Non-linear Predictive Control of a Fermentor in a Continuous Reaction-separation Process

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1 , Otober 9-2, 20, San Franiso, USA Non-linear Preditive Control of a Fermentor in a Continuous Reation-separation Proess Edwin G. Boza-Condorena, Daniel Ibraim Pires Atala, and Aline Carvalho da Costa Abstrat In this paper a non-linear preditive ontroller with an empirial internal model based on Artifiial Neural Networs (ANNs) is proposed. The ANN has high non-linear approximation apability and maes possible the use of plant information to generate future ontrol ations. The results show the high potential of the proposed proedure when applied to the ontinuous extrative fermentation proess of bioethanol prodution, an integrated reation-separation proess with highly omplex non-linear dynamis. Index Terms Artifiial neural networs, ontinuous extrative fermentation proess, non-linear preditive ontrol. T I. INTRODUCTION HE inreasing demand for energy aused by the global eonomi growth generates a series of environmental problems and, in this ontext, there is a great interest in developing tehnologies for sustainable bioenergy prodution. Among several options, the ethanol obtained by fermentation of sugarane is an attrative biofuel to be used as a substitute for gasoline and an help to redue gas emissions that produe the greenhouse effet []. This harateristi has inreased the demand for bioethanol, whih maes the development of more effiient prodution tehnologies desirable. One alternative is to apply proess intensifiation tehniques in ontinuous prodution proesses. Integrated proesses of reation-separation provide alternative solutions [2], suh as the prodution of ethanol by fermentation with a ontinuous withdrawal of the ethanol produed using a flash separation unit. This ation regulates the onentration of ethanol in the fermentor to ranges where the inhibitory effet of the produt on the yeast ativity dereases, improving the proess produtivity [2] [3] [4]. However, these bioproesses are highly nonlinear, its mathematial modeling is omplex and there are additional diffiulties to alulate the vapor-liquid equilibrium due to the omposition of the fermented liquid [5]. These harateristis also mae the use of lassial ontrol tehniques to ontrol the proess diffiult [6]. In this Manusript reeived July 6, 20; revised August 03, 20. This wor was supported in part by the CAPES and FAPESP. E.G. Boza-Condorena is the orresponding author.phone: ; eboza2003@ yahoo.es. He is with the Shool of Chemial Engineering, State University of Campinas, , Campinas, SP, Brazil D.I.P. Atala is with Centro de Tenologia Canavieira, Piraiaba,SP, Brasil A.C. da Costa is with the Shool of Chemial Engineering, State University of Campinas, , Campinas, SP, Brazil. ( aosta@feq.uniamp.br). paper neural networ model preditive ontrollers, NNMPC, are designed to ontrol the ontinuous prodution proess of bioethanol by fermentation and separation via flash evaporation. The ontroller is based on the dynami matrix ontrol (DMC) algorithm, whih is representative of the MPC tehnology [7] [8]. II. PROCESS DESCRIPCION A. Experimental Stage The researh experimental stage was onduted at the Bioproess Engineering Laboratory of the State University of Campinas, Brazil. The extrative fermentation proess is integrated by: one reation unit (fermentor), one ell reyle system (rossflow mirofiltration), one vauum separation system (flash tan for ethanol-fermented broth separation and vauum pump), two helial pumps, three peristalti pumps, and one ondensing unit. The total woring volume is approximately 5 L. Fig. shows a diagram of the extrative fermentation proess with vauum flashing [4]. Feed Fo So E Frf Xrf Srf Prf Ev Vapour Condenser Return F re Flash X, S, Filter Permeate Fermentor Fp S Purge, F, X, S, G X, S, Fig.. Diagram of the extrative fermentation proess with vauum flashing A 3 liters "Bioflo III System" (New Brunswi Sientifi Co., In., NJ, USA) bioreator with PID (Proportional, Integral and Differential) ontrol of temperature and agitation was used as the reation unit. A ross-flow mirofiltration unit (Ceraflow model, Millipore Co.) with a filter element made of high purity alumina, 0.22 mm pore and m 2 filtration area was used in the ell reyle system. The flash tan was a 2.5 liters (woring volume) adapted Chemap reator. The devie to measure the input flow was an eletromagneti flowmeter (IFS 400 KC F in X S

2 , Otober 9-2, 20, San Franiso, USA model, signal onverter IFC 090 model; Conaut, Brazil) with an operating range from 0 to 200 L/h. Temperature in the fermentor and flash tan was measured using K type thermoouples (N. Brunswi Sientifi Co.). A Cold trap, - 25 ºC woring temperature (MA-055 model, Maroni laboratory equipment, Brazil), was used in the ondensing system. The yeast used was Saharomyes erevisiae obtained from an industrial fermentation plant. The medium used in the fermentation was sugarane molasses ontaining about 77% of purity in sugar, diluted in water with to a onentration of 80 g / L of reduing sugars. A stage of bath fermentation was initiated shortly after the addition of the inoulum. The objetives in this stage were to promote the total onsumption of substrate and to reah a high biomass onentration before the seond stage begins. The end of the bath fermentation stage was observed by the stabilization of turbidity and ondensate volume readings. The ontinuous extrative fermentation was initiated by turning on the permeate pump of the filtration system. The removal of fluid with the permeate and purge pumps dereased the fermentation broth level into the fermentor ativating the feeding pump (onneted to an on-off level ontroller) that supplied fresh medium, by this ation the level was ept onstant throughout the fermentation. The temperature in the fermentor was maintained onstant at ± 0.25 ºC, the feed of substrate onentration was onstant at 80 g/l throughout the fermentation proess, while the dilution rate of the fermentor was maintained onstant in the levels of 0.03 h - (33.33 h residene time), 0.0 h - (0 h residene time), 0.5 h - (6.67 h residene time), 0.20 h - (5 h residene time) and 0.35 h - (2.85 h residene time). Woring with this last dilution rate it was possible to obtain a produtivity of 25 g/l h, whih is three times higher than the value obtained in the traditional fermentation proess. The flash tan was operated with a feed flow rate of 200 L/h, vauum pressure at 50 ± 40 mmhg, temperature at 33.8±0.4 ºC. The liquid remaining in the flash tan ontaining the fermentation broth with lower onentration of ethanol returned to the fermentor using a helial pump. B. Variables seletion In this wor two ontrol alternatives using the modelbased approah to ontrol system design [9] were ompared. The ontrol objetive is to regulate the ethanol onentration in the fermentor (). In order to design the ontroller an empirial dynami model of the proess based on ANN was previously developed This approah was used instead of developing a phenomenologial model of the proess, as the modeling of the flash tan has been shown to be omplex [5] and lead to inaurate results. After a preliminary study of the proess, the following variables were onsidered as input variables to develop the model : ) Permeate flow rate (F P ) ; 2) Fermentor purge flow rate (F PU ); 3) Feed flow rate to the fermentor (F 0 ); 4) Fermentor biomass onentration (X) ; 5) Fermentor substrate onentration (S); 6) Residene time (tr) or Fermentor dilution (D=/tr); 7) Fermentor Glyerol onentration (G); 8) Cell viability (Cv); 9) Fermentor outlet flow rate (F); 0) Fermentor temperature (T ferm ); ) Flash tan inlet flow rate (F in ); 2) Flash tan temperature (T flash ); and 3) Flash tan pressure (P flash ). III. MODELING AND CONTROL A. Artifiial Neural Networ Modeling A two layer feedforward networ was employed to model the proess with a tan sigmoid transfer funtion on the hidden layer and a linear transfer funtion on the output layer, beause aording to Cybeno s theorem, with this struture, the ANN models are able to approximate ontinuous funtions at any desired level [0] []. The Levenberg-Marquardt method for bapropagation training was used to train the ANN. In the ANN struture seleted the inputs, x i, the weights that onnet inputs to neurons in the hidden layer, W ji, the weights that onnet neurons in the hidden layer to neurons in the output layers, W j, the bias, b, the ativation O funtions, f, and the value of the output variable E are related by the following equation: N M O 2 2 E f Wj f W ji xi b j b () j i Where: j =,, N (hidden layer neurons) ; i =,, M (inputs); =,, K (output layer neurons). The weight W ji, onnets the ith input (x i ), and the jth neurons on the hidden layer (layer ). The weight W j, onnets the jth neuron of the hidden layer, and the th neurons of the output layer (layer 2). Supersript indiates layer. Supersript 2 indiates layer 2, Supersript o indiates output layer. The ethanol onentration estimated in the th neuron of the output layer is represented by E. The number of neurons in the hidden layers was determined by seleting the lowest mean square error (mse) when using the ross-validation tehnique, whih is used to avoid model overfitting and to evaluate the performane of neural networ by its ability to predit the elements of a validation dataset whih was not used when training the neural networ. In the present wor a representative data base ontaining 800 input/output patterns orresponding to 400 h of ontinuous flash fermentation at different dilution rates (0., 0.5, 0.20 and 0.35 h - ) was used; 600 input/output patterns (75%) were used for ANN training and the remaining 200 input/output patterns (25%) was used to validate the trained ANN. B. Neural Networ Model Preditive Control (NNMPC) algorithm The rationale underlying MPC is to transform the ontrol problem into an optimization one, so that at any sampling time instant a sequene of future ontrol values is omputed by solving a finite horizon optimal ontrol problem. Then, only the first element of the omputed sequene is effetively used and the overall proedure is repeated at the next sampling time [2] [3]. O

3 , Otober 9-2, 20, San Franiso, USA In the NNMPC algorithm proposed in this wor the onvolution model used in the linear DMC algorithm is substituted by a non-linear internal model based on ANN, whih is trained using data (input/output patterns) generated by the ANN model of the proess. The preditive ontroller estimates a ontrol ation sequene (future inputs) that leads the ontrolled variables (outputs) to follow an optimal path to ahieve a referene trajetory. This optimal path is determined by optimizing the following quadrati objetive funtion [4] [5]. NP 2 NC 2 2 y i ysp u i J (2) i i Where: ysp= set point, = weighting fator (suppression fator), whih prevent large swings in the manipulated inputs, u = value of the future hange in the manipulated variable that minimize the performane index J on the ontrol horizon NC. y = predition made by the neural networ model on a predition horizon NP, orreted aording to (7). Certain restritions on the hanges of the manipulated variable are also onsidered, so the optimal ontrol ation sequene is obtained by solving a onstrained quadrati programming (QP) problem at eah sampling time. The optimization problem is written as a quadrati program: T T min ( U ) ( U ) H ( U ) f U (3) 2 Subjet to: T ( U ) (4) (5) U U min U max Where the matries H and, are related to tuning parameters [6]. U u T i (6) ( = sampling instant; i =,, NC) The vetors η and U are linear funtions of the output predition vetor, y, as well as of the tuning parameters. Although the future ontrol ations are alulated over a ontrol horizon NC ( NC NP), only the first ontrol ation is utilized. The optimization algorithm was implemented in Matlab using the quadprog routine of the optimization toolbox. The algorithm uses a orreted value for the predition y in (2), inorporating a feedba strategy. At instant, the predited value of the output is ompared to the measured value; the differene is used to orret the predited value ŷ in the NP moments ahead. For example, for the moment + i: y ˆ ( ˆ i y i y y ) (7) IV. RESULTS AND DISCUSSION A. Proess Modeling Neural networs of onfigurations 3: N: 2, where N is the number of neurons in the hidden layer (N Є [6,0]), were tested in order to selet the best ANN based model of the proess. The lowest mse and R 2 values obtained when pairing the experimental validation set with the ANN predited values were used as indiators of the best model. A neural networ with topology 3:8:, with 8 neurons in the hidden layer led to the lowest mse and R 2 values, so it was seleted as a model of the proess. Fig. 2 shows the seleted ANN model topology. Fig. 3 shows the high predition performane of the model to values of the validation data set. Inputs Hidden layer Output : b w β, w ω,, 6 w,3 b 4 w 4, 6 w 4 4, 6 ω, w 4,3 w 8, w 8, 6 w 8,3 b 8 8 Fig. 2 ANN model topology 53 R^2=0.9988, mse= time (h) experimental ANN Fig. 3. Output of ANN proess model and experimental values of the validation data set. B. Dynami Behavior Study ω,8 A proedure to determine the effet of input variables, on the output variables is by maing hanges or disturbanes in the values of the inputs one by one and observing the hanges in the outputs. In this wor random disturbanes were made on the seleted inputs one by one by simulating the dynami behavior of the proess. As inputs were utilized: a) purge flow rate, b) permeate flow rate, ) feed flow rate to the fermentor, and d) the

4 , Otober 9-2, 20, San Franiso, USA fermentor dilution; and as output it was used the fermentor ethanol onentration,. The highest assoiations between variables were obtained in two ases: ) between the purge flow rate, Fpu, and the ethanol onentration in the fermentor,, with a orrelation oeffiient, R = 0.99 and a range of variation of the output as a result of the variations in the input, r = 3.48 g/l (r=max(output)-min(output)) and 2) between the feed flow rate to the fermentor, Fo, and the ethanol onentration in the fermentor,, with a orrelation oeffiient, R = -0.9 and a range of variation of the output as a result of the variations in the input, r = g/l. Therefore Fpu and Fo ould be appropriate variables to be onsidered as manipulated variables in order to ontrol. Fig. 4 show graphially the behavior of the inputs: purge flow rate, Fpu, and feed flow rate to the fermentor, Fo; and the output ethanol onentration in the fermentor,, with normalized values in the range [0., 0.9]. a) normalized values b) normalized values time (h) purge flow rate, Fpu time (h) feed flow rate, Fo Fig. 4. Normalized values of inputs and outputs: a) Purge flow rate, Fpu, and ethanol onentration,. b) Feed flow rate to the fermentor, Fo, and Fermentor ethanol onentration,. From the results two NNMPC ontroller strutures were proposed: ontrol struture with the purge flow rate, Fpu, as manipulated variable, and ontrol struture 2 with the feed flow rate to the fermentor, Fo, as manipulated variable. The ontrolled variable is the ethanol onentration in the fermentor,. C. Internal Model Training The DMC algorithm uses an internal model (onvolution model) to generate preditions of future ontrol ations. In this wor the internal model is a neural networ with two inputs: the ontrolled and manipulated variables at the present sampling instant, t, and one output: the ontrolled variable one step ahead, (t +). The training data (input/output patterns) were obtained by maing 24 suessive random disturbanes on the inputs of the proess model and determine the respetive output. The interval between disturbanes was hosen to ensure that the system reahes new steady states, as suggested by Santos and Biegler [7]. The internal model based on ANN has a 2:4: topology with 4 neurons in the hidden layer. The model performane in desribing the training data was determined using the following equation, whih was suggested by Milton and Arnold [8]: SEE orr (8) ( )00% S N 2 WhereSEE ( ye( ) y( )), N S ( ye( ) ye) 2, y e () is an experimental output, y() is the orresponding output of the neural model, y e is the average of experimental outputs and N is the number of experimental data. The two internal models desribe the training data with orrelations (orr) of: 99.05%, and 99.2%; respetively. Another test suggested by various authors [5] [7] [9] and that was done with satisfatory results was to determine eah model's ability to predit steady states of the proess. The pratial experiene from the present wor has shown that additionally two more harateristis are important when testing the performane of the ANN internal model: ) an aurate open loop response, and 2) a wide operation range. D. Controller Performane The preditive ontrollers with nonlinear internal model based on neural networs were subjeted to various tests, onsidering a sampling time of 0 minutes. The parameter values were determined by trial and error; and omparing the ontroller performane in different ases: ) Control struture (manipulated variable: purge flow rate): predition horizon, NP =0, ontrol horizon, NC=3, λ = ) Control struture 2 (manipulated variable: feed flow rate to the fermentor): predition horizon, NP =0, ontrol horizon, NC=, λ = Regulator Performane In this test, hanges were made in different inputs variables: Fo, Fpu, Fp, and D; to simulate load disturbanes and to observe the regulatory behavior of the ontrollers [20] in eah ase disturbane variables were different from the manipulated variables. Two ases are mentioned to desribe different harateristis on the response. Fig. 5 shows the responses of the ontrol struture for disturbanes of 5 % in the value of the feed flow rate, Fo. Fig. 6 shows the responses of the ontrol struture 2 for disturbanes of 20 % in the value of the purge flow rate, Fpu.

5 , Otober 9-2, 20, San Franiso, USA %Fo NC=3 +5%Fo NC=3-5%Fo NC= +5%Fo NC= Fig. 5. Control struture : Response of the ontrolled variable,, with time to perturbations of 5 % in the feed flow rate to the fermentor, Fo. Manipulated variable: purge flow rate, Fpu %Fpu NC=2-20%Fpu NC=2 +20%Fpu NC= -20%Fpu NC= Fig. 6. Control struture 2: Response of the ontrolled variable,, with time to perturbations of 20 % in the purge flow rate, Fpu. Manipulated variable: feed flow rate to the fermentor, Fo. Figs. 5 and 6 show that both NNMPC strutures rejet the disturbane and bring the system ba to the steady state; therefore they have good regulatory performane. Three riteria were useful to desribe the regulatory performane of the ontrollers: ) the maximum deviation of the response from the referene trajetory, 2) the settling time, and 3) the IAE riterion (integral of the absolute value of the error), whih provides ontroller settings that are between the most onservative settings, given by the ITAE riterion (integral of the time-weighted absolute error) and the most aggressive settings, given by the ISE riterion (integral of the squared error) [9]. Fig. 5 show that NC=3, is the best seletion for ontrol struture, and Fig. 6 show that NC=, is the best seletion for ontrol struture 2. The deviation (d) from the referene trajetory is higher for ontrol struture (d=5.66) than for ontrol struture 2 (d = 0.90). The settling time, defined as the time to reah 5% of the maximum deviation, is 50 min for ontrol struture (NC=3) and 30 min for ontrol struture 2 (NC=). Control struture leads to a higher IAE value (IAE=04.98) than ontrol struture 2 (IAE=3.55). From the tests that were realized we an state that a arefully determination of the: dynami matrix elements, suppression fator λ, ontrol horizon NC, and predition horizon NP, is important to inrease the performane of the NNMPC ontrollers. Although ontrol struture 2 appears to have the best regulatory performane, it is neessary to do more tests using different disturbanes of similar magnitude in order to have a better onlusion. In the present ase there are strong interations between input variables, e.g. feed flow rate to the fermentor, Fo, and permeate flow rate, Fp; Fermentor dilution, D, and Fo; that give diffiulty in stating a definitive onlusion. Servo Performane In this ase suessive hanges were made in the value of the. Figs. 7 and 8 show the behavior of the preditive ontrollers with neural internal model to various hanges in the referene trajetory (). It is noted that both ontrol strutures performed well, bringing the system ba to the steady state after eah hange in the (represented in this ase by ethanol onentration in the fermentor, ). a) (g(l) b) purge flow rate (ml/h) ontrolled variable manipulated variable Fig. 7. Servo performane of the ontrol struture : a) Controlled variable and hanges b) Manipulated variable behavior (ontrol ations).

6 , Otober 9-2, 20, San Franiso, USA a) 7 b) Feed flow rate (ml/h) ontrolled variable manipulated variable Fig. 8. Servo behavior of ontrol struture 2: a) Controlled variable and hanges in the. b) Manipulated variable (ontrol ations). V. CONCLUSION In this paper a non-linear neural networs model preditive ontroller (NNMPC) was designed using the DMC algorithm. It was shown that the non-linear models based on ANN an aurately identify the experimental behavior of the studied proess and have a good performane as the internal model in preditive ontroller. The use of an ANN model to simulate the dynami behavior of the proess allowed the design of the proposed ontrol system even when an aurate phenomenologial model was not available. The preditive performanes of the ontrollers were tested with load disturbanes and disturbanes with good results, whih demonstrate the high potential of the proedures that have been used in this study for ontrol system design in integrated reation-separation proesses. Thermodynami Analysis, Appl. Biohem. Biotehnol., vol. 48, no.-3, pp.4-49, Jan [6] A. Ashoori, B. Moshiri, A. Khai-Sedigh, M. Reza, Optimal ontrol of a nonlinear fed-bath fermentation proess using model preditive approah, J. Pro. Cont., vol. 9, pp , Mar [7] D. Dougherty, D. A. Cooper, A pratial multiple model adaptive strategy for single-loop MPC, Control Eng. Pratie, vol., pp. 4 59, [8] S. J. Qin and T.A. Badgwell, A survey of industrial model preditive ontrol tehnology, Control Eng. Pratie, vol., no. 7, pp , [9] D.E. Seborg, T.F. Edgar and D.A. Mellihamp, Proess Dynamis and Control, Seond Edition, Hoboen, NJ: John Wiley & Sons, In., [0] C.L. Nasimento and T. Yoneyama, Artifiial Intelligene in Control and Automation, Sao Paulo, Brazil: Bluher- FAPESP [] E.C. Rivera, D. I. P. Atala, F. Maugeri, A. C. Costa, R. Maiel Filho, Development of real-time state estimators for reation-separation proesses: A ontinuous flash fermentation as a study ase, Chem. Eng. Pro.: Proess intensifiation, vol. 49, pp , Mar [2] R. Sattolini. Arhitetures for distributed and hierarhial Model Preditive Control A review, J. Pro. Cont., vol. 9, pp , Feb [3] Y. Zheng, S. Li, X. Wang. Distributed model preditive ontrol for plant-wide hot-rolled strip laminar ooling proess, J. Pro. Cont., vol. 9, pp , Apr [4] W. Luyben. Proess modeling, simulation and ontrol for hemial engineers, Seond Edition, New Yor, NY: MGraw-Hill, 990. [5] A.C. Costa, R. Maiel Filho. Non linear Preditive Control of a Three-Phase Catalyti Reator, Can. J. Chem. Eng., vol. 8, pp. 09-8, Ot [6] B.A. Ogunnaie and W.H. Ray. Proess dynamis, modeling, and ontrol, New Yor, NY: Oxford University Press, 994. [7] L.O. Santos, L.T. Biegler. A tool to analyze robust stability for model preditive ontrollers, J. Pro. Cont., vol. 9, pp , 999. [8] J.S. Milton, J.C. Arnold. Introdution to Probability and Statistis, New Yor, NY: MGraw Hill, 990. [9] A.C. Costa, L.A.C. Meleiro, R. Maiel Filho. Non-linear preditive ontrol of an extrative aloholi fermentation proess, Proess Biohem., vol. 38, no. 5, pp , De [20] A.R. Soeterboe, Preditive Control a unified approah, PhD dissertation, Tehnihe Universiteit Delft, Rotterdam, Holand, 990. REFERENCES [] E. Smeets, M. Junginger, A. Faaij, A. Walter, and P. Dolzan. (2006, August). Sustainability of Brazilian Bio-ethanol. Utreht University. Available: /NWS-E pdf [2] C.A. Cardona and O.J. Sánhez, Fuel ethanol prodution: Proess design trends and integration opportunities, Bioresour. Tehnol., vol. 98, no. 2, pp , Mar [3] A. C. Costa, D. I. P. Atala, F. Maugeri, R. Maiel Filho, Fatorial design and simulation for the optimization and determination of ontrol strutures for an extrative aloholi fermentation, Proess. Biohem., vol. 37, no. 2, pp.25-37, Mar [4] D.I.P. Atala, Assembly, instrumentation, ontrol and experimental development of an extrative fermentative proess of ethanol prodution, PhD dissertation, UNICAMP, SP, Brazil [5] V.H. Álvarez, E. Copa Rivera, A. C. Costa, R. Maiel Filho, M.R. Wolf Maiel, M. Aznar, Bioethanol Prodution Optimization: A