRULHV YHU\ JRRG &RPSDULVRQ RI SHUIRUPDQFH ZLWK WKH 03& EDVHG RQOLQHDU PRGHOLQGLFDWHGWKDW1103&JDYHEHWWHUUHVXOWVLQWUDFNLQJ UHIHUHQFHWUDMHFWRULHVGXULQJWKHSURFHVV

2SWLPL]DWLRQSUREOHPZDVVROYHGLQHDFKVDPSOLQJLQWHUYDO %H\RQGWKHFRQWUROKRUL]RQWKHFRQWUROVLJQDOLVDVVXPHGWR EH FRQVWDQW ǻX N  M  M 1X1  2QFH X N  LV FRPSXWHG IROORZLQJ WKH UHFHGLQJ KRUL]RQ SULQFLSOH RQO\ WKHILUVWHOHPHQWRIWKHRSWLPDOFRQWUROVHTXHQFHLVXVHGDV WKH FXUUHQW FRQWURO YDOXH 7KHQ WKH KRUL]RQ ZLOO EH VKLIWHG RQHVWHSDKHDGLQWLPHDQGWKHZKROHSURFHGXUHLVUHSHDWHG >@ $IWHUVRPHWULDOWXQLQJSDUDPHWHUVDUHVHOHFWHGDVEHORZ 1 1 1X 5 4 >@



7KHVDPSOHWLPHLVHTXDOWRPLQ

)LJ%LRPDVVFRQFHQWUDWLRQRYHUKRXUV'DVKHGOLQHUHIHUHQFH WUDMHFWRULHV6ROLGOLQH1103&UHVXOWV

7KH SURSRVHG DSSURDFK KDV EHHQ LPSOHPHQWHG LQ WKH 0$7/$% HQYLURQPHQW DQG WKH DYHUDJH RSWLPL]DWLRQ WLPH UHTXLUHG GXULQJ RQOLQH RSWLPL]DWLRQ LV DERXW  VHF WKXV VPDOOHU WKDQ WKH VDPSOLQJ WLPH  7KLV IDFW HQVXUHV WKDW LQ HDFK VDPSOH WLPH WKH 1103& FRQWUROOHU KDV HQRXJK WLPH IRU LWV FDOFXODWLRQV DQG WKH RSWLPL]DWLRQ LV SHUIRUPHG LQ D UHDVRQDEOHWLPH 7KH UHIHUHQFH WUDMHFWRULHV DUH FKRVHQ DFFRUGLQJ WR H[SHULPHQWDOGDWDREWDLQHGIURPSUHYLRXVUHVHDUFKHV>@ ,QWKHVLPXODWLRQWKHV\VWHPRXWSXWUHVSRQVHVDFFRUGLQJWR WKHUHIHUHQFHWUDMHFWRULHVDUHGLVFXVVHG )LJ DQG )LJ VKRZ WKH UHVSRQVHV RI WKH SURSRVHG FRQWUROOHU ,W FDQ EH VHHQ WKDW WKH FRQWUROOHU DSSURSULDWHO\ WUDFNV ELRPDVV DQG JOXFRVH FRQFHQWUDWLRQ WUDMHFWRULHV DQG WKHFRQWUROREMHFWLYHLVUHDFKHG

 )LJ*OXFRVHFRQFHQWUDWLRQRYHUKRXUV'DVKHGOLQHUHIHUHQFH WUDMHFWRULHV6ROLGOLQH1103&UHVXOWV

,W LV REYLRXV WKDW WKH QHXUDO QHWZRUN SUHGLFWLYH FRQWUROOHU KDVJRRGSHUIRUPDQFHDQGIDVWWUDFNLQJDELOLW\

 5()(5(1&(6

,9 &21&/86,21

,Q WKLV ZRUN WKH QHXUDO QHWZRUN PRGHO EDVHG SUHGLFWLYH FRQWUROOHU ZDV LQYHVWLJDWHG IRU UHFRPELQDQW ( FROL IHG EDWFK IHUPHQWDWLRQ XQGHU PD[LPXP DWWDLQDEOH VSHFLILF JURZWK UDWH IRU SURGXFLQJ Ȗ,QWHUIHURQ SURWHLQ ZLWK PD[LPXP FHOO GHQVLW\  J/ '&:  DQG UK,)1Ȗ FRQFHQWUDWLRQ J/ DIWHUK )RUWKLVSXUSRVHILUVWWKHSURFHVVZDVPRGHOHGE\DQ0/3 QHXUDOQHWZRUNEDVHGRQH[SHULPHQWDOGDWD7UDLQLQJRIWKH QHWZRUN ZDV GRQH ZLWK /HYHQEHUJ0DUTXDUGW DOJRULWKP 9DOLGDWLRQ UHVXOWV DSSURYH WKLV DSSURDFK ZDV DFFXUDWHO\ PRGHOHG WKH $0 SURFHVV DQG FDQ EH XVHG DV DQ LQWHUQDO PRGHOIRUQRQOLQHDUPRGHOSUHGLFWLYHFRQWUROOHU 7KH QHXUDO QHWZRUN PRGHO ZDV XVHG WR SUHGLFW WKH IXWXUH SURFHVV UHVSRQVH LQ WKH 103& ,W ZDV REVHUYHG WKDW

>@ .LP % 6 /HH 6 & /HH 6@ 5HQDUG ) :RXZHU $ 9 9DOHQWLQRWL 6 ³$ SUDFWLFDO UREXVW FRQWURO VFKHPH IRU \HDVW IHGEDWFK FXOWXUHV$Q H[SHULPHQWDO YDOLGDWLRQ´ - 3URFHVV &RQWURO      >@ 0DKPRRGL63RVKWDQ--DKHG0RWODJK00RQWD]HUL$ ³1RQOLQHDU PRGHO SUHGLFWLYH FRQWURO RI D S+ QHXWUDOL]DWLRQ SURFHVV EDVHG RQ :LHQHU/DJXHUUH PRGHO´ &KHPLFDO (QJLQHHULQJ-RXUQDO  

2369

 



>@ .LWWLVXSDNRUQ37KLWL\DVRRN3+XVVLDQ0$'DRVXG: ³1HXUDO 1HWZRUN EDVHG PRGHO SUHGLFWLYH FRQWURO IRU VWHHO SLFNOLQJSURFHVV´-SURFHVVFRQWURO  

>@7HPHQJ . 2 6FKQHOOH 3 ' PDF$YR\ 7- ³0RGHO SUHGLFWLYH FRQWURO RI DQ LQGXVWULDO SDFNHG EHG UHDFWRU XVLQJ QHXUDOQHWZRUNV´-3URF&RQW9RO  

>@ 0RKVHQL 6 9DOL $5 %DEDHLSRXUH 9 ³'HVLJQLQJ QHZ FRQWUROOHU IRU IHGEDWFK FXOWLYDWLRQ RI UHFRPELQDQW ( FROL´ 3URF2IWK&KLQHVHFRQWUROFRQIHUHQFH  

>@5RHYD 2 7]RQNRY 6 ³0RGHOLQJ RI ( FROL &XOWLYDWLRQV $FHWDWH,QKLELWLRQLQD)HGEDWFK&XOWXUH´%LRDXWRPDWLRQ   

>@ 'XWWD 3 5XVVHOO 5KLQHKDUW 5 ³$SSOLFDWLRQ RI QHXUDO QHWZRUN FRQWURO WR GLVWLOODWLRQ DQG DQ H[SHULPHQWDO FRPSDULVRQ ZLWK RWKHU DGYDQFHG FRQWUROOHUV´ ,6$ 7UDQVDFWLRQV  

>@@ 6FKORWWKDXHU * *DPHUR / * 7RUUHV 0 1LFROLQL * $ ³0RGHOLQJ LGHQWLILFDWLRQ DQG QRQOLQHDU PRGHO SUHGLFWLYH FRQWURO RI W\SH , GLDEHWLF SDWLHQW´ 0HGLFDO (QJLQHHULQJ  3K\VLFV  ±

>@0$ +HQVRQ ³1RQOLQHDU PRGHO SUHGLFWLYH FRQWURO FXUUHQW VWDWXV DQG IXWXUH GLUHFWLRQV´ &RPSXWHUV DQG &KHPLFDO (QJLQHHULQJ    ±

>@ 0 1¡UJDDUG ³1HXUDO 1HWZRUN %DVHG 6\VWHP ,GHQWLILFDWLRQ 7RROER[´ 7HFK 5HSRUW ( 'HSDUWPHQW RI $XWRPDWLRQ7HFKQLFDO8QLYHUVLW\RI'HQPDUN  

>@0$+XVVDLQ³5HYLHZRIWKHDSSOLFDWLRQRIQHXUDOQHWZRUNV LQ FKHPLFDO SURFHVV FRQWUROVLPXODWLRQ DQG RQOLQH LPSOHPHQWDWLRQ´ $UWLILFLDO ,QWHOOLJHQFH LQ (QJLQHHULQJ  ±





 





                             

2370