Design and Simulation of a Fuzzy Substrate Feeding Controller for an Industrial Scale Fed-Batch Baker Yeast Fermentor Cihan Karakuzu1, Sõtkõ Öztürk1, Mustafa Türker2 1
Department of Electronics & Telecommunications Engineering, Faculty of Engineering, University of Kocaeli, Kocaeli, İzmit, Turkey {cihankk, sozturk}@kou.edu.tr 2 Pakmaya, PO. Box 149, 41001, Kocaeli, İzmit, Turkey
[email protected] Abstract. Conventional control systems can not give satisfactory results in fermentation systems due to process non-linearity and long delay time,. This paper presents design and simulation a fuzzy controller for industrial fed-batch baker’s yeast fermentation system in order to maximize the cell-mass production and to minimize ethanol formation. Designed fuzzy controller determines an optimal substrate feeding strategy for an industrial scale fedbatch fermentor relating to status of estimated specific growth rate, elapsed time and ethanol concentration. The proposed controller uses an error in specific growth rate (e), fermentation time (t) and concentration of ethanol (Ce) as controller inputs and produces molasses feeding rate (F) as control output. The controller has been tested on a simulated fed-batch industrial scaled fermenter and resulted in higher productivity than the conventional controller.
1
Introduction
Many different products have been produced by culturing yeast. Baker yeast is the one of these products. Saccharomyses cerevisia known as baker yeast is produced using molasses as substrate by means of growing up microorganism. In controlled environment, the main energy source for growing the culture is sucrose in molasses. Energy production, maintenance and growth reaction of the yeast cells can be expressed by following macroscopic chemical reaction. CH 2O + Y NH 3 + Y O → Y CH1.83O0.56 N0.17 + n/ s o/ s 2 x/ s
(1)
H O Y CH 3O0.5 + Y CO2 + Y e/ s c/ s w/ s 2
CH2O, CH1.83O0.56N0.17 and CH3O0.5 are respectively sucrose, biomass and ethanol in C-mol unit in Eq. (1). Yi/j s are stoichiometric yield coefficients. Ethanol, which is not desired, is a by product in the process. Ethanol formation takes places either by overfeeding sucrose or oxygen limitation in process. Total receiving sucrose into the fermentor should be oxidised completely by yeast cells for maximum yield productivity during fermentation. This is possible by supplying reasonable molasses feed rate to the system. The main objective is maximum biomass production without ethanol during fermentation. Hence, amount of ethanol in the fermentor should be T. Bilgiç et al. (Eds.): IFSA 2003, LNAI 2715, pp. 458-465, 2003. Springer-Verlag Berlin Heidelberg 2003
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under control by controlling feeding rate. Fed-batch process is generally employed by the baker’s yeast industry. Fed-batch baker yeast production process is shown in Fig. 1. Essential nutrients and molasses are fed incremental to the fermentor at an predetermined rate during the growth period [1]. Because a predetermined and fixed feeding profile has been used in industry, manual manipulations are needed in some unexpected status. It is therefore desirable, to incorporate a intelligent controller into the feeding systems if possible. In this paper, a fuzzy controller is proposed to determine molasses feeding rate for keeping desired set point of specific growth rate of yeast cells. Designed fuzzy controller is tested on simulation model of the process.
Fig. 1. Block structure of baker yeast production process
2
Process Model
Process modelling for control is one of essential areas of research and industrial applications in biotechnology. Processes based on microorganisms are the most complex in all field of process engineering, and their modelling is considered a difficult task [2]. As Shimizu [3] pointed out, the control system development for fermentation is not easy due to: lack of accurate models describing cell growth and product formation, the nonlinear nature of the bioprocess, the slow process response and a deficiency of reliable on-line sensors for the quantification of key state variables. Model will be given in this section, is include cell (kinetic) and reactor (dynamic) models. 2.1 Yeast Cell (Kinetic) Model Microorganism is not still modelled exactly because of relating to many parameters, but modelling studies have gone on. Yeast cell model, which will be given, was based
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Cihan Karakuzu, Sõtkõ Öztürk, and Mustafa Türker
on simple mechanistic model of Sonnleither and Kappeli [4]. The model equations are shown in Table 1. Eq.(2) and Eq.(3) are different from the original model (1-e-t/td) and Ki/(Ki+Ce) terms in Eq. (2) and Eq. (3) were added the original model. Pham et al. [5] observed that glucose uptake was under the maximum value (qs,max) during first an hour after inoculum and shown necessity adding a delay time term to the equation. The other uptake term added to the model, Ki/(Ki+Ce), supports compatibility of model data and real data measured industrial fermentor, especially point of view changing specific oxygen consumption (qo) and ethanol concentration (Ce). we have observed that the updated model gave closer the real result than the original, in our simulation studies based on data measured from real industrial process. Especially, accuracy of the updated model simulation result have been seen on ethanol production/consumption and specific oxygen consumption kinetic variables (see Fig. 2 ). Table 1. Kinetic model of baker yeast cell
q s = q s ,max
Cs ( 1 − e −t / td ) K s + Cs Co Ki
qo ,lim = qo ,max
q s ,lim =
µ cr
K o + Co K i + Ce
qs q s ,ox = min q o / Yo / s q s ,red = q s − q s ,ox
(5) (6)
Ce Ki K e + Ce K i + C s
qe ,up qe ,ox = min ox q o ,lim − Yo / s Yo / e qe , pr = Ye / s q s ,red
(
(3) (4)
Yxox/ s
qe ,up = qe ,max
(2)
)
(7) (8) (9)
ox µ = Yxox/s .q s ,ox + Yxred / s .q s ,red + Yx / e .q e ,ox
(10)
ox qc = Ycox/s .q s ,ox + Ycred / s .q s ,red + Yc / e .q e ,ox
(11)
qo = Yoox/ s .q s ,ox + Yoox/ e .qe ,ox
(12)
q RQ = c qo
(13)
2.2 Reactor (Dynamic) Model This model describes concentrations of the main compound which are dynamically directed by manipulation of input variables and initial conditions. For the simplicity,
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mixing of both of liquid and gas phases were perfect, is assumed. Hence, model includes basic differential equations. Because main objectives of this paper is reaction taking place in liquid phase, only liquid phase reactor model is given in Table 2 in Eq. 14-18. Table 2. Reactor model of fed-batch baker yeast fermentation F dCx = µ .Cx − Cx V dt q e , pr µ F dCs = − + + q m Cx + ( So − Cs ) ox V dt Y x / s Ye / s
(14) (15)
F dCe = ( qe , pr − q e ,ox ).Cx − Ce V dt F dCo = − q o Cx − Co + k OL a ( Co* − Co ) V dt dV =F dt
(16) (17) (18)
Yeast cell and reactor models were constituted by means of a Matlab 6.0 Simulink software to use in all simulation. All of model parameters are taken from [1] and [4], ox except Ki=2.514 gr/L, Yx/s =0.585 gr/gr, td=2 h, So=325gr/L and kOLa=500 h-1. Comparison of the process model simulation results and data measured from industrial scale (100m3) fermentor are shown in Fig. 2. Process model simulation results are satisfactory based on measures in real production media as shown in Fig. 2.
(a)
(b)
Fig. 2. (a) Comparison of data from industrial scale fermentor (symbols) and simulation results (lines) by the process model for key state variables (Cx yeast concentration, Ce ethanol concentration, Cs glucose concentration, Co dissolved oxygen concentration). (b) Comparison of data from industrial scale fermentor simulation model verification for specific oxygen consumption rate, qo, (o) and respiratory quotient, RQ, (/) with simulation results (dotted line qo, line RQ).
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3 Fuzzy Controller Design for an Industrial Scale Fermentor In this paper, process control structure is proposed based on fuzzy logic. The proposed block diagram of closed loop control based on simulation model is shown as in Fig. 3. The controller determines molasses feeding rate for keeping desired set point of specific growth rate (µset) thus minimising ethanol formation to reach maximum biomass yield at the end of fermentation.
Fuzzy Control Unit
Yeast kinetic model
Other kinetic i bl
Reactor (Dynamic) Model
State variables
Fig. 3. Block diagram of proposed closed loop control for fed-batch baker’s yeast process
The first step is to determine input/output variable in controller design. The error between specific growth rate (µ) and set point (µset) was chosen as main input variable of the fuzzy controller. The other input variables of the controller are elapsed time (t) and ethanol concentration (Ce). The output variable of the controller was chosen as molasses feed rate (F). Membership functions of the inputs and the output are shown in Fig. 4(a). All of membership functions of the inputs and the output except in last of right and left sides are respectively generalised bell and gauss functions. In the last of right sides membership functions are S-shaped curve membership functions. In the last of left sides membership functions are Z-shaped curve membership functions. Fuzzy control unit in Fig. 3 employs the Mamdani fuzzy inference system using min and max for T-norm and T-conorm operators, respectively. Centroid of area defuzzification schema was used for obtaining a crisp output. The controller rule base tables are shown in Fig. 4(b). From the point of view control engineering, to choose variables, which are measured on-line in the process, are reasonable. Therefore, the designed control structure can be applied in real production media. Elapsed time (t) and ethanol concentration (Ce) are on-line measured in industrial production process. The other controller input variable (µ), is not on-line measured, but can be estimated from online measurable variables. Our studies [6,7] about µ and biomass estimation based on data given in real production media by neural network have shown that this problem could be solved. That is, on-line µ estimation is possible by using soft-sensor such as
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neural networks. Also, F can be measured on-line in process, hence, applying the proposed control structure in this paper to the industrial production process will be possible.
(a)
(b)
Fig. 4. (a) Membership functions of inputs and output variables (b) Fuzzy controller rule base table
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4 Simulation Results and Conclusions After yeast cell (kinetic) model, reactor (dynamic) model and designed fuzzy controller were integrated as shown in Fig. 3; simulation model was run by means of Matlab 6.0 Simulink software. Changes of control input determined by fuzzy controller and µ controlled variable during fermentation are given in Fig 5a. Sugar, ethanol and dissolved oxygen concentrations are shown in Fig. 5b.
Fig. 5. (a) Changing of specific growth rate, µ, and molasses feeding rate, F, (b) Changing of concentrations during overall fermentation
To observe the fuzzy controller’s adaptive behaviour, dummy distortions were added on Ce and Cs respectively at 3rd h during 15 min with 2 g/L amplitude and at 6rd h during 15 min with 0.36 g/L amplitude as shown in Fig. 5(a), response of the controller was observed as shown in Fig. 5(b). Fuzzy controller has done needed manipulation on molasses feeding. As a result; this paper presents an adaptive and robust control structure, which can applied to fed-batch baker yeast industrial production process. The proposed fuzzy controller has resulted in higher productivity than the conventional controller. Conventional controller follows a predetermined and fixed feeding profile. Hence, it doesn’t behave adaptively under undesired key state conditions during fermentation. But, controller designed in this paper determines feeding rate by itself as well as behaves adaptively under undesired media conditions. Moreover, feeding curve determined by the controller does not include sharp changing when comparing with the ones presented in [8,9,10]. Sharp changing in feeding rate may cause some problem in industrial production. In this meaner, the controller structure presented by this paper is robust and satisfactory.
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Fig. 6. Controller’s adaptive response under dummy distortions on Ce and Cs
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