Advanced Control Strategies for a Bioreactor Based on an Alternative Structured Kinetic Model

Transcription

1 Advanced Control Strategies or a Bioreactor Based on an Alternative Structured Kinetic Model Dile Pontarolo Stremel 1, Eduardo Coselli Vasco de Toledo 2* and Rubens Maciel Filho 2 1 ENGEPRO Universidade do Sul de Santa Catarina 2 Faculdade de Engenharia Química. Universidade Estadual de Campinas (UNICAMP) CP CEP Campinas, SP - Brazil. Abstract This work presents an alternative dynamic structured model, adapted rom a structured growth model to simulate and to control a high productivity tower bioreactor. Sacharomyces cerevisae growth model was adapted or ethanol production. Reduction techniques were applied in the spheric particle direction (pectin gel) and the reduced model was used in an open loop simulation under disturbances in the inlet variables to deine the control set-point and manipulated variable. Because o the slow dynamic, it was necessary to establish, through experimental planning, a relationship among the manipulated variable, eed substrate concentration and the control objective (eedorward model). The controller design involved in a SISO orm, the classic (PID), predictive (DMC) and predictive adaptive (STDMC) control algorithms that were evaluated isolatedly and coupled to the eedorward model obtained by statistical procedures. Reduction techniques were used to obtain an useul structured model or applications in simulation and control algorithms. Control procedures showed that an early action related to the manipulated variable and the set-point coupled to control eedback algorithms is the best orm to quickly stabilize the process. Keywords: Advanced Control, Tubular Bioreactor, Dynamic Model, Reduced Model 1. Introduction Although unstructured models can be advantageously applied to the description o the behaviour system, important inormation is lost in such simpliied approach and many applications in which these models are based tend to ail (Harder and Roels, 1982, p 55). Structured models are applied, particularly, to transient situations such as: batches, ed batch or continuous culture or when the biomass composition changes drastically, like in some stages o the process and early stages o batch growth (lag phenomena), and in situations where a speciic constituent (e.g protein, RNA, Enzymes) must be modelled. Despite the complexity o kinetic structured models, a very simple one was tested. In this paper, the Rotboll and Jorgensen s model (Rotboll and Jorgensen, 1993) used to predict the main biotic and abiotic compounds or batch and continuous culture, was adapted or Cybernetic and reduction techniques application purposes. Firstly, the model was modiied or a continuous type tower bioreactor by itting the parameters * Author to whom correspondence should be adressed : urso@lopca.eq.unicamp.br

2 related to the glycolysis and respiratory pathways with experimental data to represent the ethanol accumulation, growth and cell death rate, substrate uptaking and inhibition, Stremel (2001). Such a model has both structured biomass and structured metabolism, with oxidative and oxidoreductive mechanisms. Open-loop simulations have shown that the dynamic is very slow and or this reason it requires an anticipated action rom the controller to provide aster answers. Dierent algorithms and control strategies were tested. A eedorward action was developed or the manipulated variable through statistical procedure. A central composite experimental design was applied or two actors, substrate and eed low rate. A relationship was then obtained between ethanol as the dependent, and the two others (substrate and eed low rate) as independent variables. Advanced control algorithms, like predictive controller (DMC) and adaptive predictive controller (STDMC) presented better perormance when coupled to the statistical model, compared to conventional DMC e STDMC. 2. Methodology 2.1 Particle Model: Abiotic Phase The substances considered or the abiotic phase are those that diuse through cell and particle (pellet) boundaries. In the eq. (1), the brackets depend on the substance, [A] is acetaldehyde, [P], Piruvate; [E], Ethanol and [S] is substrate. The generic equation or the substances are given by equation (1). [] D[ ] 1 [] t 2 = r +ν 2 2 [ ] RP r r r (1) Several reduction techniques were tested. Compared to the experimental data, (Stremel et al 1999), it was noted that both reduced and not reduced orm presented similar perormances. In this paper, a classic reduction was applied in the Eqn. (1) to obtain a lumped model, Eqn. (2). Modiications occur in the Bi M * term, Vasco de Toledo (1999) and Stremel ( 2001). [ ] D[ ] d = R 2 p 3Bi M * [ ]{ [ ] λ [ ]} +ν [ ] The boundary conditions are symmetry at the center and resistance to mass transer at the surace. 2.2 Reduction Techniques The advantage to use reduction techniques is that the particle model has its complexity substantially reduced i.e it is possible to reconstruct the solution in the radial dimension, generating a lumped model. The classic lumped technique consists on the application o the average theorem, generating an average variable across a determined spatial direction. For the Biochemical Bioreactor the mean is determined in the pellet radial direction (spherical geometry), Eqn (3). (2) [] = r []dr m 0 (3)

3 [ ]m deines the radial mean value o the quantity enclosed in the brackets. For the classic reduction technique, the mass-modiied Biot number (Bi * M[ ]), has the same expression than the mass unmodiied Biot number, (Bi M[ ] ), Eqn.(4). Here, D [ ] is the particle diusion coeicient or each substance. k TM is the mass transer coeicient, and R P the internal particle radius. For the classic reduction, λ = 1. * BiM [ ] = BiM [ ] = R pktm / D[ ] (4) 2.3 Particle Model: Biotic Phase The biomass compartments are divided into two parts: a synthetic compartment and a structural compartment. The synthetic compartment, (g/gdw) is the active part o the cell, inluences metabolic intermediates (abiotic phase), respiratory Xr (g/gdw) and glycolytic X (g/gdw) enzyme ormation. The structural/genetic compartment, Xp (g/gdw) is the passive part o the cell. The last terms o the Eqn (5), (6), (7) and (8) accounts or the dilution o the abiotic state by the increase in the total biomass Xt (gdw/l), observing that gdw is the cell dry weight in grams. The biotic compounds do not diuse out rom the pellet, but they make part o the inner structure o the cell and they relect the inside cell mechanism. The Eqn. (5) until Eqn. (9) plus Eqn. (2) express the lumped structured kinetic model. Eqn (10) was modiied to consider inhibition by the ethanol accumulation and cell death rate. d = r - r - r - r - ( r ) (5) Xp Xr X dxp rxp ( r Xp) = (6) dxr = r ( r Xr ) (7) Xr dx dxt ( r X ) = r (8) X Xt Xt 1 X = r SAT KE [ E] e ( kd Xt) (9) 2.4 Eectiveness Factor The reduced eectiveness actor is given by the Eqn. (10) η D[ ] * [ ] = 3 Bi 2 M [ ] Rp [ ] [ ] ν [ ] (10)

4 2.5 Fluid Phase Dynamic Model The luid phase model is based on a plug-low bioreactor taking in account dispersion, convective motion, and the mass transer resistance evaluated in terms o the eectiveness actor. The brackets, [ ] and [ ] in Eqn. (10) are concentration o the substrate, ethanol, pyruvate and acetaldehyde compounds in the luid and particle, respectively. Pyruvate and Acetaldehyde are intermediate compounds o the metabolic pathway diuse rom the solid phase in low concentrations and make part o the structured metabolism. The ν [ ] term is the mean-structured kinetic reaction, which includes the stoichiometry o the metabolic network [] D 2[] [] = t ax u z 2 L 2 L z 1 ε + η ε ν [] [] For the luid phase, the boundary conditions are given by Danckwerts conditions (Froment and Bisho, 1990). A correlation or the axial dispersion coeicient was adjusted with experimental data, Stremel (2001). 2.6 General Consideration or the Bioreactor Control Design Control o physiological state o cells is oten desired to stimulate their activity in a avorable direction. These control variables to be controlled are diicult to measure; thereore, a mathematical model must be used in some way to estimate the state o the process. Diiculty in eedback control is twoold. Firstly, diiculties appear or the process to reach a new steady state. Under open-loop low rate disturbance, the time response o the process is slow. The control problems can arise because o severe nonlinear behavior, which can lead to a long time process adaptation. Although sensors and eedback controllers have ast response, the nature o the process is slow. Secondly, a continuous process with immobilized cells present problems o stability. When experimental procedure is conducted without a control or long time operation, ethanol concentration accumulates, and above certain limit (higher than 80g/L) it leads to the collapse o the process. Ater a period o operation, the recovery o the production is not possible and the process has to be re established with a new cell culture. These perplexities dictate the need or continuous monitoring and readjusting the control strategy, to be able to establish the process promptly. To improve the quality o control during the transient response a eedorward model was obtained through a central composite experimental planning, Stremel (2001). The statistical analysis was used to obtain the empirical equation that describes the ethanol production as unction o substrate concentration and eed low rate (eedorward model), given by equation (12). Through open-loop simulations under disturbances, it was veriied that the bioreactor exit was important to measure the ethanol concentration at the bioreactor exit. Because the limitation on the manipulated variables, only a SISO coniguration was possible to ensure the stability o the operation with high productivity, in this case, through manipulation o the eed low rate. (11)

5 3. Results and Discussion Figure 1 shows the proposed strategy or Feedback-Feedorward model coniguration. The parameters were adjusted empirically ater calculations under closed-loop simulations with set-point perturbation. The Feedback with a Feedorward model acts on the manipulated variable depending on the value o the parameter α 1, shown in Figure 1. The Feedorward model obtained or the manipulated low rate, u FF, is given by the Eqn (12), and such equation is used to built-up the Feedback-Feedorward controllers, statistical DMC e statistical STDMC. The variables S 0 and E,sp are eed substrate concentration and desired ethanol concentration (set-point) at the bioreactor outlet, respectively. E,sp - + S o u FF CONTROLLER PROCESS Ethanol + u FB - Figure 1- Feedback-Feedorward coniguration E,sp u FF -5 [ (6.25x10 S )] 0 = (12) where = S S (13) 1 u α u and ( ) FF 1 FB 0 0 E,sp u = 1 α + (14) Ethanol(g/L) STATISTICAL STDMC STDMC Set-Point Ethanol(g/L) DMC STATISTICAL DMC Set-Point Time(h) Figure 2 - Comparasion o Perormance o STDMC with Feedorward Statistical Time(h) Figure 3 - Comparasion o Perormance o DMC with Feedorward Statistical

6 coupled. coupled. Figures 2 and 3 depict the statistical DMC and statistical STDMC compared to the conventional predictive DMC and STDMC controller. It can be seen that the perormance o the proposed controllers are superior. In act with the proposed controller there is overshoot. Figure 4 presents the same proposed controller concept or the PID implementation, and the same conclusions may be obtained as or the implementation o DMC and STDMC controllers. The manipulated variable proiles or all the considered controllers are given in Figure 5. It is noted that the best perormance is or the statistical DMC and statistical STDMC (both curves are coincident). Ethanol(g/L) STATISTICAL PID PID Set-Point Manipulated Variable (L/h) 0,07 DMC STDMC 0,06 PID STATISTICAL-PID STATISTICAL-DMC(STDMC) 0,05 0,04 0,03 0,02 0, Time(h) 0, Tempo(h) Figure 4 - Comparasion o perormance o PID with Feedorward Statistical coupled. Figure 5 Comparision o manipulated variable Proiles or the controllers 5. Concluding remarks The study o control showed that an early action relating the manipulated variable and the set-point (eedorward) coupled to algorithms o eedback control (statistical DMC and statistical STDMC) is the best orm or stabilizing the process. It has to be pointed that with the proposed controller no overshoot was observed even or a rapid response. Reerences Harder, A. and J. A Roels, 1982, Advanced Biochemical Engineering, 22, 56: Application o Simple Structured Models in Bioengineering. Rotboll, M. and S. B. Jorgensen, 1993, European Conerence on Biotechnology. TU 048: Validation o a metabolic and Biomass Structured Model or Yeast Fermentation, Florence-Italy Stremel, D. P., Toledo, E. C. V. and R. M. Filho, 1999, The Fourth Italian Conerence on Chemical and Process Engineering, IcheaP-4, 91: Analysis o Dierent Reduction Techniques in Kinetic Dynamic Models or Biochemical and Catalytic Chemical Processes on Fixed Bed Reactors, Florence, Italy. Stremel, D.P., 2001, Development o Alternative Structured Models or Ethanol Process Production. PhD Thesis, State University o Campinas (Unicamp). Vasco de Toledo, E. C., 1999, Modelling, Simulation and Control o Fixed Bed Reactors. PhD Thesis, State University o Campinas (Unicamp).