Supervision, Control and Optimization of Biotechnological Processes Based on Hybrid Models

Suprviin, Cntrl and Optimizatin f Bitchnlgical rc Bad n Hybrid Mdl Dirtatin zur Erlangung d akadmichn Grad Dktr-Ingniur (Dr.-Ing.) vrglgt dr Vn dr Mathmatich-Naturwinchaftlich-Tchnichn Fakultät - Fachbrich Vrfahrntchnik - dr Martin-Luthr-Univrität Hall-Wittnbrg vn Dipl. Ing. Rui Manul Frita Olivira gb. am 31. Mai 1969 in Faf/rtugal Gutachtr: 1. rf. Dr. rr. nat. habil. Andra Lübbrt 2. rf. Dr.-Ing. habil. Martin Smmrfld 3. rf. Dr.-Ing. habil. Sbatiã Fy d Azvd Dkan dr Fakultät: rf. Dr. rr. nat. habil. R. Nubrt Datum dr Vrtidigung: 31. Augut 1998

I Acknwldgmnt I acknwldg Anglika and Wilhlm fr th mt frindly Willkmmn in Dutchland. Thy wr my firt cntact in Grmany and, a mattr f fact, it rvald itlf t b a vry plaant firt cntact. Thy aitd m n larning Grman and many thr thing abut Grmany, including th bt bir, th bt fd, and vral intrting plac t viit. I acknwldg Traudl and Hrbrt fr th wknd in Grnau, with marvllu mal, and alway frindly rcptin. Thi wa th idal nvirnmnt fr fighting many tr ituatin. I acknwldg thm vry pcially fr th warm rcptin n Chritma. I acknwldg all my wrk grup cllg in rtugal in FEU and UM: Antni Frrira fr th hlp n almt vrything cncrning ftwar, hardwar and prgramming, Eugni Frrira fr imprtant tip abut adaptiv ytm thry, Filmna Olivira fr th knwhw n bakr yat cultivatin, Margarida fr th tip n ptimizatin, and vry pcially Jana fr th nrmu ympathy. I acknwldg all my wrk grup cllg in Grmany in TCI and MLU. Thr ar lt f ppl I hav t acknwldg. I ll bgin with Martin Manikwki jut by aying that h wa a grat cllg and i n f th bt frind I vr had. I acknwldg Ditr fr th upprt h gav m in many difficult lif ituatin, what h did and till d in a way that nly vry gd frind can d, and f cur, fr th bakr yat data. I acknwldg ur NT pcialit, Stphan Klumann, wh btwn many thing, hlpd a lt t imprv my cial lif in Grmany. I acknwldg Dr. Lapin and Dr. Simuti fr th xcllnt cintific upprt. Thy jut knw vrything abut cmputr and bitchnlgy. T wrk with thm wa an hnur. I acknwldg Franc fr th big hlp in dvlping HYBNET hlp ytm. I acknwldg Dr. Havlik and Dr. Dr fr th hardwar and ftwar upprt. I acknwldg Wlfgang Claa mainly fr th gd dipitin. I acknwldg Dr. Vlk fr th hlp in all th prliminary papr wrk at th MLU fr th prnt hd wrk. I acknwldg rf. S. Fy d Azvd and rf. A. Lübbrt fr th cintific uprviin. Thy gav m a vry pitiv rintatin in many diffrnt apct. Bth f thm tk an activ rl n dvlping th prnt wrk fr what I mt incrly acknwldg. I acknwldg Ank jut fr th hlp n almt vry apct f my lif in Grmany. Sh vn tk an activ rl n typing thi thi bcau I brk my hand n and a half mnth bfr th dadlin. I acknwldg vry pcially my Mthr and my Fathr fr th givn pprtunity. Thy nvr dubtd that thi wa a drvd pprtunity. I acknwldg thm mt incrly fr th givn financial upprt. I ddicat my thi, which rprnt 4 yar f my lif f hard wrk, t my daughtr Linn hilmna. Sh had th magic t mak m frgt all th prblm jut by miling. rblm that md impibl t lv fw mmnt bfr. Sh wa and h i a ran t liv t b happy and t kp fighting. Whatvr it happn in th futur, I ll kp it thi way. THANK YOU LINN!

II Summary rc ptimiatin, uprviin and cntrl ar bcming incraingly imprtant iu du t hard cmptitin btwn cmpani. Still, th accptanc and implmntatin f mdlbad mthdlgi fr prc imprvmnt rmain rathr limitd in th indutry, mainly bcau th bnfit/ct rati i nt yt clarly attractiv fr uch dvlpmnt in prc pratin. Th main gal f th prnt hd thi i t dvlp mthdlgi t imprv thi bnfit/ct rati in th indutrial practic. Bichmical prc ar vry cmplx and ftn prly undrtd n a mchanitic bai, particularly in what cncrn th micrrganim grwth mchanim. In th claical apprach fr prc analyi mathmatical mdl, bad n firt principl, ar ud t rprnt th mchanitic a priri knwldg abut th prc in tudy. Mt ftn thi apprach lad t cmplx mdl mad f prly undrtd mchanim, th lattr charactrid by paramtr with a vry lw lvl f cnfidnc. It may lad t pr prc dcriptin and hav t high dvlpmnt ct invlvd. Th main ubjct f thi wrk cncrn th arch and tudy f mthdlgi fr intgratd u f all availabl a priri prc knwldg, frm mchanitic t huritic knwldg, aiming at a mr accurat prc dcriptin with lwr dvlpmnt ct. In thi rpct, th hybrid mdlling apprach ha bn xtnivly tudid and dvlpd. In particular, a nw apprach fr hybrid mdlling wa dvlpd bad n th cncpt f hybrid ntwrk. Hybrid ntwrk prvid man t incrprat arbitrarily in n cmputatinal tructur all urc f a priri knwldg in th lvl f phiticatin availabl in practic. Thy can b ud fr prc idntificatin, n-lin and ff-lin prc ptimiatin, prc cntrl and prc uprviin. Thy hav th additinal vry attractiv prprty that th backprpagatin tchniqu can b applid t upprt paramtr idntificatin and nitivity analy. A rlvant rult wa th dvlpmnt f th HYBNET ftwar packag, which implmnt th cncpt f HYBrid NETwrk. Th ftwar wa dignd t prvid all th ncary tl t lv typical tak f prc ptimiatin and cntrl uually fund in th indutry. A vry imprtant gal wa th dvlpmnt f a narly platfrm indpndnt and ay t implmnt link btwn hybrid ntwrk bad algrithm and th prc. Thi, jintly with an ur-frindly graphical intrfac, ar rcgnid t b dciiv pr-rquiit fr a gd accptanc in th indutrial nvirnmnt. Th thr imprtant iu tudid in th prnt wrk wa th prblm f fficint and ratinal u f prc infrmatin n-lin. Whn n-lin infrmatin i availabl, it i pibl t u a cmprmiing lutin, mplying algrithm bad in implifid mdl, cmplmntd with n-lin adaptatin chm. Such a cmprmiing apprach i prntd hr. Th dvlpmnt f mdl auming n knwldg abut th micrrganim grwth kintic i rathr impl and, cnquntly, ffrt wa put n dvlping tratgi fr n-lin timatin f ractin kintic frm data availabl n-lin. With thi rpct tw tabl and ay t tun n-lin ractin rat timatin algrithm hav bn dvlpd. Thy xplr th rlatinhip btwn tability and dynamic f cnvrgnc, imping cnvnint cnd-rdr trajctri fr th timatin rrr. Tuning rquir nly th tting f th paramtr charactritic f cnd-rdr rpn - th damping cfficint and th natural prid f cillatin. Thi rprnt a lwr dvlpmnt ct than th ct f th uual 'trial and rrr' tchniqu mplyd in th daily practic f indutrial prc pratin.

III Zuammnfaung rzßptimirung, Übrwachung und Kntrll wird durch dn hartn indutrilln Wttbwrb immr wichtigr. Trtzdm blibt di Akzptanz inr rzßptimirung mit Hilf vn Mdlln in dr Indutri gring, vr allm wgn ihrr zu klinn Gwinn- /Ktn-Vrhältni. Da Hauptzil dr vrligndn Arbit it, Mthdn zu ntwickln, um da Vrhältni vn Gwinn zu Ktn in dr indutrilln rduktin zu vrbrn. Bichmich rz ind hr kmplx und i.a. in mchanitichr Hinicht ungnügnd aufgklärt und vrtandn. Bim klaichn Wg dr rzßvrbrung rpräntirn mathmatich Mdll da mchanitich a priri Win d zu untruchndn rz. Di Flg davn it, daß vil dir Mdll dn rzßvrlauf ungnügnd dartlln und zu hh Entwicklungktn implizirn. Da ffizint Nutzn d vrhandnn a priri Win it in Hauptthma dir Arbit. Di Nutzung allr vrhandnn -mchanitichn und huritichn- Winqulln führt zu inr gnaurn rzßbchribung und nidrigrn Entwicklungktn. Di Mthd dr Hybrid-Mdllirung wurd xtniv untrucht und ntwicklt. Inbndr in nu Mthd dr Hybrid-Mdllirung, bairnd auf dm Knzpt in hybridn Ntzwrk, wurd ntwicklt. Hybrid Ntz lifrn di Möglichkit dr arbiträrn Intgratin allr zur Vrfügung tllndn Qulln d a priri Win in inr Mdlltruktur. Si könnn zur rzßidntifizirung, n-lin und fflin rzßptimirung, -kntrll und -übrwachung gnutzt wrdn. Zuätzlich habn i di attraktiv Eignchaft, daß di Rückkpplungtchnik angwandt wrdn kann, um di aramtridntifizirung und Empfindlichkitanalyn zu untrtützn. Ein witr wichtig Rultat war di Entwicklung d HYBNET-Sftwar akt, da da HYBrid NETzwrk intzt. Di Sftwar it ntwrfn wrdn, daß i all nötign Intrumnt zur Barbitung vn Aufgabn dr rzßptimirung und -kntrll für di Indutri lifrt. Ein hr wichtig Zil war di Entwicklung inr quai plattfrmunabhängig und inr licht intzbarn Vrbindung zwichn dm Hybridn Ntzwrk und dm rzß. Di, zuammn mit inr bnutzrfrundlichn graphichn Obrfläch, it auchlaggbnd für di Akzptanz in dr Indutri. Mit HYBNET ind di Aufgabn dr n-lin Auführung Hybridr Ntzwrk wntlich vrinfacht wrdn. Ein andr wichtig Ergbni, da währnd dr vrligndn Arbit untrucht wurd und im ngn Zuammnhang mit dn Ktn inr rzßvrbrung durch Mdlln tht, it da rblm inr ffizintn und ratinaln Nutzung dr n-lin rzßinfrmatin. Sthn n-lin rzßinfrmatinn zur Vrfügung, btht di Möglichkit auf infachn Mdlln bairnd Algrithmn zu nutzn, rgänzt mit n-lin Anpaungalgrithmn. Di it in rlvant rblm dr rzßvrbrung mit Hilf vn Mdlln: Entwdr mhr Mittl in di rzßmdllirung dr in di Entwicklung rbutr und tabilr n-lin Anpaungalgrithmn zu invtirn. Da Optimum it in Kmprmiß zwichn bidn Entwicklungn. Mdll, di di Wachtumkintik dr Mikrrganimn nicht brückichtign, ind bndr impl. E wurd vil Wrt auf di Entwicklung vn Stratgin zur n-lin Abchätzung dr Raktinkintikn au dn vrhandnn n-lin Datn glgt. E wurdn zwi tabil und licht inzutllnd n-lin Algrithmn für di Schätzung vn Raktinkintikn ntwicklt. Di Eintllung dr Algrithmn it vn ntchidndm Einfluß auf di Entwicklungktn. Di Untruchungn charaktriirn di Bzihung zwichn Eintllung, Stabilität und Dynamik dr Knvrgnz. Da Vrhaltn dr Algrithmn it brit vr ihrm rtn Einatz bkannt. In Flg dn btht kin Ntwndigkit, di im allgminn hh Ktn binhaltnd Vruch- und Fhlr- Tchnikn durchzuführn.

Cntnt Chaptr ag Acknwldgmnt Summary Zuammnfaung I II III 1 Intrductin 1-21 2 Hybrid Ntwrk: A Nw Apprach fr Biprc Hybrid Mdling 22-4 3 HYBNET, an Advancd tl fr rc Optimizatin and Cntrl 41-53 4 Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk 54-75 5 A Study n th Cnvrgnc f Obrvr-bad Kintic Etimatr in Stirrd Tank Ractr 76-89 6 On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc 9-126 7 Cncluin 127-132 Curriculum Vita 133 ublicatin Lit 134-135

Chaptr 1. Intrductin Chaptr 1 Intrductin Abtract. rc ptimizatin, uprviin and cntrl ar bcming an incraingly imprtant iu du t hard cmptitin btwn cmpani. Still, th accptanc f mdl-bad mthdlgi rmain rathr limitd in th indutry, mainly bcau th bnfit/ct rati i nt clarly attractiv fr uch dvlpmnt. In th claical mdlbad apprach, mathmatical mdl ar ud t dcrib th rlvant biprc mchanim. Mainly du t th intrinic cmplxity f bilgical ytm, biprc ar nt yt wll undrtd frm a mchanitic pint f viw. Th main implicatin t b nticd i that th ynthi f mchanitic mathmatical mdl i gvrnd by a rathr rtrictiv cmprmi btwn implicity and dvlpmnt ct. Unfrtunatly th cmmn ituatin in th indutry i that mdl dvlpd at tlrabl ct ar nt accurat nugh t lv th undrlying ptimizatin, uprviin and cntrl prblm. Th main bjctiv f th prnt h.d. dirtatin i t giv nticabl tp ahad fr incraing th bnfit/ct-rati f a mdl-bad way f prc imprvmnt. With thi rpct tw main rarch lin ar dfind: (i) Hybrid mdling a an fficint altrnativ t th claical mathmatical mdling apprach and (ii) fficint and ayt-implmnt n-lin adaptatin algrithm. 1

Chaptr 1. Intrductin 1 MODEL-BASED SUERVISION, CONTROL AND OTIMIZATION OF BIOROCESSES A bitchnlgy bcm mr dvlpd and xtndd all vr th wrld, th cmptitin btwn diffrnt cmpani i bcming hardr. Th gnral cnqunc t b nticd i that th cmpani ar taking a clr lk t cnmic f thir prductin prc. Frm th bichmical nginring pint f viw, th traightfrward way f imprving th cnmic i t invt in prc ptimizatin and cntrl. In indutrial practic, imprvmnt ar ftn achivd by mr r l ducatd trial and rrr mthd, i.. by mpirical mthd guidd by intuitin and xprinc. Gd luck i an ntial cnditin t b uccful in thi way. Othr prfr ytmatic apprach, which, n th avrag, lad t a fatr rat f imprvmnt. Th ytmatic apprach i charactrizd by a cnqunt utilizatin f th a priri knwldg abut th prc. Uually, th numbr f xprimnt rquird can b kpt much mallr in thi way. Thu, w xpct a ignificant rductin f xpn. Mt ftn, mathmatical prc mdl ar cnidrd t rprnt th a priri knwldg. Whn w pak abut mdl in bichmical nginring and in particular with rpct t prc ptimizatin and cntrl, w think f rlatinhip, which dcrib th baic apct f th ral prc that ar mt imprtant t prc prfrmanc. On main dmand i that th prc mdl allw t rprnt th rlvant prc prprti quantitativly and mak thm accibl t fficint cmputatinal analyi and ptimizatin tchniqu. In bitchnlgy, claical mathmatical mdl ar cntructd uing m mchanitic cncpt, which ar mbddd int ma balanc, i.. a rlativly impl t f diffrntial quatin (.g. Snnlitnr and Käppli, 1986). Rcntly, m altrnativ mthd f rprnting biprc wr dicud in litratur, in particular artificial nural ntwrk and fuzzy xprt ytm (Thmn and Kramr, 1994, Lübbrt and Simuti, 1994) ar ud t xtnd th claical apprach. In rdr t lv th tak f imprving th prc prfrmanc, it i indipnabl t dfin bfrhand hw t maur th prgr. What w nd i a quantitativ critrin frmulatd by man f an bjctiv functin. Such an bjctiv functin may b a rathr cmplicatd functin, inc it huld nt nly cnidr th main bjctiv,.g. th ptimizatin f th vlumtric prductivity with rpct t th main prduct, but al th practical bundary cnditin which mut b mt during prductin. Onc w hav uch an bjctiv functin fr th prc prfrmanc, w ar al abl t dfin what w ar maning by mdl prfrmanc: Th prfrmanc f a mdl i imply th advantag it bring in imprving th prc prfrmanc with rpct t th bjctiv functin. 2

Chaptr 1. Intrductin Evidntly, th numbr f indutrial prductin ractr, whr mdl upprtd prc uprviin, ptimizatin, and cntrl i applid, i vry lw. Thr ar a numbr f ran. Th mt ignificant n ari in cnnctin with th prblm f activating nugh knwldg abut th prc undr cnidratin. Mrvr, t cmplicatd mdling and ptimizatin prcdur ld t high dvlpmnt tim. Thrfr, in mt practical attmpt mad far th bnfit/ct rati appard t b t lw. Entially bth factr, th ct a wll a th bnfit, did nt jutify mdl upprtd ptimizatin and cntrl (Ryc, 1993). 2 ROCESS MODELS FOR WHAT? Mdl can b ud t upprt biprc imprvmnt in many diffrnt way. In th prnt wrk th intrt i dvtd t th apct rlatd t prc ptimizatin, cntrl and uprviin. Thr pcific applicatin f mdl ar tratd in th prnt h.d. thi. Thy ar brifly intrducd in th fllwing lin. A vry imprtant applicatin f mdl i upprting th dtrminatin f ptimal prc trajctri. Thi i cmmnly rfrrd t a prc ptimizatin r pn-lp cntrl (Simuti t al., 1997). Th main ida i th idntificatin f ptimal prfil fr th rlvant manipulatd variabl, uch a ubtrat input fd rat, with th bjctiv f imping an ptimal path t th prc, accrding t a pr-tablihd ptimal prc prfrmanc critrin. Thi ptimal critrin mut b carfully tatd in th frm f an bjctiv functin which mut cnidr th rlvant prc cntraint. Opn-lp cntrl rquir accurat mdl fr rprducing a cl a pibl th ral rpn f th prc t hypthtical prfil f th manipulatd variabl. A critical iu in thi rpct i rlatd t th xtraplatin capabiliti f th mdl. Such a dvlpmnt i prfrmd ff-lin rlying cmpltly n th accuracy and xtraplatin capabiliti f th prc mdl. Th imprtant cnqunc t b nticd i that mdl fr pn-lp cntrl mut dcrib th rlvant mchanim rlatd t th prtablihd bjctiv functin. rc dynamical mdl ar ftn ud t dign cntrl ytm, what i cmmnly rfrrd t a mdl-bad cntrl ytm dign. In thi rpct mdl can b ud t driv cntrl algrithm and t tun th cntrllr paramtr invlvd. rprti lik tability, rbutn, and tracking dynamic f cntrl variabl t thir tpint mut b carfully tudid bfr th cntrl ytm i ttd in th ral plant. Whn th undrlying dynamical mdl i narly tim-invariant, and prvidd that thr i nugh prc data t idntify it within th prc wrking rgin, th cntrl ytm dign can b dn in an ff-lin fahin. Unfrtunatly th cmmn ituatin i that bichmical prc hav trng tim-varying dynamic. T cp with th impibility f dvlping mdl (and cntrllr bad n th mdl) dcribing fully th dynamic f th prc, n-lin adaptatin chm mut b implmntd. Such a cntrl tratgy i uually trmd a mdl-bad adaptiv cntrl. Anthr imprtant applicatin f mdl i dvlping ftwar nr. Sftwar nr nabl th timatin f variabl n-lin which cannt b maurd dirctly. Th knwldg f th variabl might b imprtant t upprt thr n-lin applicatin uch a mnitring, cntrl, and fault dtctin. Quit ftn ftwar 3

Chaptr 1. Intrductin nr ar tat timatr which nabl th calculatin f unknwn variabl frm thr variabl aily accibl n-lin. Sftwar nr can al b paramtr timatr. A typical applicatin i mnitring ractin kintic. Sftwar nr rquir n-lin prc data and can al b adaptiv. 3 THE CLASSICAL WAY OF DEVELOING BIOROCESS MODELS In th claical apprach f dvlping biprc mdl, mathmatical rlatin ar mplyd fr dcribing th rlvant mchanim. Frm th nginring pint f viw, tw main ytm mut b analyzd: (i) th biractr ytm and (ii) th bilgical cll ytm. Biractr mdl dal with ma tranfr apct and flw pattrn in bth ga and liquid pha. Cll mdl dal with th kintic n th individual cll lvl and n th whl cll ppulatin lvl. Th biractr ytm and th cll ytm hav vry cmplx intractin and cannt b analyzd paratly. Th living micrrganim ar tranfrming cntinuuly th liquid pha by cnuming vral nutrint, which ar mtablizd int vral prduct, m f thm xcrtd in th urrunding mdia. Th mtablim i al influncd by vral phyical variabl, uch a tmpratur, prur, light intnity, tc. In th prnt chaptr, th dicuin cncrn a particular typ f biractr, th tirrd tank biractr, which i th n mt ftn fund in indutrial prductin prc. 3.1 Tranprt prc Whn dvlping a mdl fr a biractr w ar mainly intrtd n a dcriptin f th dynamic f th macrcpic quantiti that influnc th bhavir f th micrrganim. Thy ar cncntratin in th brth f vral cmpnnt uch a bima, ubtrat, and prduct, and al vral phyical quantiti uch a tmpratur and prur. Th variabl ar uually calld tat variabl inc thy dfin th prc tat. A mathmatical dynamical dcriptin f th tat variabl i btaind by applying gnral ma, nrgy and mmntum cnrvatin law (Rl t al., 1978). Th chic f th t f tat variabl t cnidr i vry much dpndnt n th bjctiv f th mdl. Whn, fr intanc, th tmpratur i kpt cntant by man f a vry impl ID cntrl, thr i n nd t includ th variabl tmpratur in th tat pac vctr. Thi prvnt th ncity f mplying macrcpic nrgy balanc fr dcribing th prc tat. Thy mak hwvr n if th bjctiv f th mdl i digning th tmpratur ID cntrllr, and pcially in larg cal biractr whr cling prblm ar likly t b fund (Humphry, 1998). A vry prblmatic iu cncrn th rhlgical ffct in biractr. In gnral th mdling f flw pattrn i far t cmplx. And pcially in th ca f tirrd tank biractr. Th ntial implicatin t b nticd i that in bth indutrial and rarch applicatin th ffct ar ytmatically ignrd (Klintrur, 1987). Almt invariably th aumptin i takn that bth liquid and ga pha ar wll mixd, i.. th mdium i aumd t b hmgnu. Frm th mathmatical and numrical pint f viw thi intrduc an nrmu implificatin inc, thrwi, an xtrmly cmplx analyi bad n ditributd paramtr ytm wuld hav t b prfrmd (.g. Ryc, 1996). Undr thi aumptin, and by cnidring that tmpratur, prur and ph ar uually cntrlld quantiti bing kpt at cntant 4

Chaptr 1. Intrductin valu, thr i lly th ncity f applying ma balanc principl t th rlvant cmpnnt. Thi lad t th fllwing t f rdinary diffrntial quatin: dx dt = R + F V (X in - X) + Q (1) whr X rprnt a vctr f cncntratin in th brth (th tat pac vctr), R i a vctr f ractin kintic, F i th input fd rat int th biractr, V i th brth vlum, X in i a vctr f cncntratin in th input fd rat F, and Q a vctr f gau utflw rat (uch a xygn and carbn dixid tranfr rat). 3.2 Mdling ma tranfr btwn ga-liquid pha With xcptin f cling limitatin prblm uually fund in larg biractr (Klintrur, 1987), th mt frquntly ncuntrd limitatin t grwth in arbic frmntatin i dilvd xygn in th brth (Thrnhill and Ryc, 1991). Oxygn ha a vry lw lubility in frmntatin mdia in cmparin t thr typical ubtrat (Stanbury and Whitakr, 1984). Thrfr it mut b cntinuuly upplid, uually by aratin. Th ma tranfr capacity btwn ga and liquid pha i a cntral prblm in arbic biprc dign and pratin. Th mathmatical dcriptin f th xygn tranfr rat frm th ga pha int th liquid pha i bad n gnral cncpt f ma tranfr thry. Th main ritanc fr xygn tranfr frm th gau pha int th mdium li in th liquid-id bundary layr f th ga-liquid intrfac. In gnral th fllwing ma tranfr law appli: OTR = k L a (O * - O) (2) whr OTR i th xygn tranfr rat frm th gau pha int th liquid pha, O i th dilvd cncntratin in th brth, O * i th xygn aturatin cncntratin in th brth, and k L a th glbal ma tranfr cfficint. Th applicatin f law (2) p tw main difficulti, namly th knwldg f k L a and th knwldg f O *. Th lubility f xygn in th brth i a functin f th mdia cmpitin, tmpratur and prur. Th dpndncy with tmpratur and prur can b quantifid accuratly nugh by applying Hnry law. Hwvr, th dpndncy with th mdium cmpitin i rathr difficult t dcrib and i nrmally nglctd (irt, 1975). Th glbal ma tranfr cfficint i a vry cmplx functin f th biractr gmtry, th impllr gmtry, mdium rhlgy, th aratin flw, th tirrr pd, and th cmpitin f mdia whr, fr intanc, vicity i an imprtant paramtr. Th mathmatical dcriptin f k L a i uually mad by man f mpirical crrlatin, uch a (Humphry, 1998): g a b k L a =K vl ( V) ( ) ¹ c (3) 5

Chaptr 1. Intrductin whr ( g /vl) i th gad pwr pr unit vlum, (V ) th uprficial ga vlcity and ( th brth vicity. Frm th practical pint f viw, a vry imprtant iu i that th knwldg f th maximum k L a dfin th mt imprtant cntraint in biprc ptimizatin. Th crrlatin btwn k L a, tirrr pd and air flw i al imprtant fr digning cntrl ytm fr dilvd xygn in th brth. Carbn dixid i a byprduct f cll mtablim. In many prductin prc, uch a antibitic prductin prc, th dilvd CO 2 inhibit th mtablim. Thu it mut b trippd ff th mdia. Thi i dn with th am aratin quipmnt ud t upply xygn. In th ca f CO 2 th ma tranfr ccur in th ppit dirctin, i.. frm th liquid pha int th gau pha. Th gnral ma tranfr law appli: CTR=k L a (C * C) (4) whr CTR i th carbn dixid tranfr rat frm th liquid pha int th gau pha, C i th cncntratin f dilvd carbn dixid in th brth, C * i th dilvd CO 2 cncntratin dirctly at th phyical intrfacial ara, and k L a th glbal ma tranfr cfficint. Undr th aumptin f mall-cal biractr and prfctly mixd ga and liquid pha, th valu f k L a fr CO 2 and O 2 tranfr ar rlatd accrding t th fllwing rlatinhip (Thrnhill and Ryc, 1991): (k L a)c 2 =(k L a) 2 Dc 2 D 2 (5) whr D i rfr t th diffuiviti f xygn and carbn dixid in th liquid pha. 3.3 Mdling micrrganim kintic Th ractin trm R in qn. (1) i th rult f an xtrmly cmplx mtablic ractin ntwrk n th cll lvl and n th whl cll ppulatin lvl. A mathmatical dcriptin f th cll mtablim i far t cmplx and nt f ral practical u fr indutrial applicatin. In many apct uch an analyi i impibl bcau many mtablic mchanim ar till unknwn r cannt b validatd with xprimntal maurmnt. Th cmmn ituatin i that mathmatical dcriptin f micrrganim kintic ar rugh implificatin f th rality. Svral kind f cll mdl hav bn prpd in th litratur. In gnral thy can b claifid in tructurd/untructurd and grgatd/nn-grgatd (Tuchiya t al., 1966). Cll mdl cnidring th xitnc f intracllular cmpnnt ar trmd tructurd, thrwi thy ar trmd untructurd. Thy may al aum th xitnc f a mrphlgical tructur, bing thn trmd grgatd mdl, r may aum that all cll ar idntical (nly n mrphlgical frm) bing thn trmd nn-grgatd mdl. 6

Chaptr 1. Intrductin Fr biprc ptimizatin, cntrl and uprviin, untructurd and nn-grgatd mdl ar th nly n f practical intrt. In dvlping uch mdl, principl f macrcpic tichimtry and mpirical kintic crrlatin ar mplyd. Th tarting pint f uch an analyi i th tablihmnt f a t f bichmical quatin dcribing th mt rlvant mchanim in th cll. In th mt impl vrin f uch an analyi, nly a ingl bichmical ractin i cnidrd, dcribing th whl cll mtablim. Fr intanc, a bichmical arbic ractin whr n ubtrat, ammnia and xygn ar cnumd, prducing bima, n prduct, carbn dixid and watr, with a cnvrin rat f i tatd in th fllwing way: CH O anh bo zch O N ych O N xco m l 3 2 p n q r t 2 2 (ubtrat) (ammnia) (xygn) (bima) (prduct) (carbn dix.) (watr) ch O (6) Whn th lmntal cmpitin f all th pci invlvd i knwn it i pibl t valuat th mlar tichimtric cfficint a, b, y z x and y by applying gnral ma and nrgy balanc principl (Rl, 1978; Minkvich and Erhin, 1975). Th wllknwn yild cfficint in bitchnlgy ar rlatd t th tichimtric cfficint by impl mlar- t ma-ba tranfrmatin. Fr intanc, th yild cfficint f bima prductin pr 1 gram f ubtrat cnumptin i givn by th fllwing quatin: Y x/ =z M x /M (7) whr M x and M ar th mlcular wight f bima and ubtrat rpctivly. Onc th yild cfficint ar knwn, a furthr mdl fr th pcific grwth rat i ncary. Th cnumptin and prductin kintic f all th pci ar linkd tgthr by th tichimtry, and th pcific grwth rat. Fr intanc th cnumptin rat f ubtrat i givn by: R =X/Y x/ (8) Th mathmatical dcriptin f pcific grwth rat ar in gnral bad n mimpirical crrlatin. Fr th mt indutrial applicatin th fllwing fur mdl ar mplyd: 1. Th Mnd mdl (Mnd, 1942). Thi mdl cnidr ubtrat limitatin at lw cncntratin: = max S K S +S (9) 2. Th Mr mdl (Mr, 1958). Thi i an xtnin f th Mnd mdl. = max S N K S +S N (1) 7

Chaptr 1. Intrductin 3. Th Haldan mdl (Haldan, 1942). Thi mdl cnidr ubtrat limitatin at lw cncntratin and ubtrat inhibitin at high cncntratin max S = (K S +S)(S+K i /S) (11) 4. Th Cnti mdl (Cnti, 1959). Th Cnti mdl i an xtnin f th Mnd mdl, cnidring an inhibitry ffct f cll cncntratin n grwth (uful in high cll dnity cultivatin). = max S K S X+S (12) Th u f th abv mntind kintic mdl rquir a prviu idntificatin f th paramtr invlvd. Fr intanc, whn uing th Mnd mdl (9) th maximum pcific grwth rat max, and th aturatin cfficint K mut b idntifid fr th actual cultivatin cnditin. Unfrtunatly vn fr uch a impl kintic rlatinhip a th Mnd mdl, thi idntificatin i rathr difficult, rquiring a carful xprimntal planing (Balt t al., 1994; Munack, 1989). In gnral th cupling f Mnd-typ kintic mdl with ma balanc quatin frm nn-linar dynamical ytm, which, dpnding n th it tructur, may nt b idntifiabl. In th ca whn thy ar idntifiabl thrtically, a carful (and xpniv) xprimntal dign i rquird. 4 THE HYBRID MODELING AROACH Hybrid mdling i mrging in th lat yar a a valid altrnativ t th claical mdling apprach (Schubrt t al., 1994a; ichgi and Ungar, 1992; Thmn and Kramr, 1994; Fy d Azvd t al., 1997). It i furthr a vry attractiv mthdlgy fr applicatin t bichmical prc du t it intrinic cmplxity. In th prnt ctin, th diffrnt kind f knwldg uually availabl fr bitchnlgical prc ar charactrizd. Th mdling mthd uitabl fr fficint rprntatin f ach kind f knwldg ar brifly dicud. Finally, m typical hybrid mdl tructur uually fund in th litratur ar vrviwd. 4.1 Knwldg and rprntatin f knwldg Nrmally thr i a varity f infrmatin urc n bitchnlgical cultivatin prc (Schubrt t al., 1994a; Lübbrt and Simuti, 1994). Thr ar 3 main typ f knwldg availabl, namly (i) th mchanitic (phnmnlgical) knwldg, (ii) huritic knwldg and cmmn n, and (iii) knwldg hiddn in th prc data rcrd. Th urc f knwldg can b claifid accrding t it lvl f phiticatin and rlutin f dtail ( Fig. 1). 4.1.1. Th mchanitic (phnmnlgical) knwldg. Thi kind f knwldg i uually rprntd by mathmatical mdl. Thi i th claical apprach fllwd by chmical and bichmical nginr fr dvlping thir prc mdl (.g., Vlky and Vtruba, 1992; Niln and Villadn, 1994; Rl, 1983). It ha th hight lvl 8

Chaptr 1. Intrductin f phiticatin, invlving th undrtanding f th baic tranprt and kintic mchanim. Th mchanim ar ftn prly undrtd r vn cmpltly unknwn. Thrfr thi kind f knwldg i uually th n availabl in minr quantiti. 4.1.2. Huritic knwldg and cmmn n. Thi kind f knwldg i mr qualitativ thn th frmr, but it i uually availabl in majr quantiti in th indutrial nvirnmnt. Th Fuzzy thry, firt dvlpd by Zadh (1973), i ftn ud t build huritic knwldg bad mdl. Thi thry prvid mthd fr qualitativ knwldg rprntatin with mathmatical prciin. Huritic knwldg i ftn tatd in trm f rul f thumb. Th can b radily rprntd by th -calld knwldg bad ytm uch a fuzzy infrnc ytm and xprt ytm (.g. Sugn, 1985; Kk, 1992; Wang, 1994). Lvl f phiticatin Dtail rlvd high Mchanitic knwldg high mdium Huritic knwldg and cmmn n mdium lw rc data acquird during prc pratin lw Fig 1. Hirarchical tructur f prc knwldg, lvl f phiticatin f it cmpnnt and rlutin f dtail 4.1.3. Knwldg hiddn in th prc data acquird during prc pratin. Unfrtunatly, in many ituatin th availabl mchanitic and/r huritic i nt ufficint t dvlp a prc mdl with th dirabl accuracy. In thi ituatin datadrivn mdling mthd can b ud t imprv th accuracy f th mdl. In many indutrial plant th rlvant cau/ffct mchanim hav bn rgitrd fr dcad in th frm f prc input/utput data. Sm f th mchanim hav bn at lat brvd by th ppl prating th plant, but many f thm hav bn jut rcrdd in prc data fil and pad cmpltly unawar. Th mdling f unknwn part f th prc can b mad uing th -calld black bx mthd uch a plin, plynm, furir ri, r artificial nural ntwrk (ANN). A vry cmplt urvy f black-bx mdling in ytm idntificatin i givn by Sjöbrg t al. (1995). In particular ANN hav bn gtting a grat dal f attntin frm rarchr in th lat yar. Thy prvd t b xtrmly flxibl in rprnting cmplx nn-linar rlatinhip (.g., Cybnk, 1989; Hrnik t al., 1989; ggi and Giri, 199) 9

Chaptr 1. Intrductin withut rquiring any kind f knwldg cncrning th tructur f th undrlying mdl. Svral imprtant rult hav bn publihd cncrning th applicatin f ANN fr dynamical ytm idntificatin and cntrl (.g., Hunt t. al., 1992; llard t al., 1992; Narndra and arthaarathy, 199). ANN ar f particular intrt fr biprc mdling du t th intrinic cmplxity f biprc. 4.2 Efficint knwldg fuin Nrmally th diffrnt kind f knwldg abut a prc ar cmplmntary but in many ituatin thy vrlap. Thi ntially man that m part f th prc can b imultanuly rprntd at diffrnt lvl f phiticatin. Diffrnt rprntatin can prfrm bttr in m rgin f th input pac and wrt in m thr rgin. In thi n th diffrnt kind f knwldg ar cmplmnting thmlv. A uch, in hybrid mdling mthd fr knwldg wighting ar f cntral imprtanc. Th wighting mthd hav th tak f dciding which mdl prfrm bttr fr th currnt t f mdl input, and accrding t thi, t dynamically wight th utput f ach diffrnt rprntatin fr th valuatin f th final mdl utput ( Fig. 2). Th wighting mthd ar rpnibl fr fficint knwldg fuin. MECHANISTIC KNOWLEDGE - Ma balanc quatin, - Enrgy balanc quatin, - Mmntum balanc quatin, tc... WEIGHTING BLOCK Mdl Input HEURISTIC KNOWLEDGE - Fuzzy ytm - Exprt ytm - Crrlatin, tc... KNOWLEDGE HIDDEN IN DATA - Artificial nural ntwrk - Splin - lynm - Furir ri, tc... - Clutr bad mnitring, - Fuzzy/xprt ytm, - Artificial nural ntwrk Mdl Output Fig. 2. Gnric way f incrprating diffrnt kind f a priri infrmatin in a ingl mdl tructur: phyical knwldg, huritic knwldg and knwldg hiddn in prc data. Th wighting blck mut valuat dynamically th rlativ wight f diffrnt kind f rprntatin fr th final valuatin f th mdl utput. Sm xampl f wighting mthd hav bn rprtd in th litratur, frm which th mt imprtant ar: 1

Chaptr 1. Intrductin 1) Wighting mthd bad n clutring tchniqu (.g., Simuti t al., 1995; Lnard t al., 1992) 2) Wighting mthd bad n xprt ytm (.g., Schubrt t al., 1994b) 3) Wighting mthd bad n artificial nural ntwrk (.g., Haykin, 1994) Clutring tchniqu can bn ud fr mnitring th rliability f artificial nural ntwrk (.g., Simuti t al., 1995; Lnard t al., 1992). Th main ida i t rprnt in a cmpact way th input pac ( Fig. 3) which dfin th dmain f xprinc f th artificial nural ntwrk bing mnitrd. In thi way it i pibl t valuat th xtraplatin maur f th nural ntwrk prdictin fr givn input vctr. Thi xtraplatin maur i th ba f dciin n uing th nural ntwrk mdl r m thr mdl with bttr xtraplatin prprti. y y x 1 x 2 x 1 x 2 Fig. 3. Clutring f a 2-dimninal input data pac by man f multivariat gauian hapd functin Anthr typical apprach i bad n Fuzzy ytm. It can b applid whn thr i ufficint huritic knwldg abut th mdl prfrmanc in diffrnt part f th input pac. A typical t f rul i a fllw: RULE 1. IF input pac i cmpltly unknw THEN u nly mchanitic mdl RULE 2. IF input pac i prly knwn THEN u mchanitic and huritic mdl RULE N. IF input pac i cmpltly knwn THEN u nly ANN mdl Thi apprach i again bad n th intrplatin and xtraplatin capabiliti f diffrnt kind f mdling tchniqu. An xampl f uch a Fuzzy wighting mthd i givn by Schubrt t al. (1994b). 4.3 Typical hybrid mdl tructur Svral hybrid mdl tructur hav bn publihd in th litratur. An imprtant cla f th tructur ar th nural-fuzzy ytm. Th nural-fuzzy ytm cmbin artificial nural ntwrk and fuzzy lgic in n ingl mdl tructur(.g., 11

Chaptr 1. Intrductin Gupta and Ra, 1994; Wrb, 1992; Shi and Shimizu, 1992; Lin and Grg L, 1991). Anthr imprtant apprach fr digning hybrid mdl tructur i bad n th diviin f th prc in tudy in vral mdul accrding t th kind f knwldg availabl in diffrnt part f th prc. Th rult f uch an pratin i uually xprd by a diagram f intrcnnctd mdul. Each mdul i xprd by an input-utput rlatinhip bad n a particular mdling tchniqu. Svral authr hav bn uing a vry impl hybrid mdl tructur (.g., Wiln and Zrztt, 1997; ichgi and Ungar, 1992; Mntagu and Mrri, 1994; Fy d Azvd t al., 1997) bad n th u f artificial nural ntwrk fr dcribing th micrrganim kintic mbddd int ma balanc quatin ( Fig. 4). Hwvr, thi tructur ha majr a drawback rlatd t th pr xtraplatin capabiliti f nural ntwrk. Such a mdl can b nly ud within th data pac ud bfr fr training th undrlying artificial nural ntwrk. Kintic mdl Ma balanc quatin On-lin data ARTIFICIAL NEURAL NETWORK Ractin kintic MATHEMA- TICAL MODEL Stat variabl Z-1 Fig 4. pular hybrid mdl tructur bad n an artificial nural ntwrk fr dcribing th micrrganim kintic mbddd int a t f ma balanc quatin. T imprv th gnral xtraplatin capabiliti f uch a hybrid mdl tructur Simuti t al (1996) uggtd t includ a afty mdl ( Fig. 5) which huld b ud whnvr th ANN i prating in xtraplatin cnditin. In thi way w ar imprving th glbal xtraplatin prprti f th mdl. Mt ftn th afty mdl i bad n Mnd rlatinhip r n Fuzzy mdl. Th lattr can nly b mplyd whn thr i nugh huritic knwldg in th frm f IF(...) THEN (...) rul fr dcribing th micrrganim kintic. 12

Chaptr 1. Intrductin Kintic mdl Wighting mchanim Ma balanc quatin On-lin data ARTIFICIAL NEURAL NETWORK SAFETY MODEL Mnd/fuzzy mdl SUERVISION clutr/fuzzy ANN rliability Ractin kintic MATHEMA- TICAL MODEL Stat variabl Z-1 Fig 5. Typical hybrid mdl tructur bad n th cmbinatin f a kintic mdl with ma balanc quatin. Th kintic mdl i bad n tw cmplmntary rprntatin: an ANN and a afty mdl. Th ANN and th afty mdl utput ar dynamically wightd accrding t a mchanim ruld by a uprviin blck which i cntinuuly dtcting whthr th ANN i xtraplating r nt. Whnvr th ANN i xtraplating, it rlativ wight i dcrad whil th n f th afty mdl i incrad. 5. AIMS AND SCOE OF THE THESIS Th bnfit/ct-rati i th quantity that rul th accptanc f mdl-bad prc uprviin, ptimizatin and cntrl in indutrial cal chmical and bichmical prductin prc. Unfrtunatly thi rati ha bn t lw fr th mt applicatin. Th cntral prblm dicud in th prnt h.d. thi i th fllwing: rblm: Hw i it pibl t incra th bnfit/ct-rati f a mdl-bad way f bichmical prc imprvmnt? Nwaday it i pnly accptd that bichmical prc ar vry cmplx and ftn prly undrtd. Thi i th main ran why in gnral it i vry difficult t dvlp a mchanitic mdl with th rquird accuracy. Th ynthi f a prc mdl in th claical way i lw and xpniv bcau it i bad n a prgriv cmprhnin f th phnmna invlvd. Th bttlnck hr i th acquiitin f knwldg. Clarly, th dvlpmnt f biprc mdl will alway b xpniv. But hw much can w rduc th xpn? rblm: Hw i it pibl t rduc th ct f dvlping a bichmical prc mdl fr givn accuracy rquirmnt? Sinc th accuracy f a prc mdl i a functin f th quantity and quality f th knwldg availabl, a vry imprtant iu t xplr i th ratinal and fficint u 13

Chaptr 1. Intrductin f knwldg fr mdl ynthi. Thi rprnt a vry imprtant iu in th prnt h.d. thi, namly hybrid mdling and it applicatin t bichmical prc. Hybrid mdling prvid man f activating all th urc f knwldg availabl, hnc it i a way f gtting mr accurat prc dcriptin at l ct (hnc prmiing t nhanc th bnfit/ct-rati fr indutrial applicatin) Aim 1. T dvlp th cncpt f hybrid mdling and it applicatin t biprc mdl bad imprvmnt In th ituatin whn n-lin prc infrmatin i availabl, mdl-bad algrithm can b cmplmntd with n-lin adaptatin algrithm. In thi ca, and in rlatin t th dicuin abut th bnfit and ct f a mdl-bad prc imprvmnt, a cmprmiing lutin btwn: 1) cmplxity/implicity f prc mdl 2) cmplxity/implicity f n-lin adaptatin algrithm. can b takn. Th cnd aim f th prnt h.d. thi i t dvlp algrithm bad n vry impl prc mdl cmplmntd with n-lin adaptatin algrithm. Aim 2. T dvlp algrithm bad n vry impl prc mdl cmplmntd with n-lin adaptatin algrithm Sinc th ptimal utilizatin f n-lin prc infrmatin i f crucial imprtanc, it i imprtant t xplr th pibility f uing hybrid mdl cmpltd with n-lin adaptatin tratgi. Sinc thi iu i nt yt wll dvlpd, th third aim f thi h.d. thi i: Aim 3. T dvlp n-lin adaptatin tratgi fr cmplmnting algrithm bad n hybrid mdl Th lat aim which i al f crucial imprtanc, cncrn th practical implmntatin f th mthdlgi in th indutrial nvirnmnt. Th practical implmntatin f hybrid mdl rquir apprpriat ftwar tl nt yt availabl in th markt. S th lat aim f th prnt h.d. i: Aim 4. T dvlp a cmplt ftwar packag t upprt th implmntatin f hybrid mdl-bad algrithm fr prc ptimizatin, cntrl and uprviin. Th ftwar mut b flxibl and ur-frindly that it can b accptd in a typical indutrial nvirnmnt. 6. OUTLINE OF THE THESIS Th prnt h.d. thi i rganizd in 7 chaptr. In chaptr 1 (th prnt chaptr) th mtivatin, aim and cp f th prnt dirtatin ar dicud. Sm rlvant intrductry cncpt fr th dvlpmnt in th fllwing chaptr ar al prntd. Firt f all th mtivatin i clarifid, i.. why i it imprtant t prfrm bichmical prc imprvmnt, and why i th accptanc f th mdl-bad apprach pr 14

Chaptr 1. Intrductin in th indutrial practic. It i xplaind that it i vry imprtant t rduc th ct f mdling, and with thi rpct m rarch lin wr tablihd. Thi rultd in a t f particular iu that ar ging t b ubjct t carful tudy. Chaptr 2, 3 and 4 addr th prblm f hybrid mdling and it applicatin t bichmical prc imprvmnt. In chaptr 2 a gnral framwrk fr hybrid mdling i dvlpd bad n hybrid ntwrk mdl tructur. Th apprach i illutratd by th applicatin t tat timatin and pn-lp in a fd-batch bakr yat cultivatin prc. In chaptr 3 th HYBNET ftwar packag, dvlpd in th ambit f th prnt h.d. dirtatin, i prntd. Th ftwar cncpt i illutratd by th applicatin t pn-lp and cld-lp ptimizatin f a fd-batch bakr yat cultivatin prc. Chaptr 4 dcrib an applicatin f hybrid-mdl ntwrk and f th HYBNET ftwar packag fr digning and implmnting a cld-lp infrntial cntrl ytm in a pnicillin prductin prc. Chaptr 5 and 6 addr th prblm f timating prc tat and prc paramtr n-lin and in ral-tim. Th tw chaptr fcu n mthdlgi that u n-lin infrmatin t incra rbutn. Thy xmplify hw it i pibl t u n-lin prc data ratinally t cp with mdl inaccuraci. Thi i furthr n f th fundamntal qutin in th mdl-bad way f prc imprvmnt: huld mr rurc b invtd int mdl dvlpmnt r int rbut chm fr n-lin adaptatin t cp with th impibility f th mdl t dcrib fully th dynamic f th prc? Th dvlpmnt f accurat kintic mdl i a critical iu in biprc mdling. Th 2 chaptr cvr xtnivly th ubjct f ractin kintic timatin frm variabl uually availabl n-lin. Th algrithm ar xampl f mthd that avid t rly n mdl f part f th prc that ar prly undrtd. Th mthd ar illutratd uing imulatin xprimnt. In chaptr 7 th gnral cncluin t b takn frm th prnt dirtatin ar prntd. Cncrn i givn t xplain in which way th prliminary dfind aim in th intrductin chaptr wr achivd. Chaptr 2 t 6 ar bad n 5 publicatin. Thy ar brifly ummarizd in th fllwing lin. Chaptr 2. Hybrid Ntwrk: A Nw Apprach fr Biprc Mdling. A nw apprach t ytm idntificatin fr prc uprviin and cntrl uing hybrid mdling tchniqu i prntd and illutratd with implmntatin at bakr yat fd-batch cultivatin prc. Th cncptual bai f th nw mthd i th arrangmnt f th mdul f th hybrid mdl in th frm f a ntwrk. Thu, a hybrid ntwrk i a cmputatinal tructur cniting f a ntwrk f cmputatinal nd, which rprnt prc knwldg at diffrnt lvl f phiticatin. Tw main apct f hybrid ntwrk mdling ar addrd: (i) cntructin f hybrid ntwrk by cmbining diffrnt a priri infrmatin r knwldg abut th prc undr cnidratin, and (ii) fficint paramtr idntificatin fr hybrid ntwrk. Th mt imprtant prprty f hybrid ntwrk i that th rrr backprpagatin tchniqu can b applid in rdr t ignificantly implify variabl nitivity analyi and paramtr idntificatin. Th backprpagatin tchniqu wa xtndd t dynamic 15

Chaptr 1. Intrductin ytm. Tw applicatin rv t dmntrat th advantag f th cncpt f hybrid ntwrk: (i) bima timatin, (ii) pn-lp ptimizatin. Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl. Thi papr dcrib th ftwar packag HYBNET dvlpd during th prnt h.d. wrk. HYBNET i a ftwar packag that upprt advancd mdl-bad prc dign and pratin. HYBNET tand fr HYBrid NETwrk, inc it i abl t cmp th prc mdl in a mdular way and allw t cnnct th nd in frm f a ntwrk. It i hybrid in diffrnt rpct: Firt, th mdl rprnting th diffrnt part f th prc r it bhaviur in diffrnt ituatin can b frmulatd at diffrnt lvl f phiticatin, crrpnding t th knwldg availabl abut that particular apct f th prc. In mt applicatin th mdul ar frmulatd in diffrnt rprntatin lik nural ntwrk, fuzzy rul-bad mdl and claical diffrntial quatin. Mr than a hundrd f uch diffrnt nd can b intrcnnctd in a mt flxibl way in rdr t frm a wll prfrming prc mdl a th ba fr ytmatic prc ptimizatin, prc uprviin and cld-lp cntrl. Th narly arbitrarily tructurd mdl can b idntifid in rughly th am way a th training f artificial nural ntwrk, namly by man f rrr backprpagatin chm. On f th mt ntial advantag frm th practical pint f viw i that th ftwar packag i narly platfrm indpndnt. It nly rquir a link,.g. with a TC/I prtcl, t th prc cntrl cmputr ud. Th cncpt f th ftwar i illutratd at th xampl f a bakr yat prductin prc. Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk. Thi chaptr prnt a mdl-bad cld-lp cntrl prcdur bad n a hybrid prc mdl. An infrntial cntrl tratgy nt yt dicud in litratur wa chn t kp th cncntratin f ammnia and prcurr in pnicillin prductin xprimnt undr tight cntrl. It main cmpnnt, th timatr fr th ammnia and prcurr cnumptin rat, i an indirct maurmnt prcdur, which u vral diffrnt n- and ff-lin maurmnt data. An hybrid prc mdl wa takn t cmbin vral kintic mdl, which wa capabl f larning during it applicatin uing autmatic training tchniqu. articularly, th nural ntwrk cmpnnt f th hybrid ntwrk wa rtraind during thi n-lin larning prc. Al, all th thr cmpnnt f th hybrid mdl ar autmatically r-tund, nc nw data bcm availabl. Th prpd prcdur wa ttd in 22 frmntatin run whr it prvd t b rbut and tabl. Th mthd xmplifi hw i it pibl t u hybrid mdl bad algrithm tgthr with n-lin adaptatin. Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kintic Etimatr in Stirrd Tank Ractr. In thi papr a mdl-bad paramtr timatr i prpd fr th n-lin timatin f ractin rat in tirrd tank biractr. A particular attntin i givn t th tability rquiit and th dynamic f cnvrgnc f th timat t th tru valu. Th tw fundamntal iu ar dicud in rlatin t th tuning prcdur f th gain paramtr. Th applicatin f th algrithm i illutratd with a impl micrbial grwth cultivatin prc. Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc. In thi papr algrithm fr tat brvatin and kintic 16

Chaptr 1. Intrductin timatin ar dvlpd and applid t a bakr yat fd-batch cultivatin prc. An imprtant dign cnditin wa t kp th numbr f rquird n-lin maurmnt a lw a pibl. Th vrall timatin chm aim at th timatin f thr tat variabl and thr pcific grwth rat rquiring n-lin maurmnt f dilvd xygn, dilvd carbn dixid and ff-ga analyi. A grat dal f attntin i givn t th timatin prblm f ractin kintic. In thi rpct a nw algrithm i prpd -th Scnd Ordr Dynamic Etimatr (SODE)- and cmpard t an Obrvr Bad Etimatr (OBE). Stability and dynamic f cnvrgnc ar iu ubjct t dtaild analyi. Th numrical implmntatin rlatd t th vrcming tability prblm i al tudid. It i hwn that a dicrt-tim frmulatin p additinal tability cntrain. Th can b aily vrcm by uing a rbut variabl tp intgratin algrithm. It wa cncludd that th OBE ha tw main diadvantag: i) th tuning f th dign paramtr mut b dn n a trial-andrrr bai, whil in th SDOE th ur can t a 2 nd rdr dynamic f cnvrgnc frm timatd kintic t tru kintic, and ii) th dynamic f cnvrgnc f th OBE ar tim-varying whil in th ca f th SDOE thi rpn i tim-invariant. 17

Chaptr 1. Intrductin REFERENCES Baily, J.E., D.F. Olli (1986). Kintic f ubtrat utilizatin, prduct frmatin and bima prductin in cll cultur. In Bichmical Enginring Fundamntal, McGraw-Hill, Nw Yrk, USA, pp. 658-752 Balt, M., R. Schnidr, C. Sturm, M. Ru (1994). Optimal Exprimntal Dign fr aramtr Etimatin in Untructurd Grwth Mdl. Bitchnl. rg., 1, pp. 48-488 Cnti, D.E. (1959). Kintic f bactrial grwth: Rlatinhip btwn ppulatin dnity and pcific grwth rat f cntinuu cultur, J. Gn. Micrbil., 21, pp. 4 Cybnk, G. (1989) Apprximatin by Suprpitin f a Sigmidal Functin, Math. Cntrl, Signal Sy., 2, pp. 33-314 Fy d Azvd, S., B. Dahm, F.R. Olivira (1997) Hybrid Mdlling f Bichmical rc: A cmparin with th cnvntinal apprach, Cmputr chm. Engn, 21, Suppl., pp. 751-756 Gupta, M.M. and D.H. Ra (1994). On th principl f fuzzy nural ntwrk. Fuzzy St and Sytm, 61, pp. 1-18 Haykin, S. (1994). Nural Ntwrk: a Cmprhniv Fundatatin. IEEE r, Nw Yrk Hrnik, A. K. and M. Stinchcmb, H. Whit (1989) Multi-Layr Fdfrward Ntwrk ar Univral Apprximatr, Nural Ntwrk, 2(5), pp. 359-366 Humphry, A. (1998). Shak Flak t Frmntr: What Hav W Larnd? Bitchnil. rg., 14, pp. 3-7 Hunt, K.J., D. Sbarbar, R. Zbikwki and. J. Gawthrp (1992) Nural Ntwrk fr Cntrl Sytm-A Survy, Analitica, 28(6), pp. 183-1112 Knintrur, C. (1987). Analyi f bilgical ractr. In Advanc in Bichmical Enginring, H. Bungay and G. Blfnt, d., Wily, Nw Yrk, USA, pp. 33-78 Kk, B. (1992). Nural ntwrk and fuzzy ytm: a dynamical ytm apprach t machin intllignc. rntic-hall, Englwd Cliff, Nw Jry Lnard, J.A., M.A. Kramr, L.H. Ungar (1992). A nural ntwrk that cmput it wn rliability. Cmp. Chm. Eng., 16, pp. 819-835 Lin, Chin-Tng and C.S. Grg L (1991).Nural-Ntwrk-Bad Fuzzy Lgic Cntrl and Dciin Sytm. IEEE Tranactin n cmputr, 4(12), pp. 132-1336 Lübbrt, A., R. Simuti (1994) Adquat u f mauring data in biprc mdling and cntrl, Trnd in Bitchnlgy, 12, pp. 34-311 Minkvich, I.G. and V.K. Erhin (1975). Stud. Biphy., 49, pp.43 Mnd, J. (1942). Rrch ur la crianc d cultur bactrinn, ari: Hrrmann t Ci 18

Chaptr 1. Intrductin Mntagu, G., J. Mrri (1994). Nural ntwrk cntributin in bitchnlgy. Trnd Bitchnl., 12, pp. 312-324 Mr, A. (1958). Th dynamic f bactrial ppulatin maintaind in th chmtat, ublicatin 614, Wahingtn, DC: Th Carngi Intitutin Munack, A. ( 1991) Optimizatin f Sampling, In Bitchnlgy, Rhm and Rd, Ed.; Vrlag Chmi: Winhim,; Vl.4: pp. 252-264. Munack, A. (1989). A Optimal fding tratgy fr idntificatin f Mnd-typ mdl by fd batch xprimnt. In Rprint f th 4 th Intrnatinal Cngr n Cmputr Applicatin in Frmntatin Tchnlgy, N.M. Fih, R.I. Fx, Ed., Elli Hrwd Limitd: Chichtr, U.K. Narndra, K.S., and K. arthaarathy (199). Idntificatin and cntrl f dynamical ytm uing nural ntwrk. IEEE Tran. Nural Ntwrk, 1, pp. 252-262 Niln, J., and J. Villadn (1994). Biractin Enginring rincipl. lnum r, Nw Yrk irt, S.J. (1975). rincipl f Micrb and Cll Cultivatin. Haltd r, Wily & Sn, Nw Yrk, USA ggi, A. T. and F. Giri (199) Ntwrk fr Apprximatin and Larning, rc. IEEE, 78(9), pp. 1481 llard, J.F., M.R. Bruard, D.B. Garrin, K.Y. San (1992). rc idntificatin uing nural ntwrk. Cmp. Chm Eng., 16, pp. 253-27 ichgi, D.C. and L.H. Ungar (1992). A hybrid nural ntwrk - Firt principl apprach t prc mdlling. AIChE J., 38, pp. 1499-1511 Rl, J. (1983). Enrgtic and kintic in bitchnlgy. Elvir Bimdical r, Amtrdam Rl, J.A., N.W.F. Kn (1978). On th mdlling f micrbial mtablim. rg. Ind. Micrbil., 14, pp 45-58 Ryc, M. (1996). Frmntatin th rlatin btwn intracllular mtablim and ractr dynamic. In rcding f th 1 t Eurpan Sympium On Bichmical Enginring Scinc, Dublin, Irland, Sptmpr 19-21, pp. 3 Ryc,.N. (1993) A dicuin f rcnt dvlpmnt in frmntatin mnitring and cntrl frm a practical prpctiv, Critical rviw in Bitchnlgy, 13(2), pp. 117-149. Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994). Biprc ptimizatin and cntrl: Applicatin f hybrid mdlling. Jurnal f Bitchnlgy, 35, pp. 51-68 Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994a). Hybrid Mdlling f Yat rductin rc Cmbinatin f a priri knwldg n Diffrnt lvl f Sphiticatin. Chm Eng. Tchnl., 17, pp. 1-2 Shi, Z. and K. Shimizu (1992). Nur-fuzzy cntrl f biractr ytm with pattrn rcgnitin. J. Frmnt. Bing., 74, pp. 39-45 19

Chaptr 1. Intrductin Simuti, R., I. Havlik, F. Schnidr, M. Dr, A. Lübbrt (1995). Artificial Nural Ntwrk f Imprvd Rliability fr Indutrial rc Suprviin. rprint f th 6 th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy, Garmich- artnkirchn, Grmany, pp. 59-65, May 14-17, 1995 Simuti, R., R. Olivira, M. Manikwki, S. Fy d Azvd, A. Lübbrt (1997). Hw t incra th prfrmanc f mdl fr prc cntrl and ptimizatin. J. Bitchnl., 59, pp. 73-89 Sjöbrg, J., Q. Zhang, L. Ljung, A. Bnvnit, B. Dlyn,. Glrnnc, H. Hjalmarn, A. Juditky (1995). Nnlinar Black-bx Mdling in Sytm Idntificatin: a Unifid Ovrviw. Autmatica, 12, pp. 1691-1724 Snnlitnr, B., O. Käppli (1986) Grwth f Saccharmyc crviia i cntrlld by it limitd rpiratry capacity: Frmulatin and vrificatin f a hypthi, Bitchnl. Bing., 28, pp. 927-937 Standbury,., A. Whitakr (1984). rincipl f Frmntatin Tchnlgy. rgamn r Sugn, M. (1985). Indutrial applicatin f fuzzy cntrl. Nrth-Hlland, Amtrdam Thmn, M.L., M.A. Kramr (1994) Mdling chmical prc uing prir knwldg and nural ntwrk, AIChE J., 4, pp. 1328-134. Thmn, M.L., M.A. Kramr (1994). Mdling chmical prc uing prir knwldg and nural ntwrk. AIChE J., 4, pp. 1328-134. Thrnhill, N.F.,.N.C. Ryc (1991). Mdlling Frmntr fr Cntrl. In Mauring and Cntrl in Biprcing, K.G. Carr-Brin, d., Elvir, Nw Yrk, USA, pp. 74-77 Villrmaux, J. (1996) Futur rpct fr Chmical Enginring Rarch and Tchnlgy, Chm. Tch. Eurp, January/Fbruary, pp. 21-23 Vlky, B. and J. Vtruba (1992). Mdling and Optimizatin f frmntatin prc. Elvir, Amtrdam Wang, H. Y., C.L. Cny, D.I.C Wang (1977). Cmputr aidd bakr yat frmntatin. Bitchnl. Bingng, 19, pp. 69-86 Wang, Li-Xin (1994). Adaptiv fuzzy ytm and cntrl: dign and tability analyi. rntic-hall, Englwd Cliff, Nw Jry Wrb,.J. (1992). Nurcntrl and Fuzzy Lgic: Cnnctin and Dign. Intrnatinal Jurnal f Apprximat Raning, 6(185), pp. 185-219 Wtrtrp, K., J. van Dirndnck, J. Kraa (1963). Intrfacial ara in agitatd galiquid cntactr. Chm. Engng Sci., 18, pp. 157-176 Wiln, J.A., L.F.M. Zrztt (1997) A gnralid apprach t prc tat timatin uing hybrid artificial ntwrk/mchanitic mdl, Cmputr chm. Engng, 21(9), pp. 951-963 Zadh, L.A. (1973). Outlin f a nw apprach t th analyi f cmplx ytm and dciin prc. IEEE Tran. Sy. Man Cybrn, 3, pp. 28-44 2

Chaptr 1. Intrductin Tuchiya, H.M., A.G. Frdrickn, R. Ari (1966). Dynamic f Micrbial Cll pulatin. Adv. Chm. Eng., 6, 125 21

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling Chaptr 2 Hybrid Ntwrk A Nw Apprach t Biprc Mdling Abtract. A nw apprach t ytm idntificatin fr prc uprviin and cntrl uing hybrid mdling tchniqu i prntd and illutratd with implmntatin at bakr yat fd-batch cultivatin prc. Th cncptual bai f th nw mthd i th arrangmnt f th mdul f th hybrid mdl in th frm f a ntwrk. Thu, a hybrid ntwrk i a cmputatinal tructur cniting f a ntwrk f cmputatinal nd, which rprnt prc knwldg at diffrnt lvl f phiticatin. Tw main apct f hybrid ntwrk mdling ar addrd: (i) cntructin f hybrid ntwrk by cmbining diffrnt a priri infrmatin r knwldg abut th prc undr cnidratin, and (ii) fficint paramtr idntificatin fr hybrid ntwrk. Th mt imprtant prprty f hybrid ntwrk i that th rrr backprpagatin tchniqu can b applid in rdr t ignificantly implify variabl nitivity analyi and paramtr idntificatin. Th backprpagatin tchniqu wa xtndd t dynamic ytm. Tw applicatin rv t dmntrat th advantag f th cncpt f hybrid ntwrk: (i) bima timatin, (ii) pn-lp ptimizatin. Thi chaptr ha bn ubmittd fr publicatin: Olivira, R., S. Fy d Azvd, R. Simuti, A. Lübbrt (1998). Hybrid Ntwrk - A Nw Apprach t Biprc Mdling. (ubmittd) 22

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling 1 INTRODUCTION Mdl ar cnidrd a vhicl fr rprnting ur currnt knwldg abut th rlvant prprti undr cnidratin in rdr t implify th lutin f th variu tak t b lvd. Hr w rtrict urlv t tak in prc uprviin and cntrl f bichmical prductin prc. In thi dmain, it wa trid t ba mt mdl n phyical inight and t frmulat thm by mathmatical quatin. A it i th amunt f knwldg that can b activatd what i limiting mt practical cntrl applicatin, it i ncary t mak u f all infrmatin and knwldg availabl, irrpctiv f th lvl f phiticatin by which it can b rprntd. In indutrial practic, mt knwldg i availabl in th frm f huritic rul gaind frm xprinc with variu prductin prc, whil crip mchanitic dcriptin in frm f mathmatical mdl ar availabl nly fr m part r apct f th prc undr cnidratin. Schubrt t al. (1994a) hwd fr a vry impl hybrid ytm th advantag f cmbining mchanitic knwldg with huritic rul f thumb and infrmatin till hiddn in data frm xprimnt undrtakn prviuly. Thr ar vral apprach t hybrid mdling dicud in litratur (Schubrt t al., 1994; ichgi and Ungar, 1992; Thmn and Kramr, 1994; Fy d Azvd t al., 1997). Thy all divid th prc int ubytm and dcrib thm by diffrnt kind f rprntatin. In bichmical cultivatin prc, fr xampl, it i mt cnvnint t dcrib th macrcpic ma balanc by an rdinary diffrntial quatin ytm and th bichmical cnvrin rat by man f an artificial nural ntwrk (Schubrt t al., 1994b). Othr apprach cmbin huritic rul ytm, rprntd by fuzzy rul and prcd uing fuzzy lgic with th infrmatin frm xtndd data rcrd which can b rprntd by artificial nural ntwrk. Such nural-fuzzy ytm (.g., Gupta and Ra, 1994; Wrb, 1992; Shi and Shimizu, 1992; Lin and Grg L, 1991) can b cnidrd a man f intrducing huritic a priri knwldg int th black-bx mdl rprntd by artificial nural ntwrk in rdr rduc th iz f th data rquird t tach thm bhaving lik th prc undr cnidratin. Th diffrnt mdul in hybrid mdl, hwvr, nd nt ncarily dcrib diffrnt part f th prc, diffrnt mdul might al dcrib th am part. Thn, thy can b takn a diffrnt vt t th valu f th crrpnding utput variabl f that prc cmpnnt, i.. th mdul ar cnidrd a altrnativ dcriptin prfrmd frm diffrnt pint f viw. Thn, hwvr, a rliabl wighting f th diffrnt rult i rquird. A high flxibility f cmping th final prc mdl frm th variu mdul can bviuly b btaind by arranging thm in frm f an xtndd ntwrk. Whn thi i dn in uch a way that th flw f infrmatin frm th mdul cntaining th input variabl f th prc t th n that prvid th prc utput valu i imilar t a fdfrward nural ntwrk, thn a vry fficint paramtr idntificatin prcdur bcm pibl. Thn it i pibl t mak u f th rrr backprpagatin tchniqu that allwd t implify th tuning f th wight f artificial nural ntwrk. Hnc, th apprach prpd by Schubrt t al. (1994b) can b xtndd t th gnral ca f an xtndd ntwrk. Thi ida and it implmntatin i labratd in thi papr. 23

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling 2 METHODOLOGY 2.1 Building blck f th hybrid ntwrk In it implt frm a hybrid mdl cntain tw cmpnnt dcribing tw diffrnt part f th ntir prc (Schubrt t al., 1994b). In th ca f a bichmical cultivatin prc, fr xampl, it i traightfrward t ba th mdl n a macrcpic ma balanc frmulatd by man f a t f rdinary diffrntial quatin and dcrib th kintic in m thr way,.g. by man f a phnmnlgically btaind mathmatical xprin lik th -calld Mnd mdl r by man f an artificial nural ntwrk. Th altrnativ f dcribing diffrnt part f th mdl ar uually nt quivalnt. Th tw pibiliti f dcribing th kintic in thi xampl, ar diffrnt in th n that th Mnd xprin ha a mr glbal applicability, frm th pint f viw that it can b mr rliably xtraplatd t ubtrat valu nt xprincd during th prviu xprimnt. On th thr hand th artificial nural ntwrk i abl t cnidr th influnc f mr prc variabl n th cnvrin rat, hwvr, it prvid rliabl rult nly in ara f th tat pac that hav bn mt many tim during prviu xprimnt frm which th data wa takn t train th ntwrk. In th ara, hwvr, th nural ntwrk uually prvid much mr accurat rat valu. Hnc, bth rprntatin hav thir pr and cn. Cnquntly, it i f advantag t mak u f thm imultanuly and t cmbin th rult thy dlivr. Thi rquir a way t adquatly wight bth rat valu. Thr ar diffrnt pibiliti t rprnt a particular part f th prc. In a mr frmal way, n can b ditinguihd btwn mchanitic dcriptin, huritic dcriptin and pur prc data crrlatin. Whn, a uggtd, thy ar t b applid imultanuly, thn a dynamically wightd avrag f thir rult i ncary, t btain a ingl rult that can b ud in furthr calculatin. Diffrnt wighting tchniqu hav bn prpd in litratur: 1. Wighting uing clutring tchniqu (.g., Simuti t al. 1995, Lnard t al. 1992) 2. Wighting with xprt ytm (.g., Schubrt t al. 1994a) 3. Wighting bad n nural ntwrk (.g., Haykin, 1994) It i traightfrward t cmbin th diffrnt rprntatin f a particular part r apct f th prc undr cnidratin tgthr with th wighting mdul in a parat blck within th ntir mdl a chmatically ktchd in Figur 1. Such a blck i cnidrd th baic building blck f th hybrid ntwrk mdl prpd in thi papr. 24

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling MECHANISTIC KNOWLEDGE - Ma balanc quatin, - Enrgy balanc quatin, - Mmntum balanc quatin, tc... WEIGHTING MODULE Mdl Input HEURISTIC KNOWLEDGE - Fuzzy ytm - Exprt ytm - Crrlatin, tc... KNOWLEDGE HIDDEN IN DATA - Artificial nural ntwrk - Splin - lynm - Furir ri, tc... - Clutr bad mnitring, - Fuzzy/xprt ytm, - Artificial nural ntwrk Mdl Output Fig. 1. Cmbining diffrnt way f dcribing a particular part f th prc. Uually, mdul bad n mchanitic prc dcriptin ar cmbind with mdul which rprnt huritic knwldg and thr which cntain crrlatin-typ prc dcriptin. Thir rult mut b cmbind t frm a wightd avrag a a uniqu utput f thi part f th ntir mdl. It huld b mntind that it i nt ncary t incrprat all thr typ f knwldg rprntatin int uch a building blck. Fr xampl, it bviuly d nt mak n t dcrib m part f th prc, which i wll invtigatd and fr which wll tablihd mathmatical mdl ar alrady availabl, by huritic r t larn th rlvant rlatinhip nc mr frm prc data. Hnc, th xtnin f th blck i diffrnt frm ca t ca. 2.2 Cmpitin f th hybrid ntwrk Th ba f mt mdl ud in biprc uprviin and cntrl i a ytm f ma balanc quatin fr all prc cmpnnt that ar macrcpically changing during th prc in a ignificant amunt. Th mt imprtant xampl fr uch cmpnnt ar th amunt f ubtrat, bima and prduct a wll a carbn dixid, xygn, tc.. articularly, n i intrtd in th quantiti that ar influncing th prfrmanc f th prc undr cnidratin, pcially th amunt f prduct dvlpd. 25

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling Such balanc quatin can b frmulatd in a traightfrward way in frm f rdinary diffrntial quatin ytm. Thr i n nd t lk fr altrnativ dcriptin, prvidd apprpriat xprin can b frmulatd fr th bichmical cnvrin and th rlvant tranprt rat lik th xygn ma tranfr, which ar an ntial part f th balanc quatin. It i traightfrward t rgard th t f ma balanc quatin a th backbn f th mdl and rprnt thm by a cntral mdul f th ntir mdl. Thi mdul mut b cmplmntd by additinal mdul dcribing variu diffrnt cmpnnt f th ma balanc quatin. Fr xampl, th variu tranprt prc, lik xygn tranfr, which ar f majr imprtanc in indutrial prductin prc, inc thy finally limit th prductivity which can b btaind with a givn train in a givn biractr, can b dcribd by parat mdul. Of gnral imprtanc ar th mdul fr th rat xprin, which by thmlv may b dividd int diffrnt part,.g., tichimtric rlatinhip and kintic rlatin btwn th variu primary variabl, th cncntratin f th ky cmpnnt. In rdr t wrk tgthr, th mdul mut b intrcnnctd. Thy thu can b rprntd by a ntwrk f mdul. It i wll knwn that uch a mdularizatin f a prc mdl immdiatly nhanc th tranparncy f th mdl and a uch hlp t avid rrr. Anthr ntial advantag i that uch a tructur implifi th practical mdling wrk by allwing t mak u f prdfind ftwar mdul that nd t b adaptd nly lightly t fit int th mdl. 2.3 aramtr idntificatin in hybrid ntwrk In practic, hybrid ntwrk ar ud fr bichmical prc f cnidrabl cmplxity. Th mdl, thrfr, cntain many paramtr. Cnquntly, a cnidrabl amunt f data i rquird t idntify th mdl paramtr. In uch ca, th cmputing tim bcm an iu. It i a particular advantag f th hybrid ntwrk that thi paramtr timatin can b prfrmd in a vry fficint way uing th rrrbackprpagatin tchniqu. Thi tchniqu applid with high advantag t train artificial nural ntwrk can al b applid t hybrid ntwrk, i.. ntwrk in which th cmputatinal nd ar f diffrnt quality and f much highr cmplxity than in nural ntwrk. Entially, paramtr timatin i an ptimizatin prblm. Uually gradint-bad ptimizatin tchniqu wr ud t tackl that prblm. If th mdl cntain trngly nnlinar fatur, th traightfrward altrnativ ar th randm arch algrithm (.g. Simuti and Lübbrt, 1997). Th will lad t crrct idntificatin rult, hwvr, thy tak t much cmputing tim in xtndd hybrid ntwrk mdl. Th altrnativ, prpd in thi wrk, th backprpagatin tchniqu blng t th gradint-bad tchniqu. A hwn by Lnard and Kramr (1992), th rrr backprpagatin tchniqu i a vry ffctiv way t dtrmin th Jacbian and/r Hian matric dirctly, which ar dtrmind numrically in mt cnvntinal gradint-bad ptimizatin tchniqu. 26

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling Fr a impl cmbinatin f a ingl nural ntwrk and a balanc quatin ytm Schubrt t al. (1994a) alrady hwd that thi can b uccfully applid t hybrid mdl. Hr thi tchniqu i xtndd t arbitrarily cmplx hybrid mdl. Th mathmatical dtail ar dcribd in th Appndix. 2.4 ractical cnidratin In rdr t mak paramtr timatin f hybrid ntwrk faibl in practic, xtndd ftwar upprt mut b prvidd. An xampl f an apprpriat ftwar packag i HYBNET (Olivira t al., 1997), which cntain a numbr f prcdur which can b applid in rdr t dign, idntify and validat hybrid ntwrk. Thi ftwar alrady prvd itlf t upprt th mplymnt f th mdl in indutrial applicatin lik prc ptimizatin, uprviin, and cntrl. 3 EXAMLES 3.1 Bima timatin with a impl hybrid ntwrk Th firt xampl i a mdl-upprtd bima timatin. Th backbn f th mdl ud i a impl ma balanc quatin fr bima. Th cnd cmpnnt f th mdl i an timatin fr th pcific bima grwth rat µ. A wll knwn, th pcific bima grwth rat µ can b timatd frm th rat by which th gau ractin cmpnnt O 2 and CO 2 ar cnumd r prducd. Th baic cmpnnt dcribing th pcific grwth rat µ i an artificial nural ntwrk. Altrnativly, an mpirical rlatinhip ha bn ud in th mdl. Thi cmpnnt i rprntd by th vry impl crrlatin prpd by Wu t al (1985): = Y x (OUR/X-m ) (1) Th 2 paramtr invlvd ar th yild, Y x, f bima prducd pr-xygn cnumd and, m, th pcific amunt f xygn cnumd by th yat fr maintnanc purp. A lat-quar minimizatin f th dviatin btwn th bima valu maurd ff-lin and th n timatd by th crrlatin wa ud. Th quai-nwtn (QN) algrithm wa ud with inqualty cntrain dfining uppr and lwr bund fr Y x and m. Sinc th impl claical rlatinhip btwn pcific grwth rat and OUR i bad n aumptin abut th kintic which ar nt a tablihd a th baic ma balanc quatin, it i traightfrward t dtrmin th rlatin altrnativly by man f an artificial nural ntwrk, prvidd thr i nugh xprimntal data availabl t train th nural ntwrk. In th prnt xampl a impl fdfrward artificial nural ntwrk wa ud t timat th pcific grwth rat µ ANN frm data frm carbn dixid prductin rat CR and xygn uptak rat OUR. 27

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling A bth th claical crrlatin and th nural ntwrk dpict diffrnt glbalizatin prprti, thy ar ud imultanuly t dtrmin th pcific grwth rat µ. Th qutin hw t wight th tw rat can aily b lvd in thi particular ca: Th mt dirct apprach t wighting i th clutr tchniqu, which attach a wighting factr btwn and 1 t th nural ntwrk cmpnnt and th cmplmnt t n t th claical apprach. Th wight fr th ntwrk cmpnnt attachd t a givn pint in th tat pac, i.. hr t a givn input vctr X, i dtrmind frm th numbr f data maurd in th vicinity f X in th tat pac. Thi wight i dtrmind by a data clutr analyi a dcribd by Simuti t al. (1995). Whn µ i dtrmind, th ma balanc quatin fr th bima can b lvd. Th ntir mdl i dpictd in Figur 2. CORRELATION =Yx(OUR/X - m) C V, OUR, CR, F CLUSTERS =(EM) $11 ( C MASS BALANCE dx/dt = ( - F/V) X X ANN {2,7,1} ANN X Fig. 2. Hybrid ntwrk fr bima timatin in a bakr yat cultivatin cniting f tw main part: A blck cntaining tw altrnativ t dtrmin th pcific grwth rat µ and a balanc quatin fr th bima. In rdr t giv an imprin f th wighting prcdur, typical rult ar hwn in Figur 3 thrugh 4. Figur 3 hw th utput µ ANN f th nural ntwrk fr th pcific grwth rat a a functin f th crrpnding input variabl OUR and CR. A th xprimnt dlivr maurmnt data pair fr th variabl in a narrw ara f th (OUR, CR)-pac nly, w can cnidr µ ANN rliabl nly in a mall rgin a hwn in Figur 4 by man f th vidnc maur EM, which i a nrmalizd indicatr f th maurmnt infrmatin availabl fr th diffrnt (OUR, CR)-pair. 28

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling.569 --.65.488 --.569.46 --.488.325 --.46.244 --.325.163 --.244.81 --.163 --.81 CR CTR 2 4 6 8 1 1 8 4 6 OUR OTR 2,625,5,375,25,125, ANN Fig. 3. attrn f th pcific grwth rat µann a dtrmind frm th nural ntwrk cmpnnt f th hybrid ntwrk fr a bakr yat cultivatin prc frm th input variabl OUR and CR..875 --.1.75 --.875.625 --.75.5 --.625.375 --.5.25 --.375.125 --.25 --.125 2 1, 4 CR CTR 6 8 1 1 8 6 4 OUR OTR 2,6,8,4 EM EM,2, Fig. 4. Extraplatin maur EM charactrizing th vidnc f th nural ntwrk cmpnnt f th hybrid ntwrk frm OUR and CR data maurd during a t f bakr yat cultivatin prc 29

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling EM i ud t dtrmin th wight f th nural ntwrk cmpnnt in th blck ud t dtrmin µ. Th wight f µc, th rult f th crrlatin, i thn 1-EM. Th rulting µ a a functin f tim i dpictd tgthr with th timatin X(t) in Fig. 5. 2 timatd bima maurd bima (BTM) p. grwth rat,4 15,3 bima (g/l) 1 5,2,1 p. grwth rat (h -1 ) 5 1 15 2 tim (h), Fig. 5. Typical rult f bima timat X and timat f th pcific grwth rat µ. Th lattr i th rult f th wightd avrag btwn th tw timat µ ANN and µ C. Th ymbl ar maurmnt data frm a rprntativ xprimnt at which th timatr wa ud. Th timatin rult hw a fairly high fluctuatin in th timatin f th pcific grwth rat but a rathr gd timatin quality fr th bima X. Th bima timatin prcdur wa validatd with th cr validatin prcdur uing data rcrd frm 3 cultivatin nt ud during th paramtr idntificatin prcdur. Th idntificatin itlf wa prfrmd with data rcrd frm 7 cultivatin. In rdr t dmntrat th practical advantag f th rrr backprpagatin tchniqu fr th paramtr timatin prcdur, a cmparin wa prfrmd btwn th cnvntinal apprach f paramtr timatin uing gradint tchniqu (cnd rdr gradint mthd with numrical valuatin f th Jacbian and Hian matric) and th rrr backprpagatin tchniqu dcribd prviuly. Th man quar timatin rrr MSE a a functin f th cmputing tim CU i dpictd in Figur 6. Thi figur hw th vlutin f th MSE until a pr-tablihd rrr valu i achivd. 3

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling 3 nitiviti mthd + backprpagatin numrical gradint M an Squar Errr (M SE) 2 1 CU = 8,17 min CU = 123,1 min MSE=,141 2 4 CU (min) Fig. 6. Man quar timatin rrr MSE a a functin f th cmputing tim CU rquird t rach a pr-tablihd rrr valu. Th rult wr btaind with a 233 MHz Alpha Statin (Digital Equipmnt Crp.) uing data frm 7 cultivatin. 3.2 Fd rat prfil ptimizatin fr bakr yat prductin In bakr yat prductin, th aim i t prduc within a givn prductin tim t f a much yat bima [kg] a pibl. Thi prc i pratd a a fd-batch prc in practic. Hnc, th bjctiv functin J, which ha t b ptimizd by man f an apprpriat fding rat prfil F(t) and rlatd tart valu f th tat variabl i: J = x(t f)v(t f ) Bima [kg] = t f +t p Ttal Batch Tim [h] (2) whr t p i th tim rquird btwn tw ucciv prductin run t prpar th ractr fr th nxt batch. Th firt tp f uch a fd rat ptimizatin i th idntificatin f th rlvant prc mdl, which wa frmulatd a a hybrid ntwrk ktchd in Figur 7. 31

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling -ANN V-ANN ri,ann F t S-ANN Z-ANN CLUSTERS r=(em) rann + (1-EM) rafty r MASS BALANCE dc/dt=r+(f/v)(cf-c) +T(*-) dv/dt=f c ri,afty SAFETY MODEL c Fig. 7. Hybrid ntwrk ud during a fd-rat ptimizatin fr a bakr yat prductin prc. A in th frging xampl, th bai f th mdl i a ma balanc. Fr th fur cncntratin that ignificantly chang during th cultivatin and fr th vlum, w btain th fllwing rdinary diffrntial quatin ytm dc dt = r x + F V (c f-c) + T(*-) dv dt = F (3a) (3b) with th cncntratin vctr c = [x,,, ] T fr bima, ubtrat, thanl and xygn and th ablut rat vctr r = [µ, V, S, Z ] T, µ, V, S, Z bing th crrpnding pcific rat. T=[,,, k L a], whr k L a i th xygn ma tranfr cfficint. Th pcific rat xprin fr µ, V, S, Z rprnting th bichmical cnvrin prc ar dcribd by diffrnt artificial nural ntwrk. Frm xprinc with uch ytm, thi mdularizatin i mt ftn f advantag in mdling uch ytm (.g. Haykin, 1994). Whn thr i nugh training data, thn artificial nural ntwrk prvd t b vry gd mdl fr th prc kintic. At lat thy can b built at th bt bnfit/ct ratin. In th xampl rprtd hr, data t frm 1 frmntatin prfrmd in th am rgin f th tat pac wr availabl. In thi ca, thi prvd t b nugh t train a rliabl nural ntwrk fr th thr pcific rat xprin µ, V, S, Z. It huld b trd, that th quality f th rprntatin f th pcific rat i much dpndnt n 32

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling th quality f data and th cmplxity f th kintic. Thr i n gnral rul abut th amunt f data rquird fr th training f th ntwrk. Nvrthl a claical mdl mut b mplyd t mak ur that w can al prvid a ufficintly rliabl rat whn th tat vctr run ut f th rgin in th tat pac in which w hav nugh maurmnt vidnc. Th crrpnding mdul can b cnidrd a afty mdul. Th afty mdl ud in thi xampl i a claical mdl bad n impl Mnd xprin. Equatin imilar t th dvlpd by Snnlitnr and Käppli (1986) wr ud. Th paramtr wr fittd t th am data a wr ud t train th nural ntwrk. Th wighting f th tw pcific rat vctr wa prfrmd in th am way a in xampl 1. Fr all th pcific rat prducd by th fur nural ntwrk cmpnnt th am wight wr ud. Th cmplmnt t n wa takn a th wight fr th cnvntinally btaind pcific rat vctr. Onc th mdl i idntifid it can b ud t prfrm th vry tak it had bn dignd fr, th fd rat ptimizatin. In rdr t prfrm thi ptimizatin tak, a cnvnint frm f rprntatin f th fding prfil F(t) mut b chn. Whil mt ftn a plynmial apprach wa favrd (.g. Mntagu and Ward, 1994), w tk th mr flxibl chic f an artificial nural ntwrk t rprnt thi nnlinar prfil. A uch, a impl fdfrward ntwrk with tim a input, 5 hiddn nd and with F a ingl utput wa chn. Nw th tak i t ptimiz th paramtr f th fding prfil, i.. th wight in nural ntwrk ud t dcrib F(t) a wll a th final frmntatin tim t f, uch that th prfrmanc critrin J i maximizd. Fr th initial vlum v and th initial ubtrat cncntratin typical fixd valu fr th cultivatin quipmnt wr ud. Th cntraint undr which th ptimum mut b fund ar: v max = 13 L F max =.35 L/h Th rult btaind undr th cnditin ar dpictd in Figur 8. A charactritic fatur f thi rult i that it allw th frmatin f a cnidrabl amunt f EtOH during th frmntatin in rdr t kp th bima prductin rat at a high valu. In th cnd half f th prductin thi EtOH i thn cnumd in rdr t kp th vrall ubtrat cnvrin int bima cl t 1%. 33

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling 3 8 25 bima (g/l) 2 15 1 5 gluc (g/l) 6 4 2 5 1 15 2 tim (hur) 5 1 15 2 tim (hur) 8 1 6 8 thanl (g/l) 4 2 O2(%) 6 4 2 5 1 15 2 tim (hur) 5 1 15 2 tim (hur),35 13, 12,5,3 12,,25 vlum (l) 11,5 11, fd (l/hr),2,15 1,5,1 1,,5 5 1 15 2 tim (hur) 5 1 15 2 tim (hur) Fig. 8. Typical rult f th dcribd fd rat ptimizatin prcdur. Th prfil f th fding rat F i hwn tgthr with th crrpnding prfil f th tat variabl bima, ubtrat, thanl, and xygn (po2) cncntratin a wll a th vlum dvlpmnt. 4 CONCLUSIONS Hybrid ntwrk can b cmpd f mdul that rprnt part r apct f a cmplx bichmical prductin prc n diffrnt lvl f phiticatin. Th ky advantag f hybrid ntwrk i that thy allw t mak u f a much largr knwldg ba t cntruct prc mdl. Hnc, it i t b xpctd that th mdl mr accuratly dcrib th fatur f th prc that ar rlvant t th tak t b lvd. Th rurc that can b xplitd ar nt nly th wll undrtd mchanim but al th wid ara f th huritic accumulatd in th prductin plant a wll a th data rcrd frm many prductin run. 34

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling A a mdular rprntatin f th prc hybrid ntwrk gnrally hav th furthr advantag t kp th prc mdl highly tranparnt. With mdular mdl it i air t dtct and thu avid mdling rrr. Al, with mdular mdl it i air t maintain th mdl and t adapt thm t th vr changing cnditin in prductin plant. A dciiv advantag f hybrid mdl i that, whn thir utput can b rprntd a cntinuu and diffrntiabl rprntatin f thir input, th backprpagatin mthd wll knwn frm th training f impl nural ntwrk can b ud t ignificantly rduc th cmputatinal rquirmnt fr mdl idntificatin. Thi i f high imprtanc t mdl that cntain vral artificial nural ntwrk cmpnnt, a uch cmpnnt uually hav many paramtr and th crrpnding idntificatin tak much tim. Th hybrid mdling tchniqu alrady prvd t b f high valu in indutrial applicatin. Acknwldgmnt. R. Olivira acknwldg th financial upprt prvidd by th rtugu Scinc Fundatin JNICT - Junta Nacinal d Invtigaçã Cintífica Tcnlógica (BD/251/93-RM) 35

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling AENDIX - SENSITIVITY ANALYSIS OF HYBRID NETWORK MODELS Hr w dicu a gnral nitivity analyi with rpct t hybrid ntwrk mdl f bichmical prductin ytm. Lt u aum that th ytm can frmally b dcribd by th rdinary diffrntial quatin ytm dx = f(, X, U, t) dt (A-1a) Y = g(, X, U, t) (A-1b) with initial cnditin, X(t ) = X (A-1c) whr X i th vctr f tat variabl, Y a vctr f maurmnt variabl, U a vctr f xtrnal influnc variabl, a vctr f mdl paramtr and t th indpndnt variabl tim. Thi aumptin man that th ntwrk rprnt a cntinuu rlatinhip btwn th tat variabl X a wll a btwn th tat variabl and th maurmnt variabl Y. Sinc a hybrid ntwrk i a ntwrk f cmputatinal nd w additinally nd a gnral mdl dcriptin f th nd. W aum fr an arbitrary nd k that it vctr Y k f utput variabl i dpndnt n a vctr f input Z k. Thi dpndncy i dfind by a t f cntinuu and diffrntiabl quatin H k cntaining a t f paramtr that can b rprntd by th vctr k Y k =H k (Z k, k ) (A-2) By nitiviti w man th utput/input and utput/paramtr nitivity matric: wy k = G wz k (Z k, k ) k wy k = E w k (Z k, k ) k (A-3a) (A-3b) Th nitivity xprin ar nt nly valuabl fr cnvntinal quatin ytm but al fr th input-utput rlatinhip n which th thr main mdul typ f hybrid ntwrk ar fundd, in particular fuzzy rul ytm and artificial nural ntwrk: Fuzzy ytm. If all th mmbrhip functin f all th fuzzy t in th fuzzy rul ytm ar cntinuu and diffrntiabl, th rul-bad ytm can b mappd int a t f cntinuu and diffrntiabl rlatinhip H k (Wang 1994). Thu, th 36

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling rlatinhip G k and E k can b drivd frm H k. An xampl f uch fuzzy ytm i dicud in dtail by Simuti t al. (1995). Th paramtr k invlvd dfin th frm and pitin f th mmbrhip functin. Th rquirmnt can aily b fulfilld whn th mmbrhip functin f th fuzzy variabl ar chn t b Gauian blltyp curv. Thn th paramtr ar th man and tandard dviatin f th Gauian curv. Artificial nural ntwrk. All th typ f ANN which can b traind with th backprpagatin tchniqu mt th rquirmnt fr th nd tatd bfr. Th nitiviti dfind by qn. (A-3a) and (A-3b) can b cmputd with th rrr backprpagatin algrithm. Th paramtr k ar th wight in th ntwrk cnnctin. Obviuly, any linar cmbinatin f mdul f typ cntinuu and diffrntiabl quatin, fuzzy ytm and artificial nural ntwrk which mt th rquirmnt al can b takn a a nd. Thu, a mr cmplx ntd ntwrk can b cntructd with th baic typ f nd. Whn w dal with a ntwrk cniting f a numbr f intrcnnctd nd thn w firt nd a dcriptin f th cnnctin. Th can b dfind by fur-dimninal matrix W=[ w i,j,k,l ] in th fllwing way: w i,j,k,l = 1 if th cnnctin xit if th cnnctin dn t xit (A-4) whr th lmnt w i,j,k,l dfin th cnnctin btwn utput j f blck i with input l f blck k>i. Thn th input t blck k can b cmputd in th fllwing way k-1 z k,l = i=1 dim(y i ) j=1 w i,j,k,l Y i,j l=1,...,dim(z k ) (A-5) Th utput f th am nd can thn b dtrmind by valuating uing qn (A-2). Nw, w cm back t th initial rprntatin (A-1) f th ntir ytm. A partial diffrntiatin f th quatin aftr th paramtr vctr and th vctr U lad t th fllwing quatin d wx dt w ¹ = wf wx wy w = wg wx d wx dt wu ¹ = wf wx wy wu = wg wx wx w + wf w wx w + wg w wx wu + wf wu wx wu + wg wu (A-6a) (A-6b) (A-6c) (A-6d) 37

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling Thy can b idntifid a diffrntial quatin fr wx/w and wx/wu and frm th ba f th nivity mthd (.g., Frank, 1978). T lv th quatin with th initial cnditin wx ¹ w t=t = wx ¹ wu t=t = (A-6) (A-6f) n nd th matric wf/wx, wf/wu, wf/w, wg/wx, wg/wu, and wg/w. Thy can imply b dtrmind with th wll knwn backprpagatin prcdur (Rumlhart t al 1986) applid t th vrall hybrid ntwrk tructur. Ntic that th principl fllwd ar imilar t rrr backprpagatin in nural ntwrk. Th main diffrnc i that th claical igmid functin, uually mplyd in th ingl nd in nural ntwrk, ar rplacd by th functin Y k =H k (Z k, k ) (qn. A-2) and th rpctiv gradint dfind by qn. (A-3). 38

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling REFERENCES Fy d Azvd, S., B. Dahm, F.R. Olivira (1997) Hybrid Mdlling f Bichmical rc: A cmparin with th cnvntinal apprach, Cmputr chm. Engn, 21, Suppl., pp. 751-756 Frank,.M. (1978). Intrductin t Sytm Snivity Thry. Acadmic r, Nw Yrk Gupta, M.M. and D.H. Ra (1994). On th principl f fuzzy nural ntwrk. Fuzzy St and Sytm, 61, pp. 1-18 Haykin, S. (1994). Nural Ntwrk: a Cmprhniv Fundatin. Macmillan. Nw Yrk Lnard, J.A., M.A. Kramr, L.H. Ungar (1992). A nural ntwrk that cmput it wn rliability. Cmp. Chm. Eng., 16, pp. 819-835 Lin, Chin-Tng and C.S. Grg L (1991).Nural-Ntwrk-Bad Fuzzy Lgic Cntrl and Dciin Sytm. IEEE Tranactin n cmputr, 4(12), pp. 132-1336 Mntagu, G.A., A.C. Ward (1994). A Sub-ptimal Slutin t th Optimiatin f Biractr Uing th Chmtaxi Algrithm. rc Bichmitry, 29, pp. 489-496 Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1997). HYBNET, an Advancd tl fr rc Optimizatin and Cntrl. (in pr) ichgi, D.C. and L.H. Ungar (1992). A hybrid nural ntwrk - Firt principl apprach t prc mdlling. AIChE J., 38, pp. 1499-1511 Rumlhart, D.E., G.E. Hintn, R.J. William (1986). Larning intrnal rprntatin by rrr backprpagatin. In aralll Ditributd rcing, 1 (D.E. Rumlhart, and J.L. McCllland, Ed). MIT, Cambridg, MA Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994a). Hybrid Mdlling f Yat rductin rc Cmbinatin f a priri knwldg n Diffrnt lvl f Sphiticatin. Chm Eng. Tchnl., 17, pp. 1-2 Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994b). Biprc ptimizatin and cntrl: Applicatin f hybrid mdlling. Jurnal f Bitchnlgy, 35, pp. 51-68 Shi, Z. and K. Shimizu (1992). Nur-fuzzy cntrl f biractr ytm with pattrn rcgnitin. J. Frmnt. Bing., 74, pp. 39-45 Simuti, R., I. Havlik, F. Schnidr, M. Dr, A. Lübbrt (1995). Artificial Nural Ntwrk f Imprvd Rliability fr Indutrial rc Suprviin. rprint f th 6 th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy, Garmich- artnkirchn, Grmany, pp. 59-65, May 14-17, 1995 Simuti, R., Lübbrt, A. (1997) A cmparativ tudy n randm arch algrithm fr bitchnical prc ptimizatin, J. Bitchnl, 52, pp. 245-256 39

Chaptr 2. Hybrid Ntwrk A Nw Apprach t Biprc Mdling Snnlitnr, B., O. Käppli (1986) Grwth f Saccharmyc crviia i cntrlld by it limitd rpiratry capacity: Frmulatin and vrificatin f a hypthi, Bitchnl. Bing., 28, pp. 927-937 Thmn, M.L., M.A. Kramr (1994) Mdling chmical prc uing prir knwldg and nural ntwrk, AIChE J., 4, pp. 1328-134. Wang, L.-X. (1994). Adaptiv Fuzzy Sytm and Cntrl: Dign and Stability Analyi. rntic Hall, Englwd Cliff, N.J. USA Wrb,.J. (1992). Nurcntrl and Fuzzy Lgic: Cnnctin and Dign. Intrnatinal Jurnal f Apprximat Raning, 6(185), pp. 185-219 4

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl Chaptr 3 HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl Abtract. HYBNET i a ftwar packag that upprt advancd mdl upprtd prc dign and pratin. HYBNET tand fr HYBrid NETwrk, inc it i abl t cmp th prc mdl in a mdular way and allw t cnnct th nd in frm f a ntwrk. It i hybrid in diffrnt rpct: Firt, th mdl rprnting th diffrnt part f th prc r it bhavir in diffrnt ituatin can b frmulatd at diffrnt lvl f phiticatin, crrpnding t th knwldg availabl abut that particular apct f th prc. In mt applicatin th mdul ar frmulatd in diffrnt rprntatin lik nural ntwrk, fuzzy rul-bad mdl and claical diffrntial quatin. Mr than a hundrd f uch diffrnt nd can b intrcnnctd in a mt flxibl way in rdr t frm a wll prfrming prc mdl a th ba fr ytmatic prc ptimizatin, prc uprviin and cld-lp cntrl. Th narly arbitrarily tructurd mdl can b idntifid in rughly th am way a th training f artificial nural ntwrk, namly by man f rrr backprpagatin chm. On f th mt ntial advantag frm th practical pint f viw i that th ftwar packag i narly platfrm indpndnt. It nly rquir a link,.g. with a TC/I prtcl, t th prc cntrl cmputr ud. Th cncpt f th ftwar i illutratd at th xampl f a bakr yat prductin prc. Thi chaptr ha accptd fr publicatin: Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1998). Hybnt, an Advancd Tl fr rc Optimizatin and Cntrl.. 7th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy CAB7, Oaka, Japan, May 31-Jun 4, 1998 41

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl 1 INTRODUCTION Thr ar numru prpal rcrdd in litratur t imprv th prfrmanc f bichmical prductin prc by mdrn mdl upprtd tchniqu lik fding prfil ptimizatin r cld lp cntrl. Hwvr, th indutrial accptanc wa rathr pr. Th cmputr hardwar availabl at prductin prc i mt ftn ud fr data acquiitin and lw lvl cntrl nly. On f th main ran i that th bnfit/ct rati fr advancd tchniqu, which i dminatd by th dvlpmnt ct and vry ftn additinally by th ct t adapt th ytm t th vr changing cnditin in a ral prductin plant, wa inufficint. Hr, w prp a ftwar packag, in which many f th btacl wr rmvd. rc dign, uprviin, and cld lp cntrl i and will b th cntral activity f biprc nginr. In indutrial practic, thr i n ran t prcd diffrntly t th way in which gd cintific wrk i bing prfrmd. Uually, th firt apprach i t cllct and tructur th knwldg abut th prc undr cnidratin. Thi rult in a ytm f intracting partial prc. Th traightfrward way t prcd, i t charactriz th bhavir f all that lmnt with rpct t thir imprtanc in trm f th bjctiv f th particular tak t b lvd. Finally, th ntir prc, which can b viwd at a a ntwrk f all it intracting cmpnnt can b ptimizd utilizing thi dtaild knwldg. Any practical ptimizatin f a ral prductin prc mut b bad n prdictin f th prc bhavir. Thi rquir a mdl that can b xplitd numrically. Thu, mdl fr th diffrnt prc cmpnnt and dynamical dcriptin f thir mutual intractin bcm ncary, and th ntir mdl can b cnidrd a ntwrk f intracting ftwar mdul. A majr btacl t putting thi gnral and wll tablihd ida int indutrial practic i miing ftwar upprt fr prc, which ar a cmplx a mt indutrial bichmical prductin prc. Intractin f many diffrnt ubytm mut b cnidrd and ftn, th mdl fr th diffrnt ub-prc cannt b frmulatd n th am high lvl f undrtanding. Thu, w prp a hybrid apprach, which man an applicatin f a mixtur f mdl n diffrnt lvl f phiticatin and crutiny. Fr intanc, th ma balanc may b frmulatd with crip mathmatical quatin, th kintic in a data drivn way with nural ntwrk and, at th am tim it bcm pibl t mak u f rul-f-thumb whr n data r mdl ar availabl by uing fuzzy rul ytm. In uch a way it i nt nly pibl t frmulat th mdl n th lvl f crrpnding knwldg availabl (thu aviding tranfr l) but al t adapt th rprntatin t th nd with rpct t th tak t b lvd (t incra th bnfit/ct-rati). 2 CONCETUAL FRAMEWORK 2.1 Guidlin fr th dvlpmnt Th cntral aim i t prvid a tl which hlp t lv typical tak in biprc nginring,.g., in digning nw prc r in ptimizing xitnt n. Th 42

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl gnral apprach i a mdl upprtd apprach auming that th particular tak can b lvd th bttr and fatr th mr rlvant knwldg can b activatd. HYBNET prvid all tl rquird t frmulat, idntify and prc hybrid prc mdl (cf. Fig. 1) a dcribd by Schubrt t al. (1994) and Simuti t al. (1996). Hwvr, it i wrth t nt, that intad f mdling, th fcu i n lving particular tak f prc nginr lik ptimizing th prc prfrmanc. Th prc mdl i nt cnidrd t p a valu by itlf. It i thu ratd by th advantag it prvid fr lving th tak. t, F, FNH3,... X, S,,...,V MONOD EQUATIONS q=qmax S/(S+K) ARTIFICIAL NEURAL NETWORK ANN{1,5,1} CORRELATION =afnh3 FUZZY INFERENCE SYSTEM rc pha STOICHIO- METRY OUR=Y q +... CR= Yc q +... Intgratin MASS BALANCE dx/dt=... ds/dt=... ddt=...... dv/dt=dv dx/dt, ds/dt, d/dt,..., dv/dt OBJECTIVE FUNCTION J Idntificatin Offlin Optimizatin Onlin Optimizatin Gnralizd Dlta Rul Fig. 1. HYBrid NETwrk gnral tructur Th ntial bjctiv f HYBNET i t prvid a gnral ftwar packag, which cntain all th tl ncary t lv typical tak f prc ptimizatin and cntrl. HYBNET i dignd t rv nt nly fr th ftwar dvlpmnt, but al fr it maintnanc and xtnin in th cur f a prc. Fr intanc, whnvr nw data bcm availabl in a prc running undr it cntrl, HYBNET allw t mi-autmatically mak u f th data fr imprving th knwldg ba it u t imprv th prc prfrmanc. Frm th gnral aim it bcm clar, that th applicatin f HYBNET firt rquir a quantitativ dfinitin f what i mant by prc prfrmanc. A typical bjctiv might b t imprv th prc prfrmanc by rducing th varianc in m quality charactritic f th prduct by man f a bttr cntrl. 43

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl HYBNET al prvid a varity f tl which ar ncary t mak it applicatin mr cnvnint. E.g. prc data acquird by m frnt nd prcr can b takn vr, prprcd and viualizd undr diffrnt apct. Thi allw a highr lvl prc uprviin. Off-lin maurd data can b mad availabl tc. 2.2 Main cmpnnt rquird Th fllwing tlbx ar rquird within th HYBNET ftwar packag 1. On fr frmulating hybrid prc mdl 2. Anthr fr data prprcing, cnditining and trag 3. A third fr ptimizatin f cmplx prc mdl 4. A furthr n fr link t th prc and prc cntrl Additinally, much ffrt mut b placd int a frindly ur intrfac, and, lat but nt lat, a managing ytm i rquird that ynchrniz th diffrnt activiti rquird t prfrm th particular tak 3 MAIN COMONENTS OF HYBNET 3.1 Frmulatin f hybrid mdl A wid varity f tl ar mad availabl by HYBNET in rdr t cntruct, paramtriz and tt hybrid prc mdl. A gnral chm i givn in Fig. 2. Mdul xhybrid upprt ur activiti in hybrid mdling by upprting him during th pha f mdl tructur dfinitin and in paramtr idntificatin prcdur. It d nt nly manag th dvlpmnt f th baic prc mdl but al th applicatin f th mdl fr th particular tak. Data managmnt Data build th backbn f a prc cntrl ytm, hnc thy mut b carfully takn up, avd and prcd. Thr ar many fact that mut b cnidrd: 1. Dirct acc t all data rlvant t th tak t b prfrmd. Thi i guarantd by man f a ral tim data ba, which hld all data rlvant t th tak undr cnidratin and which might b f imprtanc t lv it prprly. Thi data ba i dirctly placd within th wrking mmry f th cmputr, that a quick randm acc i pibl. 2. Data tranfr btwn th frnt nd prcr that prfrm th data acquiitin and lw lvl cntrl dirctly at th plant quipmnt. Mt ftn thi tranfr i bing prfrmd via an ntwrk (lcal r rmt) and prcd via an TC/I-prtcl. Thi data tranfr i ud t tak vr th maurmnt data, and t tranmit th tup fr th lcal cntrllr back t th cntrllr running in th frnt nd prcr. Th tranfr mut b ufficintly fat in rdr t allw mdl upprtd 44

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl maurmnt f ky prc variabl that cannt b maurd dirctly r which mut b uprvid by fault dtctin algrithm running undr HYBNET. 3. Cmmunicatin with th ur via an apprpriat ur frindly intrfac, which guid th ur in all ituatin whr h d nt tak th initiativ. Data which charactriz th currnt tat f th prc r it imulatin ar diplayd in a frm which allw a quick vrviw vr th currnt ituatin. Ma Strag rc Link xplink F TC-I ntwrk u, y p Onlin ptimizatin u, y p Offlin ptimizatin Data Ba xbk y m u, y p HYBrid NETwrk xhybrid J Onlin/Offlin Optimizatin F Fig. 2. Intractin btwn HYBNET main ftwar cmpnnt and th prc. An iu which i f majr imprtanc t applicatin f data managmnt ftwar in bichmical prductin prc i that in th prc a lt f maurmnt ar mad ff-lin in th analytic labratry. In n-lin applicatin it i ntial t incrprat th maurmnt at th arlit tim. Onc th data ar knwn t th ytm, it mut b ud t imprv th knwldg abut th tat f th prc and pibl cnqunc mut b cnidrd and drawn whn ncary. Althugh data managmnt i widly cnidrd a nn-attractiv tak fr cintit and thu undr-mphaizd in litratur, it i bcming wll rcgnizd by pcialit t b n f th mt imprtant apct t b cnidrd whn it cm t build an ffctiv prc mdl and t a rductin f th numbr f xprimnt during prc dign and ptimizatin. 45

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl In HYBNET, th mdul xplink i rpnibl fr th n-lin and ff-lin cmmunicatin with th prc frnt nd cntrllr ytm. Th tandard prtcl prvidd i TC/I, hwvr, diffrnt tchniqu ar pibl. Th ral tim data ba i cntrlld by th mdul xbk. It al manag data prprcing and th viualizatin. 3.3 Optimizatin rc ptimizatin i n mt prminnt tak t b prfrmd by a uprviry ytm lik HYBNET. Thr ar vral tak whr ptimizatin i th critical iu: 1. Mdl paramtr idntificatin frm prc maurmnt data i n xampl, whr th ptimizatin i aiming at a minimizatin f th rt man quar rrr btwn th prc maurmnt data and th mdl prdictin f th maurmnt ignal. 2. Th cnd apct which i f primary intrt i ptimizatin f th cntrl variabl prfil and tart paramtr lik vlum and cncntratin f variu cmpnnt in cultivatin in a pn lp fahin. 3. Th third imprtant apct cnidrd in HYBNET i th n-lin ptimizatin f th manipulatd variabl vr hrt tim hrizn. Thr ar vral rutin availabl in HYBNET fr th diffrnt apct. Thy rang frm claical backprpagatin (Rumlhart t al. 1986, Wrb 199) rutin ud t train ingl artificial nural ntwrk t vral diffrnt randm arch tchniqu which ar f gnral u (Simuti and Lübbrt 1997). 3.4 Cld-lp cntrl xhybrid wa aid t b th mdul that upprt hybrid mdl dvlpmnt, but it can d mr. It can al b ud t dfin and paramtriz cntrllr in rughly th am way a mdl dvlpmnt: by dfinitin f th cntrl ytm tructur and by th crrpnding paramtr idntificatin. It cnidr th cntrllr t b n additinal prc cmpnnt. 3.5 Cpratin with cmmrcial ftwar tl It d nt mak n t prfrm tak with a nw ftwar, whr wll tablihd ftwar tl ar alrady availabl. Hnc HYBNET wa dignd a an pn ftwar which allw t mak u f ftwar packag, which ar widly ditributd in indutry, lik Matlab, Scilab, Excl, Origin, tc. Fr intanc, tak that can cnvnintly prfrmd by Excl huld b prfrmd with thi tl. 4 EXAMLES OF TASKS THAT CAN BE SOLVED WITH HYBNET T giv m xampl f th quality f th tak that can b lvd with HYBNET, w will dicu m qutin apparing during th ptimizatin f a yat prductin 46

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl prc. Th prc prfrmanc J i aumd t b mainly influncd by th man pcific grwth rat, which i trid t kp n th dird lvl µ d and th bima/ubtrat-yild Y x/ : J = Y x/ O (µ d -µ) (1) whr O i a wighting factr dtrmining th trngth f th pnalty cnidrd whn µ i dviating frm µ d. On main cntraint i a maximum frmntatin tim t f. Th bjctiv i t maximiz th prfrmanc J. Th traightfrward way t dvlp an imprvd prc ptimizatin and cntrl tratgy i t firt find th mt imprtant charactritic f th prc with rpct t th bjctiv functin J. Thn, prfil f th manipulatabl quantiti mt ignificantly influncing th bjctiv functin ar dtrmind. Thi i th ff-lin ptimizatin tp (al calld pn lp cntrl). Finally, a cld lp cntrllr i dvlpd in rdr t kp th prc n it prdfind ptimal path. Whn thi i nt accuratly nugh pibl, crrctin dtrmind frm th maurd and th timatd tat f th prc, can b prpd by HYBNET 4.1 Fatur idntificatin Accrding t Snnlitnr and Käplli (1986) th primary bilgical fatur ruling th bima grwth in a yat prductin i th maximal rpiratry capacity q c max f th train ud. Whil in cntinuu cultur, thi fatur i rughly tatinary, it mut b aumd t b tim dpndnt in ral fd-batch prductin prc. Hnc, th firt tak i t idntify th tim varianc f thi ky quantity making u f th availabl data frm th prc undr cnidratin. Fg Maurmnt t ANN {1,3,1} q c,max (t) KINETIC, r, r MASS x,, MODEL BALANCE Z-1 E LEARNING ALGORITHM MSE Fig. 3. Hybrid ntwrk fr fatur idntificatin. An artificial nural ntwrk ANN{1,3,1} i ud t idntify th functin q c,max =f(t). Larning algrithm: Backprpagatin+Cr-validatin+Cnjugat gradint with lin arch+bacth MSE bjctiv functin. 47

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl x(g/l), (g/l), (g/l) 2 x(g/l) BTM(g/l) (g/l) 15 m (g/l) (g/l) m (g/l) 1 5 q c,max (g/l/h),24,22,2,18,16,14 q c,max (g/l/h),12 5 1 15 2 t(h) Fig. 4. Fatur idntificatin: prfil f bima (x-timatd, BTM - maurd), gluc (-timatd, m maurd), thanl (-timatd, m -maurd) and fatur (q c,max ).fr a typical frmntatin. Th hybrid apprach i: Th back bn f th mdl ud i a t f ma balanc quatin fr bima x, ubtrat and mtablic prduct thanl. In thi impl xampl, th rlvant yild cupling th ma balanc quatin ar bad n a impl tichimtry. Th kintic cntaining th fatur maximum rpiratin capacity i bad n th Mnd xprin. Sinc thr i n a priri knwldg abut q c max, it i traightfrward t u a nural ntwrk a a gnral frm t dcrib thi tim dpndnc. A hwn in Fig. 3, th prblm can b undrtd a finding q c max in an ptimizatin prcdur minimizing th ridual btwn xprimntal data and th prdictin by th mdl. HYBNET allw t u vral ptimizatin algrithm t lv that prblm. A typical rult i hwn in Fig. 4. 4.2 Opn-lp cntrl Whn th tim bhavir f q c max i knwn, thn it i an ay tak t dtrmin th ptimal fding tratgy fr th gluc with rpct t th prdfind bjctiv functin. In th xampl, w d nt prcd th cnvntinal way f pn lp cntrl f dtrmining th fdrat prfil F(t). Intad, w cncntrat n th quantity mr dirctly dcribing th ubtrat uptak f th rganim. Thi i th pcific ubtrat cnumptin rat q and w ar thu lking fr an ptimal prfil q pt (t) f thi ky quantity. Sinc th bjctiv functin i uually nt impl and th mdl rathr cmplicatd du t it nn-linarity, claical gradint prcdur d nt alway wrk prprly.,1 48

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl Fr uch ituatin, HYBNET prvid vral randm arch mthd t find th ptimum prfil (Simuti and Lübbrt 1997). Th chm f th ptimizatin prcdur i hwn in Fig. 5. Th rulting q pt (t), hwn in Fig. 6, wa btaind with an algrithm bad n an vlutinary prgramming tchniqu (Simuti and Lübbrt 1997). t ANN {1,3,1} q c,max (t) KINETIC MODEL (t) OBJECTIVE FUNCTION J Y X / S O( d ) t ANN {1,5,1} q,pt (t) OTIMIZATION MAX(J) J Fig. 5. Hybrid ntwrk fr fflin ptimizatin (ANN traind with an vlutinary prgramming algrithm) 1,6,3,25 1,4 (g-bim/g-bim/h),2,15,1,5 q,pt,max pt,pt,pt r,pt d 1,2 1,,8,6 q,pt (g-gluc/g-bim/h),,4 5 1 15 2 t(h) Fig. 6. Offlin ptimizatin rult: th dird valu fr th grwth rat i,23 g- bim/g-bim//h. Th btaind yild wa Yx/=,489.,max i th maximum grwth rat fr th gluc xidatin pathway, d i th dird valu, pt i th timatd ptimal prfil,,pt,,pt and r,pt ar timatd prfil fr gluc xidatin, thanl xidatin and gluc rductin rpctivly. 49

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl 4.3 On-lin cntrl Onc a prfil fr th ky manipulatabl quantity, in ur xampl th ptimal pcific ubtrat cnumptin rat q pt, i availabl, th traightfrward way t guarant that th prc i kpt n that path i n-lin cntrl. Hr w u a dirct mdl prdictiv cntrl tchniqu t illutrat th capabiliti f HYBNET. Mdl prdictiv cntrl dirctly mak u f th xplicit and paratly idntifid hybrid prc mdl in rdr t indirctly dtrmin th bima frm th availabl maurmnt data, it al mak u f th maurmnt valu,.g., th frmntr wight, in rdr t dtrmin a rliabl valu f th cultur vlum v. Tgthr with th ubtrat cncntratin F in th fd, th actually rquird fd rat F pt can b dtrmind by F pt = q pt x v/ F (2) Thi ignal can b tranfrrd dirctly t th phyical fding ytm. F,pt Maurmnt CONTROLLER F,pt =q,pt xv/s in F,pt x, v FEATURE IDENTIFICATION x,, ONLINE LEARNING q c,max q,pt OTIMAL GLUCOSE FLOW J Y X / S O ( d ) OTIMIZATION MAX(J) Fig. 7. Hybrid ntwrk fr nlin ptimizatin. Th fatur idntificatin and ptimal gluc flw mdul ar cndnd rprntatin f th diagram in fig 3 and 5 rpctivly. In rdr t furthr imprv th cntrl and t rpnd n mdling and maurmnt rrr, th prdtrmind fatur prfil can b crrctd n-lin. Such tuning can b dn with HYBNET in th way ktchd in Fig. 7. Th currntly availabl maurmnt ar cmpard with th mdl prdictin and a n a thr i a ignificant dviatin, 5

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl th fatur q c max will b crrctd in a rrr fd-back fahin. Any ignificant chang thn al rquir an adapttin f th q,pt prfil. With th nw data f q pt, th t pint fr th F pt valv i thn crrctd.,5 Y x/ (g-bim/g-gluc) btaind (g-bim/g-bim/h),4,3 Thrtical ptimum With nlin crrctin Withut nlin crrctin,2,1, 1 2 3 Optimizatin prcdur Fig. 8. Cmparin f th ptimizatin prcdur with a tt frmntatin: prcdur 1) Thrtical ptimum Yx=.49 btaind =.23; prcdur 2) nlin implmntatin with crrctin Yx=.48 btaind =.24, and prcdur 3) nlin implmntatin withut crrctin Yx=.42 btaind =.25. Th dciiv advantag f thi prcdur (Olivira t al. 1997) in cmparin t th claical dirct ptimizatin f th fd rat prfil F(t) i that th fcu f th cntrl i n th phyilgical ky cntrl quantity, th pcific ubtrat cnumptin prfil and th ptntial rrr in auming bima and vlum prfil (which ar ncary t dtrmin F(t)) ar ignificantly rducd (viz Fig. 8). E.g., thr ar particularly prblm in dtrmining th v(t) prfil in labratry xprimnt and pilt plant whr ba additin, vapratin, fding f antifam agnt tc. can lad t ignificant rrr in th prdictin f v(t). Al rrr in th cncntratin F can lad t ignificant rrr in practic. With tat timatin prcdur uing actual maurmnt data during th running prc, th prfil f x and v can b dtrmind with a cnidrably mallr rrr. 5 CONCLUSIONS Th widprad u f th rult f advancd mthd f prc ptimizatin and cntrl i largly dlayd by miing ftwar-tl that can hlp t kp th 51

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl xpnditur fr dvlpmnt and maintnanc in accptabl limit. HYBNET i a dvlpmnt dn in rdr t cp with that prblm. HYBNET hlp t rduc a much a pibl th frmal ffrt t dvlp a prc mdl that can b ud fr prc ptimizatin and cntrl. It prvid th crrpnding guidanc fr th bichmical nginr. Hwvr, it i nt pibl what m vndr f ftwar packag claim that mdling f cmplx bichmical prc i an ay tak. Th bichmical nginr mut prfrm hard wrk t cllct all th currntly availabl knwldg which might b rlvant t hi particular tak. It i al nt crrct that all prblm can nw b lvd mrly with artificial ntwrk r fuzzy xprt ytm aln. Fr intanc, mchanitic dcriptin alrady availabl mut b ud dirctly, it d nt mak n t larn thm nc mr frm niy data. HYBNET will hlp him t dcid whthr r nt it will hav a ignificant impact n th prc bnfit/ct-rati and in ca f a pitiv dciin t intgrat it int th ntwrk cntituting th currnt prc mdl. In HYBNET, hwvr, th prc mdl i mrly cnidrd a man t an nd. Th fcu i n th tak t b prfrmd,.g., th ptimizatin f th prductivity. Thu, th affrd t cntruct a mdl mut carfully ratd with an y n th bnfit/ct-rati. A cntral iu in HYBNET i prc ptimizatin,.g., th dtrminatin f ptimal fding prfil in fd-batch prc a wll a th tart paramtr lik tart vlum, tart ubtrat cncntratin. Svral way ar prvidd t upprt uch tak dpnding n th knwldg that can b mad availabl. In th bginning, whn thr ar nly a fw data availabl th wight i mr n knwldg frm litratur. Whn thr i mr data availabl th fcu mv mr and mr t data drivn tchniqu, inc thy mr dirctly rflct th bhavir f th particular prc undr cnidratin. Th ida f fuin f mdl i nt nw, but HYBNET i a tl which allw t bring it int practic with a ranabl xpnditur. HYBNET wa dvlpd t upprt advancd cntrl tratgi in indutrial prductin nvirnmnt. Thr prc cntrl i n majr iu. Thi prblm ha bn lvd in vry much th am way than prc mdling. Th prc i thn viwd at with th cntrllr bing an intgratd part f th prc. Cnquntly, th hybrid tchniqu dvlpd, culd b imply xtndd. And, th dtrminatin f th cntrllr paramtr bcm an ptimizatin prblm, whr th prc prfrmanc i ud a th ptimizatin critrin. HYBNET i ud in diffrnt bichmical prductin prc a wll a in labratri and pilt plant. It i cntinuuly bing xtndd in particular cncrning th ur intrfac, which i ncary t rduc th activatin barrir flt by many prc nginr in indutry fr uing ftwar tl. Acknwldgmnt. Dicuin with many cllagu frm indutry ar gratfully acknwldgd. R. Olivira acknwldg th rtugu Scinc Fundatin JNICT (BD/251/93-RM) 52

Chaptr 3. HYBNET, an Advancd Tl fr rc Optimizatin and Cntrl REFERENCES Olivira, R., G. Smldr, R. Simuti, A. Lübbrt (1997). Imprvd n-lin cntrl f bichmical cultivatin prc. (in prparatin) Rumlhart, D., D. Hintn, G. William (1986). Larning Intrnal Rprntatin by rrr prpagatin. in D. Rumlhart and F. McCllland d., aralll Ditributd rcing, 1, Cambridg, MA:M.I.T r Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994). Biprc ptimizatin and cntrl: Applicatin f hybrid mdlling. J. Bitchnl. 35, pp. 51-68 Simuti, R., A. Lübbrt (1997). A cmparativ tudy n randm arch algrithm fr bitchnical prc ptimizatin. J. Bitchnl., 52, pp. 245-256 Simuti, R., R. Olivira, A. Lübbrt (1996). Hybrid Mdling with Nural Ntwrk and it Utilizatin in Biprc Cntrl. Biractr Enginring Cur, Saltjöbadn, Jun 14-18 Snnlitnr, B., O. Käppli (1986). Grwth f Saccharmyc crviia I Cntrlld by It Limitd Rpiratry Capacity: Frmulatin and Vrificatin f a Hypthi. Bitch. Bing., 28, öp. 927-937 Sulzbach, D. (1997). An indutrial prpctiv n cintific cmputing, Http://www.twart.c.du.du Wrb, J.. (199). Backprpagatin Thrugh Tim: What It D and Hw t D It. rcding f th IEEE, 78(1), pp.155 53

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Chaptr 4 Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Abtract. Thi papr prnt a mdl-bad cld-lp cntrl prcdur bad n a hybrid prc mdl. An infrntial cntrl tratgy nt yt dicud in litratur, wa chn t kp th cncntratin f ammnia and prcurr in pnicillin prductin xprimnt undr tight cntrl. It main cmpnnt, th timatr fr th ammnia and prcurr cnumptin rat, i an indirct maurmnt prcdur which u vral diffrnt n- and ff-lin maurmnt data. An hybrid prc mdl wa ud t cmbin vral kintic mdl, which wa capabl f larning during it applicatin uing autmatic training tchniqu. articularly, th nural ntwrk cmpnnt f th hybrid ntwrk wa rtraind during thi n-lin larning prc. Al all th thr cmpnnt f th hybrid mdl ar autmatically r-tund, nc nw data bcm availabl. Th prpd prcdur wa ttd in 22 frmntatin run whr it prvd t b rbut and tabl. Thi chaptr ha bn ubmittd fr publicatin: Olivira, R., G.J.F. Smldr, R. Simuti and A. Lübbrt (1998). Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk. (ubmittd) 54

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk 1 INTRODUCTION Imprvmnt f th bnfit/ct-rati f thir frmntatin prc i n f th mt imprtant vry-day-duti f bichmical nginr. Fr ct ran, typically nly a fw xprimnt can b cnductd, particularly whn frmntatin prc fr highly cmptitiv prduct mut b imprvd. Strain lctin r cntrl prfil ptimiatin ar typical xampl f th cncrt aim. Hnc, th ncary xprimnt mut b wll dignd and tightly cntrlld in rdr t prvid ufficintly accurat infrmatin n which th rlvant dciin may b grundd. Obviuly, data frm badly cntrlld xprimnt, which dpict a batch-t-batch variability f vral prcnt cannt b ud t ditinguih btwn th bnfit r diadvantag f diffrnt cntrl prfil r train with rpct t th prc prfrmanc, whn th chang ar xpctd t b in th am rdr f magnitud. In th ca f train lctin xprimnt, whr th influnc f diffrnt train n prductivity i ttd, prc cntrl i f paramunt imprtanc, inc it mut b guarantd that th diffrnt train ar cmpard n xactly th am ba, i.. undr wll dfind cnditin. In rdr t cntrl a frmntatin prc, a cnidrabl amunt f knwldg mut b activatd. Svral apprach hav bn dicud in litratur. Hwvr, th prblm with many invtigatin n cntrl publihd in th bitchnlgical litratur i that thy ar thrtically brilliant tudi but th rult mt ftn wr nt validatd within a ufficintly larg numbr f frmntatin. Thi papr i intndd t dcrib a mdl-upprtd cld-lp cntrl prcdur that alrady prvd t wrk in practic. Th prcdur i xplaind at th xampl f th pnicillin prductin prc, which i n f th tandard prc with rpct t prc cntrl dicud in litratur vr many yar (Cntantinid t al., 197; Bajpai and Ru, 1981; Niln and Villadn, 1994; DiMaim t al. 1992; ruting t al., 1996). Mt ftn, pn lp cntrl wa dicud in litratur. Hwvr, th main diadvantag f an pn-lp cntrl i that uncrtainti in th initial cnditin and ytm paramtr may lad t larg rrr in prc pratin. Thrfr, it i advantagu, t dvlp a cld-lp ptimiatin chm which attnuat uncrtainti in th paramtr and i fairly indpndnt f th initial cnditin (.g., Mdak and Lim, 1987). Hr w addr a particular cntrl prblm in th pnicillin prductin prc that ha nt bn xtnivly dicud in litratur, th rgulatin f th cncntratin f th prcurr and th nitrgn urc. Th additin f id chain prcurr timulat th ynthi f pnicillin (Thrn and Jhnn 195), but it can b txic at t lw ph valu. Ammnium alt ar uitabl urc f nitrgn, hwvr, th cncntratin f fr NH 4 + huld b kpt cntant n an apprpriat lvl, inc thi may influnc th ynthi f crtain amin acid ndd fr pnicillin ynthi (Curt and irt 1981, Luri t al. 1976). 55

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk It wa cncludd frm prviuly prfrmd tudi that th prcurr and ammnia cncntratin huld b kpt at cntant lvl. Dviatin frm thir quai ptimal valu wr rcgnizd a t dcra th pnicillin prductivity. Hnc, it i traightfrward t rgulat th cncntratin, C n, C pa, that thy ar kpt within wll dfind bund arund thir t pint C n,p and C pa,p. Tday, uch a cntrl f prcurr and th ammnia cncntratin i bing prfrmd manually in mt factri. But thi way f cntrlling i xpniv, inc it bind cnidrabl man-pwr, rquir an xtniv prnnl training and th quality f cntrl dpnd n th prnal kill f th pratr. Th l xpniv altrnativ i cmputr bad prc uprviin and cntrl. What typ f cntrl i ncary? Sinc w ar gnrally frcd t lk fr th mt impl lutin, th firt qutin that mut b akd i whthr r nt th impl ID cntrllr can b applid. Thr ar tw ran that pak againt thi impl lutin. Th mt vr practical prblm i that th cntrl variabl, C n, C pa ar uually maurd ff-lin with a lng ampling tim incrmnt 't, which i much largr than can b accptd fr dirct cntrl. Hnc, thr i n maurmnt ignal that can b ud in th ID cntrllr. Th cnd ran i that ID cntrllr ract n dviatin in th actual valu f th cntrl variabl frm it crrpnding t pint in a prdfind way pcifid by th cntrllr paramtr. Th paramtr f impl ID cntrllr ar adjutd t th nminal prc dynamic, which i aumd t b tim-indpndnt and knwn bfrhand. Th pnicillin prductin prc, hwvr, i knwn t b a trngly nnlinar prc that dpict a ubtantially tim varying dynamic. Hnc, altrnativ cntrllr dign, which can cp with th tw prblm, mut b cnidrd. In thi papr w prp t u th infrntial cntrl tchniqu, which manatd frm mdl prdictiv cntrl tchniqu (Garcia t al., 1989). In infrntial cntrllr, th infrmatin abut th prc tat i dtrmind indirctly by man f a mdl upprtd maurmnt. Hnc, th dirct maurmnt f th cntrl variabl, ncary in a impl cntrllr, i rplacd by uing thr maurmnt infrmatin and a ufficintly accurat rlatinhip btwn th data and th cntrl variabl. In thi way it i pibl t cp with th lng tim incrmnt 't mntind bfr. Whn, th rlatinhip cnncting th maurd variabl with th cntrl variabl ar dynamic rlatinhip, th prblm cncrning th tim-varying prc dynamic i al lvd. Hnc, infrntial cntrllr ar th mattr f chic fr th prblm t b lvd. Th maurmnt variabl that can b ud in th indirct maurmnt f th ammnia and prcurr cncntratin ar: ubtrat fd rat F, ammnia fd rat F n, 56

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk prcurr fd rat F pa, frmntr wight W B, carbn dixid prductin rat CR, and xygn uptak rat OUR. In an infrncial cntrl ytm, th accuracy f th upprting timatin mdl i f majr imprtanc. Fr th prnt prblm, accurat mdl that rlat th cntrl variabl with th manipulatbl quantiti ar nt availabl in litratur. Hnc, thy had t b dvlpd. Accuracy incra with th amunt f rlvant a priri knwldg abut th prc that can b activatd t aid th cntrl tak. Fr that ca it i traightfrward t mak u f hybrid mdl a thy ar a man t tak th availabl knwldg r infrmatin abut th rlatinhip frm diffrnt urc a thy bcm availabl, thu aviding l which appar during any tranfrmatin int any thr rprntatin. In uch a hybrid mdl w mak u f mdl tructur availabl in litratur a wll a f huritic and th infrmatin till hiddn in data rcrd maurd at th prc. Sinc in th bginning f th cntructin f a mdl, th knwldg which can b activatd i limitd, it i traightfrward t adapt th mdl t th prc undr cnidratin whnvr nw data, r any thr kind f nw infrmatin abut th prc bhavir, bcm availabl. In thi papr w u an n-lin larning tratgy. 2 ROCESS MODEL Sinc th prc mdl i f dciiv imprtanc in an infrntial cntrllr, th prc mdl ud fr thi purp i paratly dicud in dtail. A th prc mdl i ud hr t aid th infrntial cntrllr, it main bjctiv i t prvid a ufficintly accurat link btwn th cntrl variabl and th maurd quantiti in uch a way that th prc cntrllr can kp th ammnia and th prcurr cncntratin within prdfind intrval f re n and f re pa arund th rpctiv tpint valu. Th dmand fr th rrr bund wr drivd frm th rprducibility rquirmnt f th prductin prc. Thy wr dtrmind in prviu invtigatin and ar cnidrd t b cncrtly givn in th wrk rprtd abut hr. 2.1 Macrcpic Balanc Th backbn f th hybrid mdl dicud in thi papr i a ytm f ma balanc quatin fr th cntral quantiti in cau. In th pnicillin prc, thr ar 7 quantiti that play a dciiv rl. Th ar th cncntratin f bima, ubtrat, prduct, prcurr, nitrgn urc, xygn and carbn dixid. It wuld b ptimal if n culd tak int accunt all th rlvant variabl. In practic, hwvr, th firt thr quantiti cannt b maurd n-lin with ufficint rliability. Evn an indirct maurmnt f th variabl can b prfrmd with cnidrabl rrr nly. Th lattr tw quantiti can b cvrd by n-lin maurmnt. Hnc, w mut dal primarily with th tw cntrl variabl C n and C pa. Thn, f cur, it mut b hwn 57

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk that thi chic uffic t cp with th cntrl prblm tatd abv. Tt calculatin hwd that th incrpratin f th balanc fr bima, ubtrat and pnicillin did nt lad t advantag with rpct t th timatin f C n and C pa. Th ttal ma f th ytm i knwn frm n-lin maurmnt and, thrfr, d nt nd t b cnidrd in th balanc quatin. Fr th fd-batch rgim, uually applid in th pnicillin prductin, th ma balanc acr th cultur within th frmntr can b rprntd by th fllwing impl ytm f rdinary diffrntial quatin dc n dt dc pa dt = -R n + F n W B C n,fn - F tt W B C n = -R pa + F pa W B C pa,fpa - F tt W B C pa (1a) (1b) whr th vctr C i rprnt th cncntratin f prcurr and ammnia and C fi. th crrpnding cncntratin in th fd int th ractr. F tt i th ttal rat f vlum chang within th ytm bundari, which bid th fd rat may al cntain cntributin f watr vapratin and l du t ampling vnt. Whn th fd rat F i ar knwn, th nly cmpnnt that drv pcial attntin ar th rat xprin R n and R pa. Th rat ar dtrmind by th prc kintic. 2.2 Kintic Th kintic mdl mut b drivd frm th availabl data f a t f xprimnt. Hnc, it i traightfrward t firt analyz thi data in a cnvntinal way (DiMaim t al. 1992). An immdiat qutin apparing in thi rpct i th qutin abut th varianc in th data f a t f xprimnt prfrmd undr cmparabl cnditin. In rdr t timat th varianc, th avrag cnumptin rat prfil wa xtractd frm a t f 32 frmntatin data rcrd. Th nmbl avragd rult ar hwn in Figur 1 and 2 tgthr with th riginal data. In rdr t judg th varianc in th data, i.. th dviatin f th maurd rat prfil (btaind in th individual frmntatin) frm th avrag prfil, and th intrval crrpnding t th rrr bund allwd, ar dtrmind. Th rrr bund fr th rat data can b timatd frm th abv mntind cncntratin rrr bund by th fllwing impl apprximatin E r = E c /'t (2) whr 't i th tim incrmnt f th data ampling prcdur. Th am apprach wa ud fr bth cntrl variabl. Th crrpnding intrval arund th nmbl avrag ar al dpictd in th Figur 1 and 2. Th tw Figur hw that bth data clud d nt tay within th prdfind rrr bund. Hnc, w can cnclud, that 58

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk bth rat mut b timatd mr accuratly. Th nmbl avrag can b rgardd a firt gu fr th rat prfil f a rprntativ frmntatin. Cnumptin ammnia (g/kg/h) Maurd man man + E r man - E r tim (h) Fig. 1. Cnumptin rat f ammnia fr 32 frmntatin Cnumptin prcurr (g/kg/h) maurd man man + E r man - E r tim (h) Fig. 2. Cnumptin rat f prcurr fr 32 frmntatin 59

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk T cntruct an accurat kintic mdl, it i ncary t knw th intrrlatinhip btwn th maurd prc variabl and th rat xprin. Thu, th apprpriat nxt tp in th tatitical analyi huld b a crrlatin analyi. Th rult f uch a crrlatin analyi ar ummarizd in Tabl I and II. Thy ar prvidd in th frm f crrlatin matric f th variabl t, R, CR, RQ and R n and th variabl t, R, CR, RQ and R pa rpctivly. Fr bth, th ammnia and prcurr cnumptin rat, it can b n that th hight crrlatin i with th gluc cnumptin rat R, fllwd by CR, t, and finally RQ. In th ca f prcurr, th crrlatin with t i ntably high, what man that th prcurr ignal ha a prminnt tructur r tim pattrn. Th rult f th crrlatin analyi can b rgardd a ranking f th variabl. Thi mut b cnidrd in a dtaild kintic mdl. Tabl I Crrlatin matrix fr th t f variabl t, R, CR, RQ and Rn t R CR RQ R n t 1.7685.8795.3368.5787 R.7685 1.929.2895.8696 CR.8751.929 1.398.7752 RQ.3368.2895.398 1.1889 R n.5787.8696.775 2.1889 1 Tabl II Crrlatin matrix fr th t f variabl t, R, CR, RQ and Rpa t R CR RQ R pa t 1.7685.8795.3368.83 R.7685 1.929.2895.9388 CR.8751.929 1.398.945 RQ.3368.2895.398 1.2936 R pa.83.9388.945.2936 1 Whn, in a firt apprach, a linar rlatinhip btwn th ammnia and prcurr cnumptin rat and th ubtrat cnumptin rat R, which appard a th firt candidat f an influnc variabl in th crrlatin analyi, i aumd thn, fr 32 frmntatin data t, w btain th rat prfil dpictd in th Figur 3 and 4. Althugh th rprntatin hw that thr i m linar cmpnnt in th data, th linar rprntatin i nt atifactry. In particular th dpndncy f th prcurr rat frm th ubtrat cnumptin rat dviat t much frm th allwd rrr bund indicatd in Figur 4. 6

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Cnumptin ammnia (g/kg/h) Maurd Linar rlatinhip Linar rlatinhip - E r Linar rlatinhip + E r Cnumptin ubtrat (g/kg/h) Fig. 3. Linar rlatinhip btwn th cnumptin rat f ammnia and th cnumptin rat f ubtrat Maurd Linar rlatinhip Linar rlatinhip + E r Linar rlatinhip - E r Cnumptin prcurr (g/kg/h) Cnumptin ubtrat (g/kg/h) Fig. 4. Linar rlatinhip btwn th cnumptin rat f prcurr and th cnumptin rat f ubtrat 61

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Th tandard dviatin f th prcurr cnumptin rat frm it man i abut 1.8 tim th valu that, fllwing th abv mntind rrr timatin, wa cnidrd t b allwd. Hnc, a mr cmplx mdl in particular fr th prcurr, but al fr th ammnia cnumptin rat i ndd. 2.3 Hybrid Mdl Ntwrk Sinc in thi particular applicatin a cnidrably xtndd t f frmntatin rcrd i availabl, it i traightfrward t u a data drivn apprach t dvlp an accurat kintic mdl that cnidr mr than a ingl influnc variabl. Hr w prp t u an hybrid mdl ntwrk t dcrib th prc kintic. A ha alrady bn rcgnizd by vral authr (ichgi and Ungar, 1992; Thmn and Kramr, 1994; Schubrt t al., 1994) uch hybrid mdl can b xcptinally pwrful in rprnting nnlinar prc kintic. In th hybrid kintic mdl prpd in thi ctin, vral blck that imultanuly dcrib th am phnmnn, ar ud in th n f prviding diffrnt vt fr th rat xprin ndd, manating frm diffrnt pint f viw. In rdr t cmbin th vt prprly, thr i an arbitr that dcid abut th rlativ wight which mut b attributd t th diffrnt cntributin. Th mtivatin fr thi apprach i that th rlvant knwldg i availabl by part in frm f mchanitic mdl, by huritic rul, and by part imply in frm f data tructur infrmatin, which i mt ffctivly rprntd by artificial nural ntwrk. Sinc any attmpt t tranfrm all thi knwldg int a ingl rprntatin, fr xampl int a mathmatical mdl man a cnidrabl l in infrmatin, th diffrnt itm ar rprntd in thir mt dirct frm. Thi i th mathmatical quatin fr th mchanitic mdl, a fuzzy rul ytm fr th huritic a wll a a nural ntwrk t rprnt th tructural infrmatin frm xtndd data t. 2.3.1 Nural ntwrk mdul. In th bginning f uch a mdl dvlpmnt, whn mchanitic knwldg i nt wll dvlpd, th nural ntwrk cmpnnt tak th main lad f an hybrid mdl, particularly frm th pint-f-viw that it can b rgardd a an advancd nnlinar crrlatin tchniqu. In thi wrk a cnvntinal fdfrward nural ntwrk wa ud with thr layr t rprnt th tw rat xprin R n and R pa cnidrd in ur kintic. A input variabl, th 4 quantiti that wr fund t crrlat bt with th rat xprin wr takn: Subtrat fd rat F, tim t, carbn dixid prductin rat CR, and rpiratin qutint RQ. 2.3.2 Fixd carbn mdul. Th cnd apprach t rprnt th kintic i th calld fixd-carbn mdl. It i bad n th huritic xprinc that th rat cnidrd d crrlat bttr with th carbn fixd in th biractin ytm than with th ubtrat cnumptin rat. Th amunt f c f fixd carbn i dtrmind frm th flw f carbn ntring th ytm by man f th ubtrat fd and th flw f 62

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk carbn laving th ytm via th CO 2 thrugh th vnt lin. Thi can b apprximatd by f c = R M CR (3a) whr (R ) i th ubtrat cnumptin rat, (M ) i th mlcular wight f ubtratct in C-ml. Th rat by which nitrgn i cnumd i aumd t b linarly dpndnt n th carbn cnumptin rat R n,fc =a 1 f c +b 1 (3b) Fr th prcurr cnumptin a imilar apprach wa fllwd, hwvr, it prvd t b ncary t aumd tim-dpndnt cfficint. R pa,fc =a 2 (t) f c +b 2 (t) (3c) Th cfficint a i ar in m n yild cfficint. Th ablut trm b i can b intrprtd a m part f th maintnanc rquirmnt. 2.3.3 Rprntativ Trajctry. Th third rprntatin f th rlvant rat i a t f rprntativ tim prfil fr th tw rat R n (t) and R pa (t) which rprnt a typical wll prfrming cultivatin. Th prfil wr cntructd frm th xprinc with th frmntatin ytm. It i f advantag t cmpri thi prfil in a m mr cnvnint rprntatin. Sinc th prfil ar rathr cmplx, th tim functin may b rprntd by man f fdfrward artificial nural ntwrk. Thi allw t wrk with vral diffrnt frmntatin prfil that can b ud latr n fr diffrnt ca. Th pratr can dcid aftrward which f th rprntativ prfil fit bt with th actual frmntatin. 2.3.4 Wighting th mdul. Th wight by which th diffrnt mdul ar takn int accunt during th mdl valuatin ar dtrmind with a mall xprt ytm. Th main mphai wa placd n th xprimntal vidnc availabl in th crrpnding part f th tat pac. Th algrithm ud t dtrmin thi vidnc i th -calld vidnc maur (Lnard and Kramr, 1992). Thi vidnc maur charactriz th crdibility f th mdl that ud th crrpnding maurmnt infrmatin. Mt pririty i attributd t th nural ntwrk dcriptin f th kintic, inc it prvd t prvid th mt rliabl rult at rgin in th tat-pac whr th vidnc maur i high. Th xtraplatin maur i a numbr btwn and 1. Thi numbr wa takn t dtrmin th rlativ influnc f th ANN n th rat xprin. Th cmplmntary wight wa ditributd n th tw thr mdl. In ca whr thr ar maurmnt rrr in th CR, th fixd carbn mdl cannt b ud. Thn, th rprntativ frmntatin prfil ar givn th prfrnc. Hnc, th 63

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk rlativ wight f th thr tw mdl wa mad dpndnt f th accuracy by which th CR culd b maurd. Only a fw rul uffic t t up th mall fuzzy xprt ytm that ch th rlativ wight. 2.4 Idntificatin Th mdl idntificatin, i.. th fit f th mdl paramtr t th availabl data t, can ntially b cnidrd an ptimizatin prblm. Th xpnditur rquird fr uch an idntificatin dpnd n th cmplxity f th mdl ud. With hybrid mdl ntwrk, w ar facd with rathr cmplx mdl whr impl ptimizatin prcdur might nt wrk prprly. In th ca f nural ntwrk th idntificatin i rfrrd t a th ntwrk training. Th mt ud training mthd fr nural ntwrk ar bad n th rrr backprpagatin tchniqu, which nabl th xact calculatin f gradint f a givn bjctiv functin with rpct t th nural ntwrk paramtr (Wrb, 199). Hwvr, in th ca f hybrid mdl ntwrk that cntain furthr diffrnt mdl cmpnnt, and in particular whn thy includ diffrntial quatin, rrr backprpagatin mut b ud tgthr with th nitivity tchniqu in rdr t calculat th rquird gradint (.g. Schubrt t al., 1994; Olivira t al., 1998). In th prnt wrk th larning mthd wa bad n th fllwing tchniqu: 1. Batch lat-quar bjctiv functin 2. Errr-backprpagatin+nitiviti mthd t calculat th bjctiv functin Gradint with rpct t th hybrid mdl ntwrk paramtr 3. Cnjugat gradint with lin-arch ptimizatin algrithm 4. Cr-validatin validatin tchniqu Th bjctiv functin cnitd n a minimizatin f prcurr and ammnia timatin rrr accrding t a lat-quar critrin: 1 E= ([ D(C pa, (t) - C pa (t)) ] 2 + [ E(C n, (t) - C n (t)) ] 2 2 ) (4) ¹ t=1 whr C pa, and C pa ar th maurd and timatd cncntratin f prcurr, C n, and C n ar th maurd and timatd cncntratin f ammnia, D and E ar caling factr drivd frm th varianc f th crrpnding variabl, and t a t f maurd valu f th ammnia and prcurr cncntratin. Th bjctiv functin gradint ar btaind by diffrntiating qn. (4) with rpct t th hybrid mdl paramtr vctr W we ww = - 1 ( t=1 D(C pa, (t) - C pa (t)) wc pa(t) ww + E(C n,(t) - C n (t)) wc n(t) ww ¹ 1 (5) 64

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Th cmputatin f vctr wc pa /ww and wc n /ww in qn. (5) can b dn with th nitiviti mthd and rrr backprpagatin in th hybrid mdl ntwrk (Olivira t. al, 1998). Th ptimizatin cnitd n a cnjugat gradint with lin-arch algrithm mplying th gradint timat givn by qn. (5). Thi tratgy prvd t b mt fficint fr training artificial nural ntwrk (Lnard and Kramr, 199) and hybrid mdl ntwrk (Olivira t. al, 1998). rc mdl can nly b ud in indutrial practic aftr thy hav bn carfully validatd (DiMaim t al. 1992). In th prnt wrk thi wa prfrmd by man f a cr-validatin prcdur (.g. lard t al., 1992) whr m part f th xprimntal data availabl, which ha nt bn ud during th idntificatin prcdur, i ud t tt th mdl. 7% f th availabl data wa ud fr prc mdl idntificatin, whil 3% wa ud fr validatin. Th rrr that appard in th validatin tt wr cl t that ndd fr th cntrl prblm tatd abv. But unfrtunatly nly in 71 % f all run cnidrd th rrr wr mall nugh. Thi man that th initially dvlpd mdl d nt prfrm wll nugh. Hnc, n-lin crrctin tratgi huld b adptd. 3 CONTROLLER DESIGN Th cntrllr algrithm i btaind frm a dirct applicatin f th prc mdl. Th cntrllr actin ar dpndnt frm th dviatin frm th t pint C n,p and C pa,p and th timat C n and C pa fr th ammnia and prcurr cncntratin. Whn thr ar trng chang in th dviatin, th uually applid cntrllr act dramatically. Jump in th dviatin btwn t pint and th timatd cncntratin ar t b xpctd in ur particular ca whnvr w btain nw ff-lin maurmnt data fr ammnia and prcurr, inc thy ar ud t crrct th actual timatin. In rdr t avid vrractin, th cntrllr actin wr cntraind that th t pint prfil i apprachd mthly but a quick a pibl. Thu, th cntrllr wa dignd t act with a firt rdr dynamic in th fllwing way dc n dt dc pa dt = - C n - C n,p W = - C pa - C pa,p W (6a) (6b) Th tim cntant W i dtrmind frm th pratr xprinc. Cmbining th quatin with th mdl (qn.1) lad t th fllwing quatin fr th manipulatbl quantiti: F pa,rc = (C pa - C pa,p )W B W C pa,fpa + R paw B C pa,fpa (7a) 65

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk F n,rc = (C n - C n,p )W B W C n,fn + R nw B C n,fn (7b) Th firt trm in th right hand id f th quatin crrpnd t th fdback cmpnnt f th cntrllr, th cnd trm t th fdfrward part. Fig. 5 prvid a chmatical viw f thi fdfrward/fdback cntrl tructur. Ntic that t lv qn. (7) th valu f C pa, C n a wll a th n f R pa and R n ar rquird. Th valu ar prvidd n-lin by th prc hybrid mdl, which wrk, a mntind bfr, a an indirct maurmnt ytm. C i, C i,p E i F i,fb FB-Cntrllr F i,ff F i U C i FF-Cntrllr R i Hybrid Etimatr Fig. 5. Fdback/fdfrward cld-lp cntrl tructur (i=ammnia, prcurr) 4 ON-LINE LEARNING ROCEDURE By n-lin larning w undrtand an imprvmnt f th kintic mdl during th applicatin f th ytm by uing th data bcming availabl with th running frmntatin. In thi way it i pibl t adapt th prc mdl ud in th mdlupprtd cld-lp. Tw apct mut b ditinguihd in thi rpct. Th firt i that with mr data, th databa fr training th mdl bcm bradr and hnc th mdl bcm mr accurat in gnral. Th cnd i that by uing th data frm th particular running prc, th mdl can b adaptd mr clly t th actual prc bhaviur. Th kintic ar dcribd with an hybrid mdl which cntain glbal infrmatin in frm f th cntrl prfil fr a rprntativ cultivatin a wll a pcific infrmatin rprntd by nural nt. Th incntiv hr i t updat th nural ntwrk cmpnnt by man f an additinal training uing th currntly incming data. Th main ida bhind th n-lin training prcdur i t u a Dynamic Rfrnc Databa which primarily cntain a t f hitrical data rcrd rprnting frmntatin prfrmd in th pat that wr claifid gd xampl. Thi data ba i cmplmntd with th maurmnt infrmatin frm th running frmntatin. Each tim a nw ff-lin valu f prcurr r ammnia cncntratin bcm 66

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk availabl, th training prcdur i activatd n th data cntaind in th rfrnc data ba. In principal, th am training prcdur a with th ff-lin training can b ud. Hwvr, n mut tak car that th nural ntwrk d nt frgt what it alrady larnd bfr. Thu an apprpriat rlativ wighting f th actual data and th alrady incrpratd infrmatin mut b prfrmd. Th tp cncrtly prfrmd ar th fllwing: 1. Th training i prfrmd with th data in th Dynamic Rfrnc Databa, cntaining data frm abut 5 rfrnc frmntatin, and th data f th running frmntatin. 2. Th maximum tp iz fr th lin-arch algrithm i fixd t a lw valu (c.a..1) t avid that th hybrid ntwrk frgt what it larnd in th pat. 3. Th maximum numbr f itratin wa t t 1 nly fr th am ran. 4. Th 3 paramtr, i) th numbr f hitrical frmntatin data rcrd in th Dynamic Rfrnc Databa, ii) th tp iz fr th lin-arch algrithm and iii) th maximum numbr f itratin wr chn huritically. Figur 6 chmatically dpict th tructur f th cld-lp cntrllr applid including th n-lin larning tratgy. Fr ca whr th additinal n-lin training d nt lad t an imprvmnt in th mdl accuracy and hnc in th cntrllr prfrmanc, th rlativ wight f th data frm th actual frmntatin i incrad that th cntrllr i mr dirctly adaptd t th currntly running prc. Th dciin i mad by anthr mall xprt ytm incrpratd in th ftwar. C i, C i,p E i F i,fb FB-Cntrllr F i,ff F i U C i FF-Cntrllr R i Hybrid Etimatr On-lin Larning J Fig. 6. Fdback/fdfrward cld-lp cntrl ytm with n-lin larning (i=ammnia, prcurr) 67

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Th practical cnqunc f th mdl imprvmnt i that nc th baic mdl chang, all what ha bn drivd frm that mdl i al adaptd. Thi i particularly th t f fding prfil fr prcurr and ammnia. Thu, whnvr th mdl wa changd th prfil ar crrctd, and by prcding in thi way, th rbutn f th cntrl ytm i cnidrably imprvd. 5 IMLEMENTATION Th infrntial cntrllr wa implmntd at a frmntatin ytm n labratry cal which wa quipd with a frnt-nd cmputr prc mnitring and lw-lvl cntrl. Th infrntial cntrllr wa implmntd n a wrktatin which wa linkd t th frnt-nd cmputr. A Digital Equipmnt AlphaStatin wa ud fr uprviin and advancd cntrl. It run undr th Digital UNIX prativ ytm. Thi wrktatin i cupld t th Cbad frnt-nd cmputr ytm placd in th frmntatin hall via a tandard TC/I ntwrk. Hybrid mdl frmulatin, hybrid mdl idntificatin, and n-lin cntrl, wr prfrmd with th HYBNET ftwar packag (Olivira t al., 1998). Thi packag wa intalld in th AlphaStatin running undr th Digital UNIX prativ ytm. Th cmmunicatin prtcl wa built n a ba f fil tranfr (FT-prtcl), in which th prc data matrix i cntinuuly nt t HYBNET and th t-pint tabl wa cntinuuly nt th thr way arund t th frnt-nd C. Th t f ftwar tl and HYBNET cnfiguratin fil implmnting th cntrl ytm wa namd BUBE ytm. BUBE i frmd by all th HYBNET cnfiguratin fil implmnting i) th prc hybrid mdl, ii) th cntrllr, and iii) th cmmunicatin prtcl. It includ additinally a fw ftwar tl pcially dvlpd t fit th nd f th ppl wrking daily with BUBE. In particular, a prnalizd graphical intrfac wa dvlpd t imprv th ur-frindlin and th viualizatin capabiliti f th ytm. 6 DISCUSSION AND CONCLUSIONS Th ftwar dvlpd wa ud t cntrl a ri f pnicillin frmntatin in th labratry. Aftr 17 frmntatin cntrlld with BUBE it i pibl t cmpar th rult f a tatitical ba with an arbitrarily chn t f manually prfrmd frmntatin. Fr cmparin a t f 12 manually cntrlld frmntatin wa takn. Th firt infrmatin f intrt i th man dviatin f th cntrl variabl frm thir crrpnding t pint a avragd vr bth t f frmntatin. A cmparin f th frmntatin rult i dpictd in Figur 7 and 8 fr th ca f ammnia. Th am prcdur can b prfrmd fr th prcurr cncntratin. Th crrpnding data ar hwn in Figur 9 and 1. 68

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk cnc. ammnia (g/kg) BUBE ammnia cntrl maurd tpint tpint-e c tpint+e c tim (h) Fig. 7. Cncntratin f ammnia fr 17 frmntatin cntrlld by BUBE cnc. ammnia (g/kg) MANUAL ammnia cntrl maurd tpint tpint-e c tpint+e c tim (h) Fig. 8. Cncntratin f ammnia fr 12 frmntatin cntrlld manually 69

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk cnc. prcurr (g/kg) BUBE prcurr cntrl maurd tpint tpint-e c tpint+e c tim (h) Fig. 9. Cncntratin f prcurr fr 17 frmntatin cntrlld by BUBE cnc. prcurr (g/kg) MANUAL prcurr cntrl maurd tpint tpint-e c tpint+e c tim (h) Fig. 1. Cncntratin f prcurr fr 12 frmntatin cntrlld manually 7

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk Th practical advantag f uch a cntrllr i that th prc can b kpt much clr t th dird ptimal prc trajctri. Hnc, th data prvid a bttr ba fr th dciin t b mad n th xprimntal rult. Scndly, th manpwr in th labratri can cncntrat mr n cncptual imprvmnt f th prc intad f acting a living prc cntrllr. Th rt man quar dviatin f th ammnia cncntratin frm thir t-pint dcrad by abut 7% with th intrductin f th nw cntrl ytm. Th crrpnding dviatin f th prcurr cncntratin dcrad by abut 14%. Th Hardwar/Sftwar cnfiguratin prvd t b tabl nugh t u it rutinly. Th cntrl ytm rvald t b rbut, a a cnqunc f it fficint fdfrward/fdback algrithm and n-lin larning. Hwvr, it i wrth nting that whil uch a ytm may allw t rduc th manpwr in th labratry, th numbr f n-lin r ff-lin maurmnt cannt b furthr dcrad inc rlvant maurmnt infrmatin abut th actual prc i indipnibl. 71

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk NOMENCLATURE a a 1,b 1 a 2 (t), b 2 (t) b C f C n C n, C n,fn C n,p C pa C pa, C pa,fpa C pa,p CR E E c E n E pa E r f c F i,fb F i,ff F n F n,rc F pa F pa,rc F F tt M OUR R n R n,fc R pa R pa,fc caling factr fr th prcurr timatin rrr tim-invariant paramtr in th fixd carbn crrlatin fr timating th ammnia cnumptin rat tim-varying paramtr in th fixd carbn crrlatin fr timating th prcurr cnumptin rat caling factr fr th ammnia timatin rrr ubtract cncntratin in th ubtract fd int th frmntr ammnia cncntratin in th brth maurd ammnia cncntratin ammnia cncntratin in th fd f ammnia int th frmntr tpint ammnia cncntratin prcurr cncntratin in th brth maurd prcurr cncntratin prcurr cncntratin in th fd f prcurr int th frmntr tpint prcurr cncntratin carbn dixid prductin rat by th muld lat-quar rrr maximum rrr allwd fr cncntratin timatin maximum ammnia cncntratin dviatin t th tpint maximum prcurr cncntratin dviatin t th tpint maximum rrr allwd fr cnumptin rat timatin rat f carbn fixd by th muld fd rat f cmpnnt i=ammnia,prcurr givn by th fdback cntrllr fd rat f cmpnnt i=ammnia,prcurr givn by th fdfrward cntrllr ammnia fd rat int th frmntr rcmmndd ammnia fd rat prcurr fd rat int th frmntr rcmmndd prcurr fd rat ubtract fd rat int th frmntr ttal fd int th frmntr ubtract C-mlar wigh xygn uptak rat by th muld numbr f xprimntal maurmnt f ammnia and prcurr cncntratin ammnia cnumptin rat ammnia cnumptin rat timatin by uing th fixd carbn crrlatin prcurr cnumptin rat prcurr cnumptin rat timatin by uing th fixd carbn crrlatin 72

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk RQ rpiratin qutint R ubtract cnumptin rat t indpndnt variabl tim W vctr f all th paramtr invlvd in th hybrid mdl W B brth wight 't ampling tim fr ff-lin maurmnt D, E caling factr drivd frm th varianc f prcurr and ammnia cncntratin rpctivly, ud t cal th timatin rrr E W(h) tim cntant 73

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk REFERENCES Atröm, K.J. and B. Wittnmark (1989).Adaptiv Cntrl. Addin-Wly, Rading, MA Bajpai, R.K., M. Ru (1981). Evaluatin f fding tratgi in carbn-rgulatd cndary mtablit prductin thrugh mathmatical mdlling. Bitchnl. Bing., 23, pp 717-738 Cntantinid, A., J.L. Spncr, E.L. Gadn (197). Optimizatin f batch frmntatin prc: II. Optimum tmpratur prfil fr batch pnicillin frmntatin. Bitch. Bing., 12, pp. 181-198. Curt, J.R., S.J. irt (1981). Carbn and nitrgn-limitd gwth f pnicillium chrygnum in fd batch cultur: th ptimal ammnium in cncntratin fr pnicillin prductin. J.Chm.Tchnl.Bitchnl., 31, pp. 235-24 DiMaim, C., G.A. Mntagu, M.J. Willi, M.T. Tham, A.J. Mrri (1992). Tward imprvd pnicillin frmntatin via artificial nural ntwrk. Cmp. Chm. Eng., 16, pp. 283-291 Fy d Azvd, S., B. Dahm, F.R. Olivira (1997). Hybrid Mdlling f Bichmical rc: A cmparin with th cnvntinal apprach. Cmp. Chm. Eng., 21, Suppl., pp. 751-756 Garcia, C.E., D. M. rtt, M. Mrari (1989). Mdl prdictiv cntrl: Thry and practic A urvy. Autmatica, 25, pp. 335-348 Gatly, E. (1996), Nural ntwrk fr financial frcating, Wily, Nw Yrk Hunt, K. J., D. Sbarbar, R. Zwikwki,.J. Gawthrp (1992). Nural ntwrk fr cntrl ytm: A urvy. Analytica, 28, pp. 183-1112 Krta, J.V., J.V. Macgrgr (1991). Multivariat tatitical mnitring f prc prating prfrmanc. Can. J. Eng., 69, pp. 35-47 Lnard, J., M.A. Kramr (199). Imprvmnt f th backprpagatin algrithm fr training nural ntwrk. Cmp. Chm. Eng., 14, pp. 337-341 Luri L.M., T.. Vrkhvtva, A.I. Orlva, M.M. Lvitr (1976). Tchnlgy f drug manufactur. Nitrgn nutritin a a factr in th intnificatin f pnicillin ynthi. harm. Chm. J., 1, pp. 218-222 Mdak, J.M., H.C. Lim (1987). Fdback ptimizatin f fd-batch frmntatin. Bitchn. Bing., 3, pp. 528-54 Niln, J., J. Villadn (1994). Biractin Enginring rincipl. lnum r, Nw Yrk Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1998). Hybnt, an Advancd Tl fr rc Optimizatin and Cntrl.. 7th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy CAB7, Oaka, Japan, May 31-Jun 4, 1998 (in pr) 74

Chaptr 4. Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk llard, J.F., M.R. Bruard, D.B. Garrin, K.Y. San (1992). rc idntificatin uing nural ntwrk. Cmp. Chm. Eng., 16, pp. 253-27 ruting, H., J. Nrdvr, R. Simuti, A. Lübbrt (1996). Th u f Hybrid mdling fr th ptimizatin f th pnicillin frmntatin prc. Chimia, 5(9), pp. 416-417. ichgi, D.C., L.H. Ungar (1992). A hybrid nural ntwrk - firt principl apprach t prc mdling. AIChE J., 38, pp. 1499-1511. Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994). Biprc ptimizatin and cntrl: Applicatin f hybrid mdlling. J.Bitchn., 35, pp. 51-68 Simuti, R., M. Dr, I. Havlik, A. Lübbrt (1995). Artificial nural ntwrk f imprvd rliability fr indutrial prc uprviin. rc. 6th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy - CAB6, Garmich-artnkirchn, Grmany Simuti, R., R. Olivira, M. Manikwki, S. Fy d Azvd, A. Lübbrt (1997). Hw t incra th prfrmanc f mdl fr prc ptimizatin and cntrl. J. Bitchnl., 59, pp. 73-89 Thmn, M.L., M.A. Kramr (1994). Mdling chmical prc uing prir knwldg and nural ntwrk. AIChE J., 4, pp. 1328-134. Thrn, J.A., M.J. Jhnn, (195). rcurr fr aliphatic pnicillin. J.Amr.Chm.Sc., 72, pp. 252-258 Wrb,.J. (199), Backprpagatin thrugh tim: what it d hw t d it?, rc.ieee, 78, pp. 155-156 75

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr Chaptr 5 A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr Abtract. In thi papr a mdl-bad paramtr timatr i prpd fr th n-lin timatin f ractin rat in tirrd tank biractr. A particular attntin i givn t th tability rquiit and th dynamic f cnvrgnc f th timat t th tru valu. Th tw fundamntal iu ar dicud in rlatin t th tuning prcdur f th gain paramtr. Th applicatin f th algrithm i illutratd with a impl micrbial grwth cultivatin prc. Thi chaptr ha bn publihd in J. rc Cntrl: Olivira, R.,E. Frrira, S. Fy d Azvd (1996). A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr. J.. Cntrl, 6(6), pp. 367-371 76

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1 INTRODUCTION Mdl-bad tat brvatin and paramtr timatin rprnt fundamntal tl fr cntrl and mnitrizatin f bitchnlgical prc. Dchain and Batin (199) tablihd a gnral thrtical framwrk fr th analyi f biractr dynamic. Th cncpt f a gnral tat pac dynamical mdl fr biractr wa prpd d[ dt KM[ ( ) D[ F Q (1) whr [ i th tat vctr (th t f n cmpnnt cncntratin), K an num yild cfficint matrix, D th dilutin rat, F th fd rat vctr with dim(f)=n and Q th gau utflw rat vctr with dim(q)=n. Thi gnral dynamical mdl cntitut th ky lmnt fr th dign f Stat Obrvr and aramtr Etimatr. A wid cla f prblm i cvrd dpnding upn th dgr f knwldg f th prc mdl. Situatin lik 'unknwn (m r all) yild cfficint', r 'unknwn r partially knwn kintic mdl' ar xtnivly tudid. Th nd f a kintic mdl cntitut a ky pint in thi dicuin. Th ractin rat M ar mt ftn a vry cmplx rlatin f th prating cnditin and f th tat f th prc. Th cntructin f a uitabl kintic mdl may cntitut a vry difficult tak, if nt an impibl n. A uch, thr i a clar incntiv t dign mnitring and cntrl algrithm fr biprc with a minimal mdlling f th kintic. Thi cncpt f minimal kintic mdlling i dicud by Batin and Dchain (199) and frmalizd a fllw: M[ ( ) H( [U[ ) ( ) (2) bing H([) a mur matrix f knwn functin f th tat, and U([) a vctr f r unknwn functin f th tat. With thi dfinitin th gnral dynamical mdl i rwrittn giving: d[ dt KH( [U[ ) ( ) D[ F Q (3) In thi wrk, an algrithm bad n mdl (3) i prpd which aim at th n-lin timatin f th unknwn functin f th tat U([) by cnidring thm a unknwn tim-varying paramtr. 77

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 2 STATEMENT OF THE ESTIMATION ROBLEM Th algrithm prntd blw addr a cla f timatin prblm which can b dfind in th fllwing fur pint: i) Th bithcnlgical prc can b dcribd by th gnral tat pac dynamical mdl (3) ii) Th yild cfficint (matrix K) ar knwn and cntant iii) Th dilutin rat D, th fd rat F and th gau utflw rat Q ar maurd n-lin. iv) Th tat variabl ar knwn n-lin ithr by maurmnt r by man f a tat brvr. A uch, th cp f th algrithm will b th n-lin timatin f U([) frm th nlin knwldg f D, F, Q and [. 3 THE ALGORITHM Th prpd algrithm i cntitutd by a tat brvr which prvid timat f "r" tat pac variabl ([ 1 ) and an additinal quatin fr th updating f th "r" paramtr timat. Th brvatin rrr, which i uppd t rflct th mimatch btwn th timatd paramtr and it tru valu, i ud a th drivn frc in th updating law. Thy ar tatd a fllw: d[ 1 dt du dt KH(, ) [ [ U D[ FQ: ([ [ ) (4a) 1 1 2 1 1 1 1 1 1 : ([ [ 2 1 1 ) (4b) whr [ 1 dnt th n-lin timat f [ 1 and Û th n-lin timat f U([). : 1 and : 2 ar quar (rur) tuning matric fr th cntrl f tability and tracking prprti f th algrithm. 4 STABILITY ANALYSIS Th dynamic f th brvatin rrr and f th tracking rrr ar btaind by ubtracting qn. (3) frm qn (4a) lading t th fllwing nn-linar ytm: d( [ 1 [ 1) dt d( UU) dt > @ K H( [,[ ) U H( [,[ ) U D( [ [ ) : ([ [ ) (5a) 1 1 2 1 2 1 1 1 1 1 d ( U : 2 [ 1 [ 1 ) (5b) dt 78

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr whr U i cnidrd a an xtrnal prturbanc. Th pint [ˆ 1 =[ 1 and Û =U i an quilibrium pint f th unprturbd ytm. A linar apprximatin f th unprturbd ytm arund [ˆ 1 =[ 1 and Û =U giv: de dt with AE (6) E ª [ º 1 [ 1 U U ¼ A ª C( [,[, U ) : K H( [,[ ) 1 2 1 1 1 2 : 2 º ¼ bing C( [, U ) dfind by C( [,[, U) K ª 1 2 1 w H( [,[ ) U > @ w[ 1 2 1 º DI N (7) ¼[ [ 1 1 Frm th dirct mthd f Lyapunv, it fllw that th unprturbd ytm i xpnntially tabl if C1. th ingnvalu f matrix A hav trictly ngativ ral part. In additin th prturbd ytm i glbally tabl (i.. th utput rrr i bundd fr all t) if U i a cntinuuly diffrntiabl bundd functin. Th cnditin undr which thi i vrifid wr tablihd by Dchain and Batin (199) C2. Th dilutin rat i bundd blw: D d min D() t t (8) C3. Th fd rat ar bundd : F t d i() F() t i t (9) C4. Each ractin invlv at lat n ractant that i nithr a catalyt nr an autcatalyt. C5. U ([) i a diffrntiabl functin f [. 79

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 5 TUNING OF THE GAIN MATRICES Th gain matric ar cmputd n-lin in rdr t imp a cnd-rdr dynamic f cnvrgnc f U t U([): W 2 i d dt du i ]W i i U i Ui i=1,...,m (1) dt 2 U i 2 2 undr th cntraint f th linarid tangnt rrr mdl., which giv: 2 : 1 ( 1, 2, ) ( ] [ [ U C [ 1,[ 2, U) diag Wi > K H @ 1 2 1 : 2 1 2 1 ([,[ ) ([,[ ) 1 diag W 2 i i ½ ¾ ½ ¾ (11a) (11b) with thi tuning, cnditin C1 i autmatically vrifid prvidd that W i and ] i ar trictly pitiv ral cntant. 6 TESTING THE ALGORITHM In thi ctin, th u f algrithm (4) i illutratd thrugh a impl applicatin: th timatin f a micrbial pcific ractin rat in a impl bilgical cultur which invlv a ingl bima (X) grwing n a ingl ubtrat (S) and yilding a ingl prduct (). T tt th capability f th algrithm at imping a cnd rdr dynamic f cnvrgnc, th pcific ractin rat i aumd t b a quar wav ignal. Th ractin chm i tatd a fllw: S M X (12) Th prc dynamic in a fd-batch frmntr ar dcribd by qn. (13). d dt ª X S º ¼ ª 1 X k k º 1 M 2 ¼ D ª S º DS in ¼ ª º ¼ (13) whr D i th dilutin rat (D=F/V bing F th input flw rat and V th lutin vlum in th frmntr), S in th ubtrat cncntratin in th fd. Th ractin rat i dfind a fllw: M XSD (14) 8

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr bing D th pcific ractin rat. In th prnt ca th bjctiv i th n-lin timatin f th tim-varying pcific ractin rat frm th n-lin knwldg f X, S,, S in, V and F. Th applicatin f algrithm (4) with [ 1 =X lad t th fllwing tw qn. dx dt d dt XSD DX Z ( X X 1 ) (15a) D Z ( X X 2 ) (15b) bing Z 1 and Z 2 givn by Z1 S D 1 XS Z 2 2 W D 2 ] W (16a) (16b) Th rult btaind ar hwn in Fig (1-1). Th dttd lin rprnt th tru pcific ractin rat whil th full lin rprnt th rpctiv timat. Th accuracy f th timat can b accd frm th ITAE rrr indx (ITAE - intgral f tim-wightd ablut rrr) givn in th lgnd. Th influnc f ] can b accd frm th plt in Fig. (1-5) whr W i kpt at a cntant valu f.15 whil ] aum.25,.75, 1., 1.25, 1.5. 1.2 D (l/gh) -.2 t (hr) 2 Fig. 1 - Rult btaind with W=.15 and ]=.25 (ITAE=14.) 81

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1.2 D (l/gh) -.2 t (hr) 2 Fig. 2 - Rult btaind with W=.15 and ]=.5 (ITAE=8.1) 1.2 D (l/gh) -.2 t (hr) 2 Fig. 3 - Rult btaind with W=.15 and ]=.75 (ITAE=7.7) 82

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1.2 D (l/gh) -.2 t (hr) 2 Fig. 4 - Rult btaind with W=.15 and ]=1. (ITAE=9.9) 1.2 D (l/gh) -.2 t (hr) 2 Fig. 5 - Rult btaind with W=.15 and ]=1.25 (ITAE=13.) 83

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1.2 D (l/gh) -.2 t (hr) 2 Fig. 6 - Rult btaind with W=.15 and ]=1.5 (ITAE=16.) Th influnc f W can b accd frm th plt in Fig. (7-1) whr ] i kpt at a cntant valu f.8 whil W aum.15,.1,.5 and.1. 1.2 D (l/gh) -.2 t (hr) 2 Fig. 7 - Rult btaind with W=.15 and ]=.8 (ITAE=7.9) 84

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1.2 D (l/gh) -.2 t (hr) 2 Fig. 8 - Rult btaind with W=.1 and ]=.8 (ITAE=4.6) 1.2 D (l/gh) -.2 t (hr) 2 Fig. 9 - Rult btaind with W=.5 and ]=.8 (ITAE=1.5) 85

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr 1.2 D (l/gh) -.2 t (hr) 2 Fig. 1 - Rult btaind with W=.1 and ]=.8 (ITAE=.73) Th rult uggt that th dynamic f cnvrgnc f D t D hav charactritic which ar in agrmnt f a typical cnd rdr dynamic rpn t a tp input. It i hwn that dcraing W th rpn bcm fatr whil dcraing ] th rpn turn t b mr cillatry. Anthr vidnc f thi agrmnt i that, a givn by th plt in Fig (1-6), ]=1 dfin th frntir btwn cillatry and nn-cillatry rpn. Acknwldgmnt - Thi wrk wa partially upprtd by JNICT - Junta Nacinal d Invtigaçã Cintífica Tcnlógica, undr cntract numbr BD/251/93-RM. 86

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr NOMENCLATURE C CTR D E F G H([) K k i OTR Q S S in T X xygn cncntratin carbn dixid tranfr rat dilutin rat thanl cncntratin ma fd rat vctr carbn dixid cncntratin (mur) matrix f knwn functin f th tat yild cfficint matrix yild cfficint Oxygn tranfr rat rat f ma rmvl in gau frm vctr gluc cncntratin gluc cncntratin in th fd ampling prid bima cncntratin Grk lttr M r U(t) U W i ractin rat vctr pcific grwth rat vctr vctr f timatd pcific grwth rat pcific grwth rat fr th rpiratry grwth n gluc pathway pcific grwth rat fr th frmntativ grwth n gluc pathway pcific grwth rat fr th rpiratry grwth n thanl pathway vctr f cmpltly unknwn tim-varying paramtr vctr f timativ f U(t) natural prid f cillatin Z i, J i diagnal lmnt f : and * [ tat pac vctr [ timatd tat vctr [ 1 maurd tat pac vctr [ 2 nn-maurd tat pac vctr 87

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr [ 2 timatd vctr f nnmaurd tat variabl ] i damping cfficint :, * gain matric 88

Chaptr 5. A Study n th Cnvrgnc f Obrvr-bad Kinitic Etimatr in Stirrd Tank Ractr REFERENCES %DVWLQ * 'RFKDLQ ' 2Q/LQH (VWLDWLRQ DQG $GDSWLYH &RQWURO RI %LRUHDFWRUV (OVHYLHU $VWHUGD 3RHUOHDX < DQG 3HUULHU (VWLDWLRQ RI XOWLSOH 6SHFLILF *URZWK 5DWHV LQ %LRSURFHVVHV $,&K( -RXUQDO 9RO Q 3RHUOHDX < RGpOLVDWLRQ HW FRQWU{OH GXQ SURFpGp IHGEDWFK GH FXOWXUH GHV OHYXUHV j SDLQ 3K ' 7KHVLV (FROH 3RO\WHFKQLTXH GH RQWUpDO &DQDGD 6RQQOHLWQHU % DQG.lSSHOL 2 *URZWK RI 6DFFKDUR\FHV FHUHYLVLDH LV FRQWUROOHG E\ LWV /LLWHG 5HVSLUDWRU\ &DSDFLW\ )RUXODWLRQ DQG 9HULILFDWLRQ RI D +\SRWKHVLV %LRWHFK %LRHQJ 9RO -XQH SS '* /XHQEHUJHU $Q LQWURGXWLRQ WR REVHUYHUV,((( 7UDQV $XWRDWLF &RQWURO YRO $& SS 6 )H\R GH $]HYHGR 33LHQWD ) 2OLYHLUD ( )HUUHLUD 6WXGLHV RQ 2Q/LQH 6WDWH DQG 3DUDHWHU (VWLDWLRQ WKURXJK D 5HDO7LH 3URFHVV 6LXODWRU LQ.DUL 1 DQG 6WHSKDQRSRXORV - (GV RGHOLQJ DQG &RQWURO RI %LRWVFKQLFDO 3URFHVVHV,)$& 6\S 6HULHV 33 3HUJDRQ 3UHVV 1< 89

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc Chaptr 6 On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc Abtract. In thi papr algrithm fr tat brvatin and kintic timatin ar dvlpd and applid t a bakr yat fd-batch cultivatin prc. An imprtant dign cnditin wa t kp th numbr f rquird n-lin maurmnt a lw a pibl. Th vrall timatin chm aim at th timatin f 3 tat variabl and 3 pcific grwth rat rquiring n-lin maurmnt f dilvd xygn, dilvd carbn dixid and ff-ga analyi. A grat dal f attntin i givn t th timatin prblm f ractin kintic. In thi rpct a nw algrithm i prpd -th Scnd Ordr Dynamic Etimatr (SODE)- and cmpard t an Obrvr Bad Etimatr (OBE). Stability and dynamic f cnvrgnc ar iu ubjct f dtaild analyi. Th rlatin btwn th numrical implmntatin and tability ar al tudid. It i hwn that a dicrt-tim frmulatin p additinal tability cntrain. Th can b aily vrcm by th u f a rbut variabl tp intgratin algrithm. It wa cncludd that th OBE ha tw main diadvantag: i) th tuning f th dign paramtr mut b dn n a trial-and-rrr bai, whil in th SODE th ur can t a 2 nd rdr dynamic f cnvrgnc frm timatd kintic t tru kintic, and ii) th dynamic f cnvrgnc f th OBE ar timvarying whil in th ca f th SODE thi rpn i tim-invariant. Thi chaptr ha bn ubmittd fr publicatin: Olivira, R., S. Fy d Azvd (1998). On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc. (ubmittd) 9

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc 1 INTRODUCTION Tw f th majr prblm which hindr th implmntatin f advancd mnitring and cntrl mthd in biractr ar th difficulty f mdlling th grwth kintic f micrrganim and th abnc f chap and rliabl nr capabl f prviding dirct ral tim maurmnt f th tat variabl. Th dign and implmntatin f Sftwar Snr prvid a uitabl anwr t cp with th lack f intrumntal nr. Sftwar Snr ar algrithm fr th n-lin timatin f th tat variabl and th paramtr which ar nt maurabl in ral tim, frm rlatd maurmnt which ar mr aily accibl. Th mathmatical dcriptin f micrrganim grwth kintic i a critical iu in biprc mdlling. Quit ftn kintic mdl ar bad n untructurd and nngrgatd cll mdl. Unfrtunatly, in many ca, uch mdl ar nt accurat nugh t lv th prblm in tudy. Th thr critical iu i rlatd t th idntificatin f kintic paramtr. aramtr idntificatin rquir a carful and xpniv xprimntal planing. A uch, thr i a clar incntiv t dvlp algrithm fr tat timatin and paramtr timatin whil aviding th knwldg f th undrlying kintic mdl. In th prnt papr, ractin kintic timatin frm rlatd n-lin maurmnt i a cntral iu. In thi rpct a nw algrithm -th Scnd Ordr Dynamic Etimatr (SODE)- i prpd, which aim at imping 2th rdr dynamic f cnvrgnc f timatd kintic t th crrpnding tru kintic. Th prprti f th SODE ar tudid and cmpard t th Obrvr-Bad Etimatr (OBE) prpd by Dchain and Batin (199). Stability and dynamic f cnvrgnc ar ubjct f dtaild analyi. Th rlatin btwn th numrical implmntatin and tability i al tudid. Th bhaviur f th algrithm i carfully analyd by th applicatin t a bakr' yat fd-batch cultivatin prc. A gnral timatin chm i prpd, whr 3 tat variabl (bima, gluc and thanl cncntratin in th brth) and 3 kintic (pcific grwth rat rlatd t gluc xidatin, gluc frmntatin, and thanl xidatin) ar timatd, uing nly n-lin maurmnt f 2 tat variabl (cncntratin f dilvd xygn and f dilvd carbn dixid) and ff-ga analyi. 2 GENERAL FRAMEWORK Batin and Dchain (199) prpd a mthdlgy fr tat and paramtr timatin bad upn a gnral dynamical mdl fr tirrd-tank biractr: d[ dt KM ([) D[ F Q (1) 91

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc whr [ i th tat vctr (th t f n cmpnnt cncntratin), K an num yild cfficint matrix, D th dilutin rat, F th fd rat vctr with dim(f)=n and Q th gau utflw rat vctr with dim(q)=n. On qutin f majr cncrn i th dign f Sftwar Snr aviding kintic mdlling. In qn. (1) th ractin rat M([) wr dfind a: M ([) h ([) U ([) i=1,...,m (2) i i i whr h i ([) i a knwn functin f th tat whil U i( [) i an unknwn functin f th tat. Or mr gnrally: M[ ( ) H( [U[ ) ( ) (3) with H([) an mur matrix f knwn functin f th tat and U([) a vctr f r unknwn functin f th tat. Th tratgy i t inrt int H([) nly th prir knwldg rgarding th kintic and thn t cnidr U([) a a cmpltly unknwn "tim-varying" paramtr which can b timatd n-lin thrugh th u f paramtr timatr. In th fllwing ctin 3 algrithm ar prntd fr tat brvatin and kintic timatin. Th algrithm wr dvlpd auming th gnral tructur f th dynamical mdl (1). Thy ar latr ud in ctin 3 fr digning a cmplt tat timatin and kintic timatin chm fr a bakr yat cultivatin prc. 2.1 Th Obrvr-Bad Etimatr (OBE) Fr th timatin f ractin rat frm th n-lin knwldg f th tat variabl, whn th yild cfficint ar knwn and cntant, Batin and Dchain (199) prpd an brvr-bad timatr which i xprd by: Obrvr-Bad Etimatr (OBE) d[ dt du dt KH( [U ) D[ F Q :([ [ ) (4a) T [ [ [ KH( ) *( ) (4b) whr : and * ar quar nun matric which ar dign paramtr at th dipal f th ur fr th cntrl f tability and tracking prprti f th algrithm. 92

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc Th baic ida i t u a tat brvr (4a) t timat an brvatin rrr ([ [ ) which i uppd t rflct th mimatch btwn U[ ( ) and U[ ( ) and thn u it a th drivn frc in th updating law (4b). 2.1.1 Stability analyi. Th cntinuu rrr ytm can b btaind dfining th brvatin rrr ~ [ [ [ and th tracking rrr U ~ U U and ubtracting qn. (1) by qn. (4a): de dt with AE B (5) E > [ ~ U ~ @ T A ª : T > KH( )@ KH( [) [ * º ¼ B ª du dt º ¼ T Th dynamic f th rrr ytm ar linar tim-varying (LTV) du t th prnc f th tat variabl in matrix A. Th glbal tability f th rrr ytm (5) i nurd if th diturbanc vctr B i bundd and if th unfrcd ytm i xpnntially tabl. A BIBS (Bndd Input Bundd Stat) analyi f th dynamic mdl (1) (Dchain and Batin, 199) giv that if: C1. Th dilutin rat i bundd blw: D d min D() t t (6) C2. Th fd rat ar bundd : F t d i() F() t i t (7) C3. Each ractin invlv at lat n ractant that i nithr a catalyt nr an autcatalyt. thn th tat variabl [ ar pitiv and bundd fr all t. If additinally C4. U ([) i a diffrntiabl functin f [. thn th bundn f th diturbanc vctr B i nurd. On th thr hand, if: C5. : i a nun cntant matrix with all it ignvalu having trictly ral part. 93

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc T C6. * i a nun cntant matrix uch that th matrix :* *: i ngativ dfinit. C7. KH( [) i a pritntly xciting matrix. Thn th unfrcd rrr ytm i xpnntially tabl and thrfr, th prturbd rrr ytm (5) i glbally tabl. 2.1.2 Tuning f dign paramtr. A tatd abv : and * ar quar nun matric which ar dign paramtr at th dipal f th ur fr th cntrl f tability and tracking prprti f th algrithm, thu playing a dciiv rll n th prfrmanc f th timatr. A cmmn chic i t tak: : diag^z ` * diag^j i ` i=1,...,n (8) i whr Z i and J i ar 2un trictly pitiv ral cntant. With thi chic cnditin C4 and C5 ar autmatically vrifid and th tuning prcdur rduc t th calibratin by trial and rrr f 2un calar cntant. 2.1.3 Rducd-rdr Obrvr-Bad Etimatr. Th brvr-bad timatr (4) i bad n th full dynamical mdl f th prc. In practic thi i nt alway ncary. It i ftn ufficint t dign th timatr frm a ubt f th tat quatin prvidd thy invlv all th r paramtr which nd t b timatd. In particular, undr th fllwing aumptin: A1. Thr ar r=m paramtr which nd t b timatd A2. Thr i a ubt f m quatin f th full tat pac mdl that invlv all th m paramtr which nd t b timatd: d[ dt a K H( [) U ([) D[ F Q (9) a a a a A3. In qn. 9 K a i a mum full-rank matrix and by cnidring th tranfrmatin: 1 \ K a [ a (1) thn qn. (9) can b rwrittn a: d\ dt 1 H( [) U ([) D\ K ( F Q ) a a a (11) 94

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc Bad n thi rducd-rdr rfrmulatd prc mdl, th brvr-bad timatr can b writtn a: Rducd-rdr Obrvr-Bad Etimatr d\ dt du dt 1 HU D\ K ( F Q ) :(\ \ ) (12a) H T * (\ \ ) a a a (12b) 2.2 Scnd Ordr Dynamic Etimatr (SODE) Th Scnd Ordr Dynamic Etimatr i a variant f th rducd rdr Obrvr-Bad Etimatr. Thy diffr lly n th way th rgrr in th updating law f U i tatd (qn. (12b)). It can b applid undr aumptin A1 thrugh A3 and additinally: A4. Th ractin rat can b dfind by qn. (2): M ([) h ([) U ([) i=1,...,m (2) i i i maning that H([) i a mum diagnal matrix. Th cnd rdr dynamic bad timatr i writtn a fllw: Scnd Ordr Dynamic Etimatr (SODE) d\ dt du dt 1 HU D\ K ( F Q ) : (\ \ ) (13a) * H 1 (\ \ ) a a a (13b) whr : and * ar quar mum matric which a in th ca f th Obrvr-Bad Etimatr, ar dign paramtr fr th cntrl f tability and dynamic f cnvrgnc. Dfining :=diag(z i ) and *=diag(j i ), qn. (13) can b dcupld, giving: d\ dt du i dt i h U D\ U Z (\ \ ) (14a) J i h i i i i i i i i ( ) \ i \ i (14b) 95

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc with i=1,...,m 2.2.1 Stability analyi. Th rrr ytm f qn. (14) i a cnd rdr linar tim variant (LTV) ytm: d dt with ~ ª \ i º ª Zi U ~ i ¼ J ihi 1 h ~ iº \ i ª ~ dui ¼ º Ui¼ ª º dt ¼ (15) ~ i i i \ \ \ U ~ U U i i i whr du i /dt i cnidrd a an xtrnal pritnt diturbanc. It i a tandard rult f th BIBO tability thry that a LTV ytm prturbd by an xtrnal diturbanc i glbally tabl if th unprturbd ytm i unifrmly aympttically tabl and th diturbanc vctr i bundd (Narndra and Annawamy, 1989). Cnditin C1 thrugh C4 aur th bundn f du i /dt (Batin and Dchain, 199). Still, it rmain t b prfd that th unfrcd ytm i unifrmly aympttically tabl. Th radr i rfrrd t th appndix whr thi prf i prntd. 2.2.2. Dynamic f cnvrgnc and tuning. Diffrntiating qn. (14b) giv 2 d U J d\ 1 dh 2 J ~ 2 \ dt h dt h dt ~ (16) Cmbining qn (16), (14b) and th firt quatin in (15) it fllw that J 1 2 d U U J 1 d at () U U (17) 2 dt dt with a(t) givn by qn. (18). at () Z() t h 1 dh dt (18a) Supping that th trm I[ ( ) 1 h( [) dh dt (18b) 96

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc i knwn n-lin crruptd by an rrr H(t) (in practic th n-lin knwldg f I([) rquir an apprximatin t th tim drivativ dh/dt, and thrfr, th timatd valu I ([) i alway crruptd by th apprximatin rrr H(t)): I[ ( ) I[ ( ) H( t) (19) an dfining J and Z(t) by: 1 J (2a) 2 W Z () t 2] J I ([) 2 ] J I ([) H( t) (2b) thn qn. (17) bcm: W 2 2 d U d 2] W U () t U U (21) 2 dt dt bing ]( t ) rlatd t th dird valu ] d and th rrr H(t) in th fllwing way: ]() t ] d 1 WH() t 2] d ¹ (22) Hnc, th cncluin i takn that ach Ut ( ) cnvrg t it' tru valu U( t ) with a cnd rdr dynamic rpn with cntant natural prid f cillatin W and timvarying damping cfficint ](t). Ntic that dfining Z(t) by qn. (2b) impli that cnditin C7 which tat that Z(t) mut b alway largr thn -I([), i vrifid if 2] d i alway largr thn th W apprximatin rrr H(t). Ntic al that a givn by qn. (22) thi i quivalnt t tat that ](t) mut b pitiv fr all t. 2.2.3 Numrical implmntatin and tability. Th numrical implmntatin f qn. (14) rquir a dicrt-tim frmulatin. Th witch frm th cntinuu-tim quatin t th dicrt tim vrin lad t pcific tability prblm in which th intgratin tp T play an imprtant rl. On f th mt ppular apprach i th Eulr dicrtiatin f th cntinuu tim quatin. In thi ctin, th implicatin f uing an Eulr dcritiatin in th tability f th SODE ar analyd. A frward Eulr dicrtiatin f qn. (14) with Z(t) and J givn by qn. (2) rult in th fllwing dicrt-tim quatin: ( ) ( t TDt t Tht t TU t T t t t) 1 1 (23a) \ \ U Z \ \ 97

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc T U ( t1 t \ t \ t) (23b) 2 W h U with t Z t 2] ht 1 ht (24) W Th t Th dicrt rrr ytm i a fllw \ ~ ( Z )\ ~ U ~ t1 1 T t t Tht t (25a) ~ T U ~ ~ t1 \ t Ut ( Ut Ut) 2 1 W h (25b) t which i quivalnt t Et 1 AEt Bt (26) with E t ª \ ~ ht U ~ t º t ¼ A 1 2 ] T W T ª W 2 T 1 º ¼ ª U t1 U º t ¼ Th dicrt-tim rrr ytm (26) i linar tim-invariant (LTI). Th unfrcd ytm i xpnntially tabl (and hnc th utput rrr f (26) i bundd) if th ingnvalu f matrix A tay inid th unit circl. Th ingnvalu f matrix A ar givn by O1 O 2 T W ] ] 2 1 1 T W ] ] 2 1 1 (27a) (27b) Ca 1 - ]<1. Th ingnvalu ar tw cmplx cnjugat numbr O O 1 2 T 1 W ] i 1 ] T 1 W ] i 1 ] 2 2 (28a) (28b) Hnc, th tability cnditin appli 98

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc O O 1 1 2 (29) which i quivalnt t T 2]W (3) Ca 2 - ]=1. Th ingnvalu ar dubl givn by O O 1 2 1 T W (31) lading t th fllwing tability cnditin T W (32) Ca 3 - ]>1. Th ingnvalu ar tw diffrnt ral numbr givn by qn. (27). Th tability cnditin i a fllw: T W ] r ] 2 1 (33) A givn by qn. (3), (32) and (33) th rang allwd fr th intgratin tp T i bundd and cnditind by th chn W and ]. Ntic al that th rtrictin ar th am if th analyi wuld hav bn carrid ut frm th dicrt vrin f qn. (21). 2.3 Th Lunbrgr-typ aympttic brvr Eqn. (1) can b dividd in tw partitin: th firt n includ th quatin rlatd t th maurd tat variabl ([ 1 ); th cnd partitin includ th quatin rlatd t th nn-maurd tat variabl ([ 2 ). Th dynamic mdl i rwrittn a: d[ 1 dt d[ dt 2 K M ([) D[ F Q (34a) 1 1 1 1 K M[ ( ) D[ F Q (34b) 2 2 2 2 whr K 1 (a full rank matrix), K 2, F 1, F 2, Q 1, Q 2 crrpnd t th diviin f K, F and Q t ach partitin. Bad n th tranfrmatin: Z 1 [ 2 K2K1 [ 1 (35) 99

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc and n qn. (34), th Lunbrgr-typ aympttic brvr (Lunbrgr, 1971) i writtn a: dz dt Z Lunbrgr-typ Aympttic Obrvr 1 DZ ( F2 Q2) K 2K1 ( F1 Q1 ) (36a) K K 1 2 2 1 1 [ [ (36b) Ntic that th numbr f maurd tat variabl mut b qual t th numbr f unknwn ractin rat in vctr M([). 3 STATE OBSERVATION AND KINETICS ESTIMATION IN A BAKER S YEAST FED-BATCH CULTIVATION ROCESS In ctin 2 gnral-u tat brvatin and kintic timatin algrithm wr prntd. Thy ar ging t b nw applid t a bakr yat fd-batch cultivatin prc. Th bjctiv i t dvlp a tat brvatin and a pcific grwth rat timatin chm rquiring a minimum numbr f aily accibl n-lin maurmnt. Th dicuin will flw thugh th fllwing tpic: 1) Gnral dynamical mdl tructur fr a bakr yat fd-batch cultivatin prc. Thi mdl will b th ba n which th timatin algrithm ar drivd. 2) Statmnt f th timatin prblm. 3) Drivatin f th Lunbrgr-typ aympttic brvr, th rducd rdr OBE and th SODE fr th chn n-lin maurmnt Th vrall timatin chm will prmit th timatin f 3 tat variabl (bima, gluc and thanl cncntratin in th brth), 3 pcific grwth rat (rlatd t gluc xidatin, gluc frmntatin and thanl xidatin) uing maurmnt frm 2 tat variabl (dilvd xygn and dilvd carbn dixid) and ff-ga analyi (xygn tranfr rat and carbn dixid tranfr rat). 3.1 Dynamic mdl fr a bakr yat fd-batch cultivatin prc Yat grwth i charactrizd by th fllwing ractin chm (Snnlitnr and Käppli, 1986): 1

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc S S E + C X + G (rpiratry grwth n gluc) (37a) r X + E + G (frmntativ grwth n gluc) (37b) + C X + G (rpiratry grwth n thanl) (37c) whr S i gluc, C i xygn, X i bima, E i thanl and G i carbn dixid., r and ar thr pcific grwth rat which rflct th capacity f th yat t xplit thr diffrnt catablic pathway fr nrgy and baic matrial urc. Th dynamical mdl fr th fd-batch frmntr i btaind frm a ma balanc n th cmpnnt, cnidring that th ractr i wll mixd, th yild cfficint ar cntant and th dynamic f th ga pha can b nglctd. Th ma balanc, in trm f cncntratin, ar writtn a: dx dt ds dt de dt dc dt dg dt ( DX ) r (38a) r DS ( S) ( k k ) X (38b) in 1 2 r DE ( k k ) X (38c) 3 4 DC OTR ( k k ) X (38d) 5 6 r DG CTR ( k k k ) X (38) 7 8 9 and th additinal quatin: dv dt F DV (39) whr k i ar th yild cfficint, OTR i th xygn tranfr rat (dfind a * OTR kla( C C) whr k L a i th ma tranfr cfficint and C * th quilibrium cncntratin f dilvd xygn), CTR i th carbn dixid tranfr rat (dfind a CTR KVKL ag), V i th lutin vlum in th ractr, F i th input fd rat and D i th dilutin rat (dfind a D=F/V). Equatin (38) tak th matrix frm: d dt ª X º S E C G¼ ª 1 1 1 º k k 1 2 ª k3 k4 k k 5 6 k k k ¼ 7 8 9 r ª Xº ª º º S DS in X D E ¼ C OTR G¼ CTR¼ (4) 11

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc which ha th tructur f th gnral dynamic mdl (1) with n=5 tat pac variabl and m=3 ractin rat: [ T X S E C G K > @ > in @ T 1 k k k ª 1 k k k 1 1 5 7 º 2 3 8 k k k 4 6 9 ¼ T T F DS OTR Q > CTR@ A uch, th algrithm prntd in ctin 2 can b traightfrward applid t th dynamical mdl (4). 3.2 Etimatin prblm Thr ar 3 pcific grwth rat invlvd in th dynamical mdl (4). Th ar tratd a 3 unknwn prc variabl that mut b timatd uing th OBE r th SODE. A uch, th functin H([) and U([) in qn. (3) ar dfind in th fllwing way: H( ) diag( X) ( ) T r [ U [ > @ Sinc thr ar 3 unknwn kintic, th applicatin f th Lunbrgr-typ aympttic brvr (qn. 36) t mdl (4) rquir th n-lin maurmnt f 3 tat variabl. Fr th am ran, th applicatin f th rducd-rdr OBE and f th SODE mut b bad n r=3 tat pac quatin. Sinc E, C and G ar th tat variabl mr aily accibl n-lin, frm th practical pint f viw, it i imprtant t dign an timatin chm bad n thi t f maurmnt. Unfrtunatly, accrding t th yild cfficint valu, E, C and G ar linarly dpndnt, bing th crrpnding yild matrix ill-cnditind (mrlau and rrir, 1991). Sinc th invrin f thi matrix i rquird in all th algrithm dicud prviuly, th numrical implmntatin wuld rult in xtrmly nitiv algrithm t numrical rrr, thu having prfrmanc dramatically dgradd. T lv thi prblm mrlau and rrir (1991) uggtd a rfrmulatin f mdl (4). Thi rfrmulatin i bad n th diviin f th cmplt prc mdl (4) int tw partial mdl: (i) th rpir-frmntativ partial mdl (RF) crrpnding t th thanl prductin tat f th prc and (ii) th rpirativ partial mdl (R) crrpnding t th thanl cnumptin tat f th prc. Th frmntativ partial mdl (RF) i tatd a: 12

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc d dt ª X º S E C G¼ ª 1 1 º k k 1 2 ª k3 k 5 k k ¼ 7 8 r ª Xº ª º S DS in º X D E ¼ C OTR G¼ CTR¼ (41) and th rpirativ partial mdl (R) a: d dt ª X º S E C G¼ ª 1 1 º k 2 ª k3 k4 k 6 k k ¼ 8 9 ª Xº ª º S DS in º X D E ¼ C OTR G¼ CTR¼ (42) Ntic that thy hav idntical tructur with n=5 tat pac variabl but nly m=r=2 ractin rat. Th nly diffrnc btwn thm i rflctd n th way th pcific grwth rat vctr and th yild cfficint matrix ar tatd. Fr th rpirfrmntativ (RF) partial mdl thy ar: r T RF > @ T ª 1 k1 k5 k7º K RF 1 k k k 2 3 8¼ and fr th rpirativ partial mdl (R): T T R > @ KR ª 1 k2 k3 k8º 1 k k k 4 6 9¼ Th Lunbrgr brvr, th rducd-rdr OBE and th SODE mut nw b applid t bth partial mdl, rulting tw "partial" algrithm which mut b altrnativly ud in accrdanc with th actual prc tat: thanl prductin r thanl cnumptin. Th ucc f uch an timatin chm dpnd upn th dtctin capability f th crrct prc tat fllwd by th u f th prpr t f quatin. Th tranitin btwn prc tat can b dtctd by th tranitin btwn pitiv and ngativ valu f th pcific grwth rat timat rlatd t thanl cnumptin ( ) r prductin ( r ) (mrlau and rrir,1991). Fr xampl, if th actual prc tat i thanl cnumptin and if th lat timat i ngativ thn th prc tat ha witchd frm thanl cnumptin (R) t thanl prductin (RF). Th abv mntind partial mdl hav nly tw pcific grwth rat invlvd. Thi ha th vry imprtant implicatin that nly tw maurd tat variabl ar rquird. r cnvninc th variabl C and G wr chn. Th variabl ar aily accibl n-lin and th numrical prblm mntind prviuly n lngr xit. A 13

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc r uing n- uch, th timatin chm will prvid timat f X, S, E, lin maurmnt f C, G, OTR, CTR and F. 3.3 Ovrall tat brvatin and kintic timatin chm, and 3.3.1 Applying th Lunbrgr-typ aympttic brvr. Th applicatin f th Lunbrgr-typ aympttic brvr (qn. 36) t bth partial mdl (41) and (42) rult int tw partial algrithm with idntical tructur givn by th fllwing t f quatin: ª Z1 º d Z 2 dt Z3 ¼ ª X º ª Z S Z E ¼ Z ª Z D Z Z 1 2 3 1 2 3 º KK ¼ º ª DS ¼ 1 2 1 ª C º G ¼ in º K K ¼ 1 2 1 ª OTR º CTR ¼ (43a) (43b) Th diffrnc btwn partial algrithm ar rflctd in th way th matric K 1 and K 2 ar dfind. Th diffrnc ar cmpild in Tabl I. Tabl I Diffrnc btwn partial Lunbrgr-typ brvr Rpir-frmntativ tat(rf) Rpirativ tat (R) K K RF 1 1 k k k ª 5 º 7 8 ¼ (44a) K K R 1 1 k k ª 6 º k8 9 ¼ (45a) 1 1 RF K K k k ª 2 2 1 2 k k 7 8 º ¼ (44b) ª RF K K k 2 2 2 1 1 k k º 8 9 ¼ (45b) 3.3.2 Applying th rducd-rdr OBE. Th applicatin f th rducd-rdr OBE (qn. (12)) t bth partial mdl (41) and (42), uing th tat pac quatin f C and G, rult int tw partial algrithm with idntical tructur givn by th fllwing t f quatin: \ K 1 ª a C G º ¼ (46a) 14

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc d\ dt d dt 1ª OTR º X D\ Ka (\ \ ) CTR : (46b) X * (\ \ ) ¼ (46c) Th tw "partial" OBE diffr n th t f pcific grwth rat t timat, n th yild cfficint matrix K a, and n th gain matric : and *. Th diffrnc ar cmpild in Tabl II. Tabl II Diffrnc btwn th partial rducd-rdr OBE Rpir-frmntativ tat (RF) Rpirativ tat (R) RF ª º ¼ r (47a) R ª º ¼ (48a) K a K RF a k k k ª 5 º 7 8 ¼ (47b) Ka K R a ª k6 º k8 k9 ¼ (48b) ª : : 1 RF Z ª : : Z1 º Z (47c) R Z (48c) º 2 ¼ 3 ¼ * * RF ª J 1 º J 2 ¼ (47d) * * ª J º 1 R J 3¼ (48d) 3.3.3 Applying th cnd-rdr dynamic timatr. Th applicatin f th SODE (qn. (13)) t bth partial mdl (41) and (42), uing th tat pac quatin f C and G, rult int tw partial algrithm with idntical tructur givn by th fllwing t f quatin: \ d\ dt d dt K 1 a ª C G º ¼ (49a) 1ª OTR º X D\ Ka ()( t \ \ ) CTR : (49b) X 1 * (\ \ ) ¼ (49c) 15

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc 16 A in th ca f th rducd-rdr OBE, th tw "partial" SODE diffr n th t f pcific grwth rat t timat, n th yild cfficint matrix K a, and n th gain matric :(t) and *. Th diffrnc ar cmpild in Tabl III. Tabl III Diffrnc btwn th partial SODE Rpir-frmntativ tat (RF) Rpirativ tat (R) ª º ¼ RF r (5a) ª º ¼ R (51a) K K k k k a a RF ª º ¼ 5 7 8 (5b) K K k k k a a R ª º ¼ 6 8 9 (51b) ¼ º ª : : ) ( 2 ) ( 2 ) ( ) ( 2 2 1 1 X X t t RF I W ] I W ] (5c) ¼ º ª : : ) ( 2 ) ( 2 ) ( ) ( 3 3 1 1 X X t t R I W ] I W ] (51c) * * ª º ¼ RF 1 1 1 2 2 2 W W (5d) * * ª º ¼ R 1 1 1 2 3 2 W W (51d) Ntic that in qn. (51c) and (5c), I(X) i givn by: I( ) X X X XT t t t 1 (52) whr T rfr t th intgratin tp, X t+1 and X t t bima cncntratin at th tim intanc t+1 and t rpctivly. 3.3.4 Switching mchanim btwn partial algrithm. Th uccful applicatin f th partial algrithm mntind abv rquir an n-lin dtctin tratgy f th currnt prc tat: thanl prductin (RF) r thanl cnumptin (R). mrlau and rrir (1991) cncludd that thi dtctin mchanim culd b bad n th tranitin btwn pitiv and ngativ valu f th pcific grwth rat timat rlatd t thanl (cnumptin- r prductin- r ). Fr xampl, if th actual prc

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc tat i thanl cnumptin and if th lat timat i ngativ thn th prc tat ha witchd frm thanl cnumptin (R) t thanl prductin (RF). A uch, th vrall timatin chm will cnit n thr tp: 1) Intgratin f th "partial" Lunbrgr-typ brvr (qn. (43)) crrpndnt t th actual prc tat. 2) Intgratin f th "partial" rducd-rdr OBE (qn. (46)) r th partial SODE (qn. (49)) crrpndnt t th actual prc tat. 3) Chck if tranitin btwn prc tat ha ccurrd by chcking th ignal f pcific grwth rat timat rlatd t thanl. Frm th practical pint f viw, th tranitin btwn "partial" algrithm can b ralid jut by witching btwn qn. (44a-b)/(45a-b) and, btwn (47a-c)/(48a-c) whn th rducd-rdr OBE i ud r btwn (5a-c)/(51a-c) whn th SODE i ud. 4 RESULTS AND DISCUSSION Th prfrmanc f th timatin algrithm will b analyd at aid f a imulatin xprimnt. Th prc dynamical mdl (4) wa implmntd n a prc imulatr (imnta t al., 1993) auming th kintic mdl prpd by Snnlitnr and Käppli (1986) (th valu f th kintic paramtr ud ar litd in Tabl IV). Th imulatin xprimnt wa mad undr th fllwing initial cnditin: X()=1. g/l, S()=.2 g/l, E()=.15 g/l, C()=.66 g/l, G()=.8 g/l, V()=3.5 L Tabl IV - Kintic paramtr(takn frm Snnlitnr and Käppli (1986)) aramtr Valu q,max 3.5 g gluc/(g bima h) q c,max.256 g O 2 /(g bima h) q,max.236 g thanl/(g bima h) K.1 g L -1 K i.1 g L -1 K.2 g L -1 K c.1 g L -1 Th valu fr K L a, K v and C * wr aumd 1hr -1,.2 and.7 g/l rpctivly. Th valu f th yild cfficint ar litd in Tabl V. 17

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc Tabl IV - Yild cfficint (takn frm Snnlitnr and Käppli (1986)) Cfficint (Cfficint) -1 Valu Y k 1.49 g bima/g gluc Y r k 2.5 g bima/g gluc Y r k 3.1 g bima/g thanl Y k 4.72 g bima/g thanl Y c k 5 1.2 g bima/g O 2 Y c k 6.64 g bima/g O 2 Y g k 7.81 g bima/g CO 2 Y gr k 8.11 g bima/g CO 2 Y g k 9 1.11 g bima/g CO 2 A frmntatin run f 18 hur i aumd. In Fig. 1 th ud fd rat prfil and th crrpnding brth vlum vlutin ar hwn. Th prfil f th gau utflw rat, f th tat variabl, and th pcific grwth rat ar hwn in Fig. 2, 3 and 4 rpctivly. 1 F V % Sin t (hr) 18 Fig. 1. Input fd rat F(. -.5 L/h), gluc cncntratin n th fd Sin (25 g/l) and vlum V (. - 1. L) 18

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc 1 % OTR CTR t (hr) 18 Fig. 2. Gau tranfr rat: Oxygn tranfr rat OTR (. 7. g L -1 h -1 ) and carbn dixid tranfr rat CTR (. 12. g L -1 h -1 ) 1 C X % G G E S t (hr) 18 Fig. 3. Stat pac variabl: bima X (. 3. g/l), gluc S (. - 1.25 g/l), thanl E (. - 2. g/l), xygn C (. -.7 g/l) and carbn dixid G (. -.3 g/l). With th input fd rat f Fig. 1 and with th initial cnditin mntind abv th witch btwn rpir-frmntativ and rpirativ catablic tat ccurrd 6 tim. Fig. 4 includ at th tp a rulr ditinguihing th tw diffrnt prc tat: rpirfrmntativ (RF) with thanl prductin, and rpirativ (R) with thanl cnumptin. Th pint whn th prc tat witch ccur ar markd with th lttr a, b, c, d,, f, and g. 19

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc.5.45 RF R RF R RF R RF R.4.35.3-1 h.25.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 4. Spcific grwth rat prfil uing th kintic mdl prpd by Snnlitnr and Käppli (1986), with th kintic paramtr litd in Tabl IV. Thi imulatin xprimnt upplid th timatin algrithm with th rlvant maurd variabl: C, G, OTR, CTR, Sin, V and F at a ampling rat f 6 minut. Th bhaviur f th timatin chm dvlpd in th prviu ctin will nw b analyd at aid f thi imulatin xprimnt. A uch, th curv hwn in Fig.4 ar takn a th tru pcific grwth rat prfil. Th variabl C, G, OTR, CTR, and F in Fig. 1, 2 and 3 ar cnidrd a prc n-lin maurmnt, bing upplid t th timatin algrithm at a ampling rat f 6 minut. Th fllwing figur illutrat th u f th rducd-rdr OBE and f th SODE. Each f thm includ a rulr imilar t th n f Fig. 4 ditinguihing th tw diffrnt prc tat: rpir-frmntativ (RF) with thanl prductin, and rpirativ (R) with thanl cnumptin. Th pint whn th witch btwn prc tat ccur ar markd with th lttr a, b, c, d,, f and g. Th tru pcific grwth rat f Fig. 4 ar rprntd by th dttd lin whil th rpctiv timat ar rprntd by th full lin. Th accuracy f th timat can b ad by th ITAE rrr indx (ITAE - intgral f tim-wightd ablut rrr) givn in th lgnd fr th thr pcific grwth rat. Fig. 5, 6 and 7 hw th rult prducd by th rducd-rdr OBE fr thr diffrnt tuning (dfind huritically). Th quatin wr intgratd with a rbut variabl tp intgratin algrithm (4th/5th rdr Rung-Kutta typ mbddd chm du t Butchr) mplying alng th intgratin linar timat f th rlvant ampld variabl. 11

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc.5.45.4 RF R RF R RF R RF R Z 1 = Z 2 = Z 3 = J = J = J = 1 2 3 1. 1. -1 h.35.3.25 ITAE: r.97.55.26.2.15.1.5 r r r a b c d f g 18 t (h) r Fig. 5. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th rducd-rdr OBE intgratd with an 4th/5th rdr variabl tp intgratin rutin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R Z 1 = Z 2 = Z 3 = J = J = J = 1 2 3 5. 1. ITAE: 1.3 r.51.27.2.15.1.5 r r r a b c d f g 18 t (h) r Fig. 6. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th rducd-rdr OBE intgratd with an 4th/5th rdr variabl tp intgratin rutin. 111

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc.5-1 h.45.4.35.3.25 RF R RF R RF R RF R Z = Z = Z = J 1 2 3 = J = J = 1 2 3 ITAE: r 3.5 3 1.9.11.63.2.15.1.5 r r r a b c d f g 18 t (h) r Fig. 7. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th rducd-rdr OBE intgratd with an 4th/5th rdr variabl tp intgratin rutin. A carful analyi f th plt rval that th dynamic f cnvrgnc i tim-varying, i.., th rpn bcm incraingly fatr and cillatry a th run apprach th nd. Th rult yild by th SODE ar dpictd in Fig (8-14). Th quatin wr intgratd with a rbut variabl tp intgratin algrithm imilar t th n ud fr th rducd-rdr OBE. Th influnc f ] can b ad frm th plt in Fig (8-11) whr W i kpt cntant at.15 hur whil ] aum th valu.25,.5, 1. and 1.25 rpctivly. Th influnc f W can b ad frm th plt in Fig (1) and (11-14) whr ] i kpt cntant at 1. whil W aum.15,.1,.5 and.1 hur rpctivly. 112

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc.5-1 h.45.4.35.3.25 RF R RF R RF R RF R W = = =.15 1 W 2 W 3 = = =.25 ] ] ] 1 2 3 ITAE: 2.9 r.1.73.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 8. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W = = =.15 W 1 2 W 3 = = =.5 ] ] ] 1 2 3 ITAE: 2.3 r.95.78.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 9. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. 113

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc.5-1 h.45.4.35.3.25 RF R RF R RF R RF R W = = =.15 1 W 2 W 3 = = = 1. ] ] ] 1 2 3 ITAE: 3.2 r.11 1.2.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 1. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W = = =.15 W 1 2 W 3 = = = 1.25 ] ] ] 1 2 3 ITAE: 3.9 r.12 1.4.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 11. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. 114

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.1 = = = 1. ] ] ] 1 2 3 ITAE: 2.2 r.86.83.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 12. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.5 = = = 1. ] ] ] 1 2 3 ITAE: 1.2 r.51.42.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 13. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. 115

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.1 = = = 1. ] ] ] 1 2 3 ITAE:.43 r.15.14.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 14. Spcific grwth rat timatd (full lin) and tru (dttd lin) givn by th SODE intgratd with an 4th/5th rdr variabl tp intgratin rutin. A givn by th plt in Fig. (8-14) th charactritic f th dynamic f cnvrgnc f th timatd valu t th tru valu appar t b in agrmnt with a typical cnd-rdr dynamical rpn. It i hwn that dcraing W prduc fatr rpn, whil dcraing ] prduc mr cillatry rpn. Furthrmr, frm th plt in Fig (8-11) it can b cncludd that ]=1 cntitut th frntir btwn cillatry and nn cillatry bhaviur. In ctin (2.2.3) th numrical implmntatin f th SODE wa dicud. It wa hwn that a frward Eulr dicrtiatin f th cntinuu quatin p tability prblm. In particular, thr rlatin (qn. (3), (32) and (33)) wr drivd which dfin tabl intrval fr th intgratin tp T in rlatin t a pcific tuning. Th fllwing Fig. attmpt t illutrat th bhaviur f th SODE with an Eulr dicrtiatin, whn th tability limit ar dibyd. Th intgratin tp and th ampling tim wr aumd t b 6 minut. Th rult in Fig (15-17) wr btaind with ]=.75. A givn by qn. (3), if T=.1 h thn W mut b largr thn.7. Th rult btaind with W=.7, W=.75 and W=.85 hur ar hwn in Fig. (15), (16) and (17) rpctivly. 116

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.7 = = =.75 ] ] ] 1 2 3 ITAE: - r.1 1.8.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 15. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE uing Eulr dicrtiatin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.75 = = =.75 ] ] ] 1 2 3 ITAE: 3.5 r.75.88.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 16. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE with Eulr dicrtiatin. 117

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.85 = = =.75 ] ] ] 1 2 3 ITAE: 2.5 r.78.87.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 17. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE with Eulr dicrtiatin. With W=.7 th timatd curv divrg, and th algrithm i thu untabl. Incraing W t.75 th divrgnc tppd bing brvd. Nvrthl, pritnt cillatin ar xhibitd uggting that th timatr prat nar th tability limit. Fr W=.85 a nrmal utput i btaind. Th rult in Fig (18-2) wr btaind with ]=1.. A givn by qn. (32), if T=.1hr thn W mut b largr thn.1. Th rult btaind with W=.95, W=.1 and W=.15 ar hwn in Fig. (18), (19) and (2) rpctivly. With W=.95 th algrithm rval itlf untabl. Incraing W t.1 th divrgnc tppd bing brvd. Nvrthl, th rpn xhibit ccainally vrht which i nt charactritic f a cnd-rdr rpn with ]=1. Thi uggt that th timatr prat nar th tability limit. Fr W=.15 th vrht i rducd uggting that th timatr prat farthr frm th tability limit. 118

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.95 = = = 1. ] ] ] 1 2 3 ITAE: 2 r.92.82.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 18. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE with Eulr dicrtiatin. -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.1 = = = 1. ] ] ] 1 2 3 ITAE: 2.9 r.93.87.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 19. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE with Eulr dicrtiatin. 119

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc -1 h.5.45.4.35.3.25 RF R RF R RF R RF R W 1 = W 2 = W 3 =.15 = = = 1. ] ] ] 1 2 3 ITAE: 2.5 r.94.91.2.15.1.5 r r r r a b c d f g 18 t (h) Fig. 2. Spcific grwth rat timat (full lin) and tru (dttd lin) givn by th SODE with Eulr dicrtiatin. 12

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc AENDIX: rf f Unifrm Aympttic Stability f th SODE Errr Sytm Lt' firt cnidr th fllwing rfrmulatd rrr ytm and cncntrat ur attntin t th unfrcd ytm : dy dt d ~ U dt at () y Jy du dt ~ U (A-1a) (A-1b) which can b btaind frm ytm (15) by cnidring th tranfrmatin y (t implify th prnt analyi th indx "i" will b mittd), whr ~ / \ h at () Z() t h 1 dh dt (A-2) Ching th fllwing candidat Lyapunv functin: V( y, U ~ ) Jy U ~ 2 2 (A3) wh tim drivativ alng th lutin f (A-1) i givn by: dv dt 2 T 2aty () E QtE () (A-4) whr T E > y ~ ª at () U @ Qt () º ¼ thn it fllw that if at () t ttt thn Q(t) i pitiv mi-dfinit. Hnc th quilibrium tat E= i unifrmly tabl (Narndra and Annawamy, 1989). Supping that cnditin C1 thrugh C3 hld, th cnditin undr which at () t ttt ar tatd a: C5. h([) i a diffrntiabl functin f [, which man that h i bundd C6. h([) i bundd a fllw: h d h ( ) d h min C7. Z( t) i [ max ttt 1 t ttt h dh dt Still, inc Q(t) i pitiv mi-dfinit and tim-varying, it can nt b cncludd that ytm (A-1) i unifrmly aympttically tabl. In th lin bllw, th xpnntial tability f (A-1) i prfd. A qualitativ utlin f th prf can b givn in tw tp: i) in ytm (A-1) y(t) ha t aum a larg valu at 121

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc m intanc in vry intrval [t, t+t ], ii) inc V i a givn by qn. (A-3), thi impli that V(t) dcra vr vry intrval f lngth T which aur unifrm aympttic tability. rf. Supp that y () t E () t i D i t > t, t T @ whr D > 1, @. Intgrating (A-1a) vr th tim intrval > t2, t2 G @ > t, t T @, it fllw that t G t G ³ max ³ t2 t2 2 2 yt ( ) yt ( ) ~ G UW ( ) dw a y ( W ) dw t 2 2 (A-5) whr a max i th maximum valu f at (). Thrfr t 2 yt ( ) ~ G t UW ( ) dw ( Ga 1 ) up y ( W ) ³ G 2 t2 max W t2, t2g > @ (A-6) inc yt ( 2 ) i alway l thn up y( W ) in W > t2, t2 G @. On th thr hand t 2G G G t2 t 2 2 UW ~ ( ) d W t U ~ ( t ) d W U ~ ( t ) UW ~ ( ) d W ³ ³ ³ t2 2 2 t2 t G U ~ ( t ) G up U ~ ( t ) U ~ ( W ) 2 2 W > t G @ 2, t2 t G 2 t G U ~ ( t ) G U ~ d W 2 ³ t2 t (A-7) inc th ditanc btwn t pint U ~ ( t 2 ) and UW ~ ( ) i alway l thn th arc lngth t2g ~ ³ UdW. Hnc, valuating U ~ frm (A-1b), qn. (A-7) bcm t2 t 2G ~ ( ) ~ U W dw tg U ( t2 ) ³ b up y ( W ) (A-8) t2 W t2, t2g > @ whr b JG 2 a max G 1. Frm th initial uppitin rgarding yt (), it fllw that up y( W ) in W > t, t G @ i alway l thn D Et ( G ), and al U ~ ( t 2 ) i 2 2 2 alway largr thn 1 D Et ( 2 ). Sinc 2 det () at () y d 2 dt min( J, 1) d t t t 122

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc thn Et ( ) t Et ( G ). Hnc qn. (A-8) bcm 2 2 t yt 2 ( G ) G 1 D b D Et ( G ) (A-9) 2 Ching 2 2 2 G D 2 2 G ( 1b) (A-1) thn qn. (A-9) bcm t yt ( G ) D Et ( G ) (A-11) 2 2 which i a cntradictin f th initial aumptin rgarding yt (). int i) i thrfr prfd. Lt' nw intgrat qn. (A-1b) vr a tim intrval > t, t T @ > t, t T @ t1t 1 1 2 V( t1) V( t1t) t 2amax ³ y( W) dw (A-12) and by th Cauchy-Schwarz inquality t1 t T 2 2a 1 max V( t1) V( t1 T) t y( ) d T ³ W W (A-13) t1 Furthr, by cnidring that t1t t1t t2g ³ ³ ³ t1 y( ) d t y( t ) d yd W W 1 W W t1 t2 ¹ 2 ttyt ( 1) T det ( 1 ) (A-14) whr d amax 1, thn ching t1 t2 G w hav that t1t y( W) dw TD ³ t Td E( t1) (A-15) t1 Hnc qn. (A-13) bcm V ( t ) V ( a t T ) max 2 Td Td E t d ( ) 1 1 t 2 D 1 2 (A-16) 123

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc bing T l than D/d. Sinc Et () 2 i alway largr thn V()/max( t J1,,) thn ching T min( t T t, D / d) w cnclud that 1 V( t T ) dv( t T) d( 1E) V( t ) d( 1E ) V( t ) (A-17) whr 1 1 E 2amax 2 D J 1 d Td ( max(, ) Td ) (A-18) Sinc a max / d i alway l thn 1 and T=D/(3d) i a maximum pint f th functin f ( T ) Td( D Td ) 2, w cnclud that E D ª 3 º > @, 27 J 1 1 max(, ) ¼ 8, (A-19) and, hnc, th final cncluin can b takn that th timatr (A-1) i unifrmly aympttically tabl. 124

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc NOMENCLATURE C CTR D E F G H([) K k i OTR Q S S in T X xygn cncntratin carbn dixid tranfr rat dilutin rat thanl cncntratin ma fd rat vctr carbn dixid cncntratin (mur) matrix f knwn functin f th tat yild cfficint matrix yild cfficint Oxygn tranfr rat rat f ma rmvl in gau frm vctr gluc cncntratin gluc cncntratin in th fd ampling prid bima cncntratin Grk lttr M ractin rat vctr [ timatd tat vctr r pcific grwth rat fr th frmntativ grwth n gluc pathway pcific grwth rat fr th rpiratry grwth n thanl pathway pcific grwth rat fr th rpiratry grwth n gluc pathway [ 2 timatd vctr f nnmaurd tat variabl vctr f timatd pcific grwth rat :, * gain matric W i natural prid f cillatin pcific grwth rat vctr U vctr f timativ f U(t) U(t) vctr f cmpltly unknwn tim-varying paramtr Z i, J i diagnal lmnt f : and * ] i damping cfficint [ tat pac vctr [ 1 maurd tat pac vctr [ 2 nn-maurd tat pac vctr Mathmatical ntatin up min max diag{.} uprmun minimum maximum diagnal matrix 125

Chaptr 6. On-lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc REFERENCES Batin, G. and D. Dchain (199) On-Lin Etimatin and Adaptiv Cntrl f Biractr, Elvir, Amtrdam. mrlau, Y. and M. rrir (199) Etimatin f Multipl Spcific Grwth Rat in Biprc, AIChE Jurnal, 36(2), pp. 27-215. mrlau, Y. (199), "Mdéliatin t cntrôl d'un prcédé fd-batch d cultur d lvur à pain", h. D. Thi, Ecl lytchniqu d Mntréal, Canada. Snnlitnr, B. and O. Käppli (1986) Grwth f Saccharmyc crviia i cntrlld by it Limitd Rpiratry Capacity: Frmulatin and Vrificatin f a Hypthi, Bitch. Bing., 28, pp. 927-937. Lunbrgr, D.G. (1971) An intrdutin t brvr, IEEE Tran. Autmatic Cntrl, AC-16, pp. 596-63. Fy d Azvd, S.,. imnta, F. Olivira, E. Frrira (1992) "Studi n On-Lin Stat and aramtr Etimatin thrugh a Ral-Tim rc Simulatr, in Karim, M. N. and Stphanpul, J. (Ed.), Mdling and Cntrl f Bitchnical rc, IFAC Symp. Sri 1, 453-458, rgamn r N.Y. Narndra, K.S. and A.M. Annawany (1989) "Stabl Adaptiv Sytm," rntic Hall, Englwd Cliff 126

Chaptr 7. Cncluin Chaptr 7 Cncluin Th ct f dvlping mathmatical mchanitic mdl fr biprc imprvmnt ar ftn t high and th bnfit t lw. Thr ar vral ran fr thi. Th main ran i rlatd t th intrinic cmplxity f bilgical ytm. Unfrtunatly many biprc mchanim ar nt yt wll undrtd. Thi i particularly critical in what th micrrganim grwth kintic cncrn. In gnral, mathmatical dcriptin f grwth kintic aum hard implificatin bad n untructurd and nn-grgatd cll mdl. Th mdl ar ftn nt accurat nugh at dcribing th undrlying mchanim. An accuracy incra can nly b achivd by activating mr knwldg. Thi i prcily th critical iu. Acquiitin f mchanitic knwldg i lw and xpniv. A uch, th bttlnck in dvlping a mchanitic mathmatical mdl with th rquird accuracy li in th acquiitin f mchanitic knwldg. Anthr critical iu i rlatd t th natur f biprc mdl. Thy ar in gnral cmplx nn-linar dynamical ytm, invlving kintic paramtr that mut b idntifid fr th actual cultivatin cnditin. Du t th cmplx nn-linar tructur 127

Chaptr 7. Cncluin f uch mdl, ftn th paramtr invlvd ar nt idntifiabl. Additinally, frm th practical pint f viw, uch an idntificatin wuld rquir data frm pcific xprimnt which ar thmlv difficult t dign and t raliz. A uch, th ct f paramtr idntificatin ar in gnral high. Fr th ran biprc mathmatical mdl ar ftn viwd with pimim in indutry. Thi lack f accptanc f mdl i trngly rflctd n th way prc imprvmnt ar achivd: th imprvmnt ar ftn achivd by mr r l ducatd trial and rrr mthd guidd by intuitin and xprinc, and ldm by a ytmatic apprach charactrid by a cnqunt utiliatin f th a priri knwldg availabl. It i wll-knwn that thr i a crtain inrtia n intrducing nw pratin tratgi in prductin plant. rc pratr and cintit ar lking at th prc with diffrnt pint f viw. Opratr try t kp th prc undr cntrl with thir xprinc and intuitin, whil nginr and cintit try t intrduc nw and maningful pratin tratgi, but ar ftn unawar f th practical implmntatin prblm thy invlv. Thi ituatin i, f cur, nt ptimal. T incra th accptanc f a mdl-bad way f prc imprvmnt it i imprtant t fmnt a cprativ wrk btwn all th factr prducing knwldg r inight abut th prc, i.. prc pratr, cintit and nginr, and tchnlgy. Th mdl ud t dcrib thi knwldg huld b capabl f incrprating urc f knwldg thr thn th mchanitic n. Tw thr urc f knwldg ar vry imprtant: 1) Th huritic knwldg i vry imprtant in th indutrial nvirnmnt inc uually prc imprvmnt i guidd by xprinc and intuitin. In gnral, huritic knwldg i availabl in larg quantiti in th indutrial nvirnmnt. 2) Knwldg hiddn in prc data rcrd. Many mchanim hav bn xplaind nithr mchanitically nr huritically. Hwvr thir cau/ffct rlatinhip hav bn rcrdd in prc data fil. Mdlling mthd lik ANN can b ud t xtract thi kind f knwldg hiddn in prc data rcrd. Efficint intgratin f all th urc f knwldg in th prc mdl i th traightfrward way f incraing th bnfit and f rducing th xpn. A uch th hybrid mdlling apprach i mt prmiing fr indutrial applicatin. Hybrid mdlling i mrging a a nw rarch fild. Unfrtunatly thr i n gnral framwrk fr dvlping biprc hybrid mdl. On imprtant aim f th prnt h.d. thi wa t dvlp th hybrid mdling apprach, and pcially it applicatin fr bichmical prc imprvmnt. Thr ar fur main iu in hybrid mdling: 1) Hybrid mdl tructur dfinitin 2) aramtr idntificatin in hybrid mdl 3) On-lin adaptatin in hybrid mdl-bad algrithm 4) ractical implmntatin in an indutrial nvirnmnt Th firt thr tpic cncrn mthdlgi whil th furth tpic cncrn mainly ftwar lutin. 128

Chaptr 7. Cncluin Hybrid mdl tructur, paramtr idntificatin and n-lin adaptatin ar rlatd tpic. In th prnt h.d. wrk a gnral framwrk fr hybrid mdl tructur dfinitin, paramtr idntificatin and n-lin adaptatin wa prpd bad n hybrid mdl ntwrk tructur. Thr ar vral ran that jutify th u f hybrid mdl ntwrk. Th firt n rpct it ntwrk tructur. Th diffrnt kind f knwldg abut diffrnt part f th prc can b rprntd and intgratd in a mt flxibl way by man f a ntwrk f mdul, whn th mdul ar capabl f rprnting knwldg at diffrnt lvl f phiticatin. Th ntwrk tructur i furthr vry flxibl fr dfining pcial purp mdl-bad algrithm uch a cntrl ytm, tat timatr and paramtr timatr. It i wll-knwn that uch a mdularizatin f a prc mdl immdiatly nhanc th tranparncy f th mdl and a uch hlp t avid rr. Anthr ntial advantag i that uch a tructur implifi th practical mdling wrk by allwing t mak u f prdfind ftwar mdul that nd t b adaptd nly lightly t fit int th mdl. Th thr rlvant ran i that hybrid ntwrk, lik thr ntwrk-lik tructur, blng t th cla f rdrd ytm t which th tchniqu f frward prpagatin and rrr backprpagatin can b applid. A uch, th larning mthd bad n rrr backprpagatin, which ar mt ppular fr nural ntwrk applicatin, can al b applid t th ca f hybrid mdl ntwrk. Ntic that an artificial nural ntwrk i viwd a a particular mdul in th hybrid mdl ntwrk, in th am way a th igmid functin i viwd a a particular nd in th artificial nural ntwrk. Hybrid mdl ntwrk fr bichmical prc ar ftn f cnidrabl cmplxity. Such mdl cntain many paramtr. Cnquntly, a cnidrabl amunt f data i rquird t idntify th mdl paramtr. In uch ca, th cmputing tim bcm an iu. Th applicatin f ptimizatin algrithm mplying gradint timat btaind by th rrr backprpagatin tchniqu, prvd t rduc ignificantly th cmputatin tim fr paramtr idntificatin f hybrid mdl ntwrk. Bad n thi paralll btwn hybrid mdl ntwrk and artificial nural ntwrk, many algrithm uually applid fr artificial nural ntwrk wr xtndd and applid t hybrid ntwrk: 1) Errr backprpagatin 2) Snitiviti mthd 3) Clutring algrithm 4) Batch/rial larning 5) Cr-validatin and rgulariatin validatin tratgi 6) Gntic algrithm, chmtaxi and vlutinary prgramming Th dvlpmnt allwd t xtnd and implify th practical applicatin f hybrid mdling tchniqu t bichmical prc ptmizatin, cntrl and uprviin. Th widprad u f th rult f advancd mthd fr prc ptimizatin and cntrl i largly dlayd by miing ftwar tl that can hlp t kp th xpnditur fr dvlpmnt and maintnanc in accptabl limit. Thi prblm i 129

Chaptr 7. Cncluin vn mr critical fr th implmntatin f hybrid mdl-bad mthd. In th prnt h.d. wrk th HYBNET ftwar packag wa dvlpd t cp with thi prblm. HYBNET implmnt all th mthdlgi bad n HYBrid NETwrk dicud abv. Th ftwar wa dignd t prvid all th tl ncary fr ptimizatin uprviin and cntrl f indutrial prc. A vry imprtant gal wa th dvlpmnt f a narly platfrm indpndnt and ay t implmnt link btwn hybrid ntwrk bad algrithm and th prc. Thi, jintly with an ur-frindly graphical intrfac, ar rcgnid t b dciiv pr-rquiit fr a gd accptanc in th indutrial nvirnmnt. HYBNET ha bn ud in diffrnt bichmical prductin prc a wll a in labratri and pilt plant. It i cntinuuly bing xtndd in particular cncrning th ur intrfac, which i ncary t rduc th activatin barrir flt by many prc nginr in indutry fr uing ftwar tl. Th thr imprtant aim f th prnt h.d. wrk wa t dvlp mthd fr ratinal and fficint u f n-lin prc infrmatin t cp with th impibility f mplying prc mdl dcribing fully th dynamic f th prc. Whn n-lin infrmatin i availabl, it i pibl t u a cmprmiing lutin, mplying algrithm bad in implifid mdl, cmplmntd with n-lin adaptatin chm. Such a cmprmiing apprach wa tudid in thi wrk. Th dvlpmnt f mdl auming n knwldg abut th micrrganim grwth kintic i rathr impl and, cnquntly, ffrt wa put n dvlping tratgi fr n-lin timatin f ractin kintic frm data availabl n-lin. With thi rpct tw tabl and ay t tun nlin ractin rat timatin algrithm hav bn dvlpd. Thy xplr th rlatinhip btwn tability and dynamic f cnvrgnc, imping cnvnint cnd-rdr trajctri fr th timatin rrr. Tuning rquir nly th tting f th paramtr charactritic f cnd-rdr rpn - th damping cfficint and th natural prid f cillatin. Thi rprnt a lwr dvlpmnt ct than th ct f th uual 'trial and rrr' tchniqu mplyd in th daily practic f indutrial prc pratin. Hwvr it i wrth t ntic that th dign f pcial-purp rbut and tabl adaptiv algrithm i a wrk that tak vry much tim and ffrt, rquiring highly qualifid manpwr. Th claical tchniqu ar vry pwrful and hav a wll-tablihd thrtical backgrund. Hwvr, th ral dangr prit that thir cmplxity hindr th practical applicatin at ranabl ct t indutrial prductin plant. Th gnral lutin prpd in thi h.d. thi t incra th bnfit/ct rati f a mdl-bad prc ptimizatin, uprviin and cntrl i chmatically ktchd in Fig 1. Thi lutin i bad n a ratinal and fficint u f all knwldg urc, uually availabl abut th prc in qutin. Thi impli a cprativ wrk btwn all factr prducing knwldg, i.. cintit, prc pratr, and tchnlgy. Th mr knwldg i bcming availabl th mr accurat ar th hybrid mdl, and th mr fficint ar th nw dvlpd hybrid mdl-bad prating tratgi. Th rat f prc imprvmnt can b ignificantly augmntd by uing uch an apprach. 13

Chaptr 7. Cncluin KNOWLEDGE HYBRID MODELLING LANT Scintit rc pratr Data acquiitin/cntrl ytm hyi. undrtanding Huritic. Cmmn n rc data Math. mdll. Fuzzy y. Empiric crr. Nn-paramtric mdl (nural nt., furir ri, plin,...) Mnitring Cntrl Stratagi HYBNET Fig. 1. Gnral apprach fr bichmical prc uprviin, cntrl and ptimizatin bad n HYBrid mdl NETwrk and HYBNET ftwar packag Thi apprach ha bn uccfully ud in many indutrial prductin plant 1) Cld-lp cntrl in a pnicillin prductin prc (Git Brcad) (http:/rrzn.uni-hannvr.d/nhchliv/bub; Olivira t al., 1998) 2) Opn-lp cntrl in a pnicillin prductin prc (Git Brcad) (ruting t al., 1997) 3) rc dign f a cmplx antibitic cultivatin prc (Git brcad) (in prgr) A wll a in m Lab-cal applicatin: 4) Opn-lp cntrl and tat timatin in an cli cultivatin prc fr rcmbinant prtin prductin (in prgr) 5) Stat timatin, ptimizatin and cntrl in a yat cultivatin prc (Schubrt t al., 1994) Finally it i imprtant t tr that th mt bviu thing t d in rdr t kp th bnfit/ct-rati a high a pibl, i t dfin vry clarly th prblm bing lvd in trm f an prc/mdl bjctiv functin ( th wrk f Simuti t al., 1997). Car huld b takn t avid mdling phnmna irrlvant t th bjctiv functin in qutin. Uually th ct f dvlping a mdl i an xpnntial functin f accuracy, hnc th dird quality f th mdl huld b al bfrhand dfind. 131

Chaptr 7. Cncluin REFERENCES Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1998). Cld-lp Cntrl Uing an On-lin Larning Hybrid Mdl Ntwrk (ubmittd) ruting, H., J. Nrdvr, R. Simuti, A. Lübbrt (1997). Th u f Hybrid mdling fr th ptimizatin f th pnicillin frmntatin prc, Chimia, 5(9), pp. 416-417 Schubrt, J., R. Simuti, M. Dr, I. Havlik, A. Lübbrt (1994). Hybrid Mdlling f Yat rductin rc Cmbinatin f a priri knwldg n Diffrnt lvl f Sphiticatin. Chm Eng. Tchnl., 17, pp. 1-2 Simuti, R., R. Olivira, M. Manikwki, S. Fy d Azvd, A. Lübbrt (1997). Hw t incra th prfrmanc f mdl fr prc cntrl and ptimizatin. J. Bitchnl., 59, pp. 73-89 132

Curriculum Vita Gnral rnt itin Schl ducatin Nam: Rui Manul Frita Olivira Dat f birth: May 31, 1969 lac f birth: Faf, rtugal Citiznhip: rtugal Civil tatu: Marrid h.d. Studnt at Martin-Luthr-Univrität, Hall-Wittnbrg, Intitut für Bivrfharntchnik und Raktintchnik 1975-79 Baic Schl in Faf 1979-87 Highchl in Faf Diplma: 12 th chl yar diplma 1987 with final mark 17/2 Graduatin 1987-92 Graduatin in Chmical Enginring at th Univrity f rt Spcializatin: Indutrial Infrmatic Diplma: Diplma Chmical Enginring 1992 with final mark 15/2 Grant ublicatin 1991-92 Grant fr yung rarchr frm JNICT Libn (JNICT BJI 774/91) 1992-93 Rarch grant frm JNICT Libn (JNICT BIC 636/92) 1993-95 h.d. grant frm JNICT Libn (JNICT BD/251/93/RM) 15 ublicatin 133

ublicatin lit (15 ublicatin) [1] Olivira, R., E. Frrira, F. Olivira, S. Fy d Azvd (1994). A Study n th Cnvrgnc f Obrvr-Bad Kintic Etimatr in Stirrd Tank Biractr. 5th Intrnatinal Sympium n rc Sytm Enginring - SE 94, Kyngju, Kra, May 3-Jun 3 [2] Olivira, R., E. C. Frrira, S. Fy d Azvd (1995). Mdl-Bad Etimatin f Ractin Rat in Stirrd Tank Biractr. 6th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy - CAB6, Garmich-artnkirchn, Dutchland, May 14-17 [3] Olivira, R., E. Frrira, F. Olivira, S. Fy d Azvd (1996). A Study n th Cnvrgnc f Obrvr-Bad Kintic Etimatr in Stirrd Tank Biractr. J. rc Cntrl, 6(6), pp. 367-371 [4] Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1996). HYBNET, a nw tl fr advancd prc mdling, rcding f th 1 t Eurpan Sympium n Bichmical Enginring Scinc, Dublin, Irland, 182-183. [5] Olivira, R., N. Vlk, R. Simuti, A. Lübbrt (1998). Hybrid Mthdn zur Optimirung bitchnichr rduktinprz. Mn, Sturn, Rgln, (in pr) [6] Olivira, R., S. Fy d Azvd, R. Simuti, A. Lübbrt (1998). Hybrid Ntwrk: A Nw Apprach fr Biprc Mdling (ubmittd) [7] Olivira, R., R. Simuti, A. Lübbrt (1998). Cld-lp Cntrl Uing an Onlin Larning Hybrid Mdl Ntwrk (ubmittd) [8] Olivira, R., S. Fy d Azvd (1998). On-Lin Stat Obrvatin and Ractin Rat Etimatin in a Bakr Yat Cultivatin rc. (ubmittd) [9] Olivira, R., R. Simuti, S. Fy d Azvd, A. Lübbrt (1998). Hybnt, an Advancd Tl fr rc Optimizatin and Cntrl.. 7th Int. Cnfrnc n Cmputr Applicatin in Bitchnlgy CAB7, Oaka, Japan, May 31-Jun 4, 1998 134

[1] Fy d Azvd, S., R. Olivira, F. Olivira (1993). DIGICON - A Gnralizd Fdback-Fdfrward DIGital CONtrllr. CHEMOR-93, Int. Chm Engng Cnf., rt, April 4-6 [11] Frrira, E., R. Olivira, F. Olivira,. imnta, S. Fy d Azvd (1993). Mdl-Bad Idntificatin and Cntrl n Bakr Yat Fd-Batch Frmntatin. 6th Eurpan Cngr n Bitchnlgy, Firnz, Italy [12] Simuti, R., R. Olivira, A. Lübbrt (1996). Hybrid mdling with nural ntwrk and it utilizatin in biprc cntrl. In: Biractr Enginring. Cur nt (Ed)., Larn, G., Förbrg, C., EFB, Saltjöbadn, Stckhlm, pp. 38-46. [13] Simuti, R., R. Olivira, M. Manikwki, S. Fy d Azvd,A. Lübbrt (1997). Hw t incra th prfrmanc f mdl fr prc ptimizatin and cntrl. J. Bitchnl., 59, pp. 73-89 [14] Simuti, R., R. Olivira, A. Lübbrt (1996). Mdl - bad ptimizatin: hw t incra th prfrmanc f hybrid mdl fr cultivatin cntrl, rcding f th 1 t Eurpan Sympium n Bichmical Enginring Scinc, Dublin, Irland, 31. [15] Simuti, R., R. Olivira, N. Vlk, A. Lübbrt (1997). Optimirung dr rduktin rkmbinantr rtin mit Hilf Hybridr rzßmdll, Rfrat dr DECHEMA Fachauchußitzung GVC-Raktintchnik, Würzburg, Dutchland, 4.4. 135