Model Based Control of Large Scale Fed-Batch Baker s Yeast Fermentation

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1 Model Baed Control of Large cale ed-batch Baker Yeat ermentation Akif Hocalar and Mutafa Türker Pakmaya, P.K. 49, 4 İzmit, Kocaeli, Türkiye akifh@pakmaya.com.tr mutafat@pakmaya.com.tr Abtract : Two different control method are applied to the technical cale (5 m fed-batch baker yeat fermentation. eedback linearizing control deign i ued to manipulate the ubtrate feeding rate in order to maximize the bioma yield and minimizing the production of ethanol. irtly, the pecific growth rate controller i developed and applied to maintain the pecific growth rate at pecified trajectory. econdly, the minimal ethanol controller i developed to maximize bioma productivity, by controlling pecific growth rate jut above the maximum idative growth rate by controlling ethanol concentration. The both controller worked uccefully and can be combined to follow requi pecific growth rate trajectory and repond uccefully to diturbance in overflow fermentation uch a accharomyce cereviiae. Keyword: Nonlinear control, feedback linearizing control, fed-batch, baker yeat, pecific growth rate, ethanol concentration, biocalorimetry.. INTRODUCTION ed-batch bioprocee have extenive application in indutry for production of baker yeat, enzyme, antibiotic, growth hormone, microbial cell, vitamin, amino acid and other organic acid (Perulekar and Lim, 985; Yamane and himizu, 984. accharomyce cereviiae i ued in many application uch a beverage product (beer, wine, baker yeat for bread production, heterologou protein production, bio-tranformation, flavour component, ingle cell protein, bio-ethanol, glycerol and food additive (Walker, 998; Renard and Wouwer, 8. The pecific growth rate i a key variable for the growth-aociated biotechnological procee and determine the phyiological tate of the cell and the capacity of cell protein-yntheizing machinery that i important for recombinant protein production or bioma production in everal fermentation (Cannizzaro et. al., 4; Gnoth et. al., 8. imilarly, Echerichia coli how imilar metabolic behaviour in the preence of exce ubtrate and hortage of ygen. In the production of recombinant protein with E. coli, acetate i produced a an overflow metabolite both when E.coli grown under anaerobic or ygen limiting condition. It i important to maintain the pecific growth rate below a certain threhold in order to avoid the accumulation of acetate throughout the fermentation (Rocha and erreira, ; Jana and Deb, 5. In the literature, many work have been reported by everal author for the control of fed-batch fermentation, mot of thee tudie report experimental reult either at laboratory cale or imulation reult (Chen and Batin, 995; Pomerleau and Viel, 99; oon et al., 6; Rocha and erreira, ; Cannizzaro et al., 4; Valentinotti et al.,. The main objective of thi tudy i to develop a robut control cheme to cope with changing proce dynamic during fermentation, et point tracking, requi minimum proce meaurement and batch-to-batch conitency for the technical cale fed-batch baker yeat fermentation. The control method are baed on previouly developed and verified tate etimation model and reliable meaurement ytem (Hocalar et. al., 6. In thi work, different key proce variable are controlled with the tate feed-back linearizing control cheme at technical cale fermentation:. nonlinear control of pecific growth rate,. nonlinear control of ethanol concentration. In the firt part, the derivation of nonlinear pecific growth rate controller ant it reult are dicued. The retrictive condition of the controlling of pecific growth rate are given at the end of firt ection. In the econd part, the control of nonlinear ethanol concentration i preented. By mean of controlling of overflow metabolite concentration at minimal concentration, pecific growth rate can be maintained near the maximum value.. TOICHIOMETRY O THE PROCE General toichiometry of the baker yeat fermentation proce can be written with repect to reaction rate a (Türker, ; Türker, 4 :

2 r CH ON x r CH.8 O.5 rn NH ro O (.5 N. r CH O and the rate vector i p.5 r CO r H O r c T ( r, rn, ro, rx, r p, rc, rw, r ( q r Metabolic heat production rate i added to reaction rate. The unknown proce tate are determined by the metabolic black-b modeling and the integration of etimated reaction rate. The undant reaction rate are ued in the derivation of reconciliated reaction rate (Hocalar et. al., 6.. REULT AND DICUION.. Nonlinear Control of pecific Growth Rate The feedback linearizing control of the pecific growth rate i baed on the aumption of the preence of ufficient ygen concentration and the abence of ethanol in the fermentation broth (Clae, 999. In order to implement the control approach, the ygen concentration ha to be maintained high enough not to run into ygen limitation throughout fermentation and the pecific growth rate ha to be below the critical value in order not to form ethanol. The tarting point for the derivation of the controller expreion i the general dynamical ma balance equation for the ubtrate feeding a hown in Eq.. d μ q x e,pr D ( in m X Y X/ Y ( E/ By rearranging the Eq., Eq. 4 can be written a; dc σ X ( C,in C (4 V where μ q x, m, C σ i ubtrate Y X/ Y E/ concentration, X bioma, ubtrate feed rate. The econd tep i to et up a table linear reference model for tracking error. The reference model determine to the decreaing trajectory of the tracking error. d (C C λ (C C (5 The λ i arbitrary adjutment coefficient and have to be choen uch that the differential equation (Eq. 5 i table. At teady tate condition, the ubtrate concentration can be accepted zero, ( d C and Eq. 5 can be written a λ dc ( C C and by ubtituting the Eq. 4 in the Eq. 5, σ X λ(c, in C V (6 C,in C obtained a a final controller equation. Under idative condition and in the abence of ethanol in the fermentation broth, pecific growth rate i a function of ubtrate concentration. Therefore, pecific growth rate ( μ can be w q written intead of ubtrate concentration term in Eq. 6. By rearranging the Eq. 6, the expreion for ubtrate feed rate controller can be written a follow; μx X λ ( μ μ YX/ V (7 C,in where i the arbitrary adjutment coefficient for the decreae of tracking error. When the Eq. 7 i applied to the fermentation, teady tate error are oberved between the etimated pecific growth rate and et profile. In order to eliminate thi difference, an integral term i added to the Eq. 7. and the obtained reult are preented in ig. for the controlling of time varying pecific growth rate profile. μx X λ ( μ μ ( μ μ P YX/ λi V (8 C,in The reult of the implementation of Eq. 8 in a fed-batch fermentation are given ig.. The adjutment parameter are λ p.4, λ i 8 for the acending and λ p. 7, λ 8 for the decending pecific growth rate region. i pecific growth rate (h - Bioma Concentration (g/l a off-line et etimated b et off-line etimated ubtrate off-line bioma bioma igure.a- pecific growth rate b- bioma concentration and ubtrate. The etimation of bioma concentration can be accepted uccefully (ig. -b and i ued in the calculation of pecific growth rate (fig. -a. The pecific growth rate etimation and off-line meaurement are cloe to each other 45 5 ubtrate feed rate (L/h

3 with acceptable accuracy. The time varying pecific growth rate profile i controlled uccefully by the controller and obtained ubtrate feed rate reemble the petermined ubtrate feeding profile widely ued in practice. In ig., the reult of different pecific growth rate controlled fermentation are given. In thi fermentation, ethanol formation i oberved at the different time during the proce and caue decreae in the pecific growth rate. The controller increaed the ubtrate feed rate in order to compenate the decreae in the pecific growth rate that caued more ethanol formation (ig. -a. The unexpected decreae in the pecific growth rate etimation are given in ig. -b. The exce in the ubtrate feed rate put the proce more intability and reult in failure of the control of pecific growth rate. A a reult, the ubtrate feed rate i manually intervened to conume the ethanol in the broth. ubtrate feed rate (L/h pecific growth rate (/h a ubtrate feed rate (controller output -b controller output ethanol manual intervention ubtrate (meau ethanol lab. online profile igure.a- ubtrate feed rate and ethanol concentration, b- pecific growth rate. Thi controller ha uccefully controlled the pecific growth rate at trajectory under defined condition a hown in ig.. Once the fermentation went to beyond the retrictive condition the controller failed a hown in ig.... Nonlinear Control of Minimum Ethanol Concentration An alternative way to control the pecific growth rate at maximum idative rate i to ue the overflow metabolite a an indicator of how cloe the actual value to critical growth rate to maximize bioma production. If ethanol concentration can be controlled at contant minimal concentration, it i poible to keep the pecific growth rate lightly above the critical value (Cannizzaro et. al., 4. In order to control the ethanol concentration, the regulator Ethanol (% deign i baed on a feedback linearization of a uced-order model of the proce obtained by ingular perturbation of the tate pace model under the following aumption: the toichiometric (yield coefficient are known, the gaeou outflow rate (ethanol, CO, O are meau on-line, the influent ubtrate concentration in i fixed and known, the pecific growth rate i unknown. The ingular perturbation technique can be ued for ytem in which ome reaction proceed at much fater rate than the other (Batin and Dochain, 99; Pomerleau and Viel, 99; Chen et. al., 995. The dynamical proce equation for five proce tate with known yield coefficient can be given a follow; X X Y X / Y X / (9 x Din d eth E Y X / E Y X / E x X D E O eth Y X O X O O r / Y / o e C eth C rc Y X / C Y X / C Y X / C The general tate pace dynamical model can be written a follow (Batin and Dochain, 99; d K ( D Q ( ξ T X,,E,O, C where,q, involve n component, involve m reaction rate ve K i (NxM ize yield coefficient matrix. In Eq. 9, the firt term K ( decribe the kinetic of microbiological reaction, the remaining term D Q decribe the tranport dynamic of the component through the bioreactor. The yield coefficient ued in the deign i hown in Table. Table. Parameter ued in nonlinear controller deign (Cmol/mol (Beşli et. al k, Y X /.65 k, Y X /.6 k, X E.9 k 4, eth Y X / E.5 k 5, Y X / O.56 k 6, k 7, Y X / C.45 k 8, k 9, eth Y.99 X / C eth Y X / O.8 Y X / C. By the ytematic application of ingular perturbation technique, fully uced model can be etablihed and in the cae of dim (ξ M and K full rank, the proce tate can be partitioned a low ξ T X, E and fat varying tate variable ξ T, O, C. The ubtrate, ygen and carbondiide are fat varying tate variable and bioma and ethanol are low varying tate variable for the fed-batch yeat fermentation proce. The general dynamical model can be written a given in Eq. by the aumption of the fat

4 varying tate variable dynamic allow the ingular perturbation (Batin and Dochain, 99; dξ K D ξ K Q Q The reaction rate vector, (, can be written a; K ( Q ( ( By ubtituting Eq. in Eq., the dynamic of low varying tate variable can be obtained a in Eq.. d X X D E E k4 Din * inv( K ro k rc ( In teady tate, ingular perturbation allow the fat varying tate dynamic to conider to equal to zero and unknown reaction rate can be determined by imple matrixe operation a hown below if the invere of the yield coefficient matrice can be calculated (Hocalar, 7. e K D ro rc in (4 By inerting the Eq. 4 in Eq., low varying proce tate can be calculated by mean of baic matrice operation: k7 k6 k k5k9k kk8 k4kk6 kkk5 ψ k4kk9 kk k7 kkk8 k k k k k k k k k ψ det(k ψ ψ de D E D in r o k r 6 c (5 By inerting the Eq. 5 into the firt order reference model equation in Eq. 6, the controller law for ubtrate feed rate can be obtained a in Eq. 7. d * ( y * y ( x( y y ( (6 * de λ λ (, Xˆ (E E DE r c ro (7 The tracking ethanol error i tried to minimize uing adjutment parameter. everal fed-batch experiment were conducted in a 5 m fermentor to validate the control trategy. The reult are given in ig.. Ethanol concentration (% ubtrate feed rate (L / h Bioma concentration (g/l pecific growth rate (/h a b on-line fixed et point off-line c d etimated off-line etimated off-line igure : a- Ethanol concentration, b- ubtrate feed rate, c- bioma concentration and d- pecific growth rate curve obtained from the indutrial fermentation. The controller wa tarted at econd hour and two fixed et point were tried to control for certain period with ethanol et value E = %. and then with E = %.5. The ethanol concentration wa uccefully controlled at different et value from the 7 th hour to the end of fermentation. The manipulated variable ubtrate feed rate and bioma concentration are given in ig. -b and -c repectively. The bioma concentration increaed exponentialy (ig..c and the pecific growth rate etimation i given in ig. -d and quite cloe to experimental reult. The controller developed table repone to the tep change in the ethanol et point. The controller automatically adapted the feed rate of ubtrate to compenate for tep change. The difficulty of controlling the ethanol concentration can be een in firt

5 hour of fermentation (exponential growth phae. During the firt hour, the controller increaed the ubtrate feed rate and becaue of the time delay of the ethanol formation, lightly exce ubtrate feeding uggeted by the controller. 4. CONCLUION The tate feedback linearizing control trategy i applied to the indutrial fed-batch baker yeat fermentation. The control of pecific growth rate and minimal ethanol concentration are attempted at technical cale fermentation. The control of pecific growth rate at pecificed trajectory i requi in many fermentation procee. In thi work, thi approach ha been uccefully applied to baker yeat fermentation. In order to maximize bioma concentration and productivity, the proce ha to be controlled at it maximum idative growth rate, minimizing by-product ethanol formation. Thi trategy i applied in econd controller and pecific growth rate wa maintained lightly above maximum idative growth rate by maintaining and controlling by product ethanol at minimal concentration. Thi approach can alo be applied to imilar overflow procee uch a the growth of E. coli. The ethanol concentration wa controlled uccefully at minimal concentration. Both controller can be combined to control pecific growth rate at any trajectory and to minimize ethanol production. NOMENCLATURE ae aerobic in inlet C i concentration of i (kg/m out outlet D dilution rate (/h T tranpoe i flow rate of i (m / h n nitrogen K yield coefficient matrice o ygen M i molar weight of i (kg e ethanol q i pecific converion rate of i c carbon (kg/kgh, C-mol/ C-mol h q metabolic heat production ubtrate concentration (kg/m ubtrate X bioma (kg/m p product V volume (m x bioma yield of i over j w water Y i/j ubcript Greek Letter idative pecific growth rate, (h - uctive tate variable eth ethanol m maintenance adjutment coefficient REERENCE Batin, G. and Dochain, D. (99 On-line etimation and adaptive control of bioreactor. Elevier. Beşli, N., Türker, M., Gül, E. (995. Deign and imulation of a fuzzy controller for fedbatch yeat fermentation. Bioproce Engineering. :4-48. Cannizzaro, C., Valentinotti,., von tockar, U. (4. Control of yeat fed-batch proce through regulation of extracelluler ethanol metabolite. Bioproce Bioytem Engineering. 6: Chen, L. (99. Modelling, identifiability and control of complex biotechnological ytem. PhD Thei. aculte de cience Appliquee. Univerite Catholique de Louvan. Chen, L., Batin, G., Van Breuegem, V. (995. A cae tudy of adaptive nonlinear regulation of fed-batch biological reactor. Automatica. :: Clae, J.E. (999. Optimal adaptive control of the fed-batch baker yeat fermentation proce. PhD Thei. Katholieke Univeriteit Leuven. Gnoth,., Jenzch, M., imuti, R., Lubbert, A. (8. Control of cultivation procee for recombinant protein production: a review. Bioproce and Bioytem Engineering. : 9. Hocalar, A. (7. Model baed control of indutrial fed-batch baker yeat fermentation proce. PhD Thei. Univerity of Kocaeli, Turkey. Hocalar, A., Türker, M., Öztürk,. (6. tate etimation and error diagnoi in indutrial fedbatch yeat fermentation. AIChE Journal. 5:: Jana,., and Deb, J. (5. trategie for efficient production of heterologou protein in

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