Biochemical Reactor

Process Biochemistry 37 (2001) 461– 469 www.elsevier.com/locate/procbio

Design of a fuzzy system for the control of a biochemical reactor in fed-batch culture Ruy Sousa Jr, Paulo I.F. Almeida * Departamento de Engenharia Quı´mica, Uni6ersidade Federal de Sa˜o Carlos, P.O. Box 676, 13565 -905, Sa˜o Carlos, SP, Brazil Received 14 December 2000; received in revised form 18 April 2001; accepted 8 June 2001

Abstract The present work seeks a set of reasoning rules that permit the automatic selection of the start point for inverted sucrose feeding in the Cephalosporin C batch production process, using fuzzy methodology. By monitoring the percentage of CO2 in the outflow gases, it is possible to observe a point of maximum evolution when the microorganism growth phase finishes. Therefore, the moment when the feeding should begin is characterized by a transition from increasing (positive variations) to decreasing (negative variations) CO2 evolution rates. A fuzzy controller was then conceptualized to operate on three reasoning levels: attention, action and a protection level to prevent errors produced by the exchange of the drying column used before the analyzer for CO2 measurement. The algorithm was implemented in C. Two experiments were accomplished to establish, adjust and validate the fuzzy system. The results obtained indicated that the algorithm is robust for the tested conditions, allowing a safe automatic operation. © 2001 Elsevier Science Ltd. All rights reserved. Keywords: Fed-batch culture; Antibiotic; Cephalosporin C; Fuzzy logic; Supervisory control; Inverted sucrose feeding

1. Nomenclature

CPC A Ai A(x) B Bi B(y) k R VC1 x y X

cephalosporin C input linguistic value input linguistic value in the ith rule membership function for A output linguistic value output linguistic value in the ith rule membership function for B kth reading performed by the acquisition system fuzzy relationship generated from all the fuzzy rules degree of tolerance to uncertainties input value output value scope interval of the input linguistic variable

* Corresponding author. Fax: + 55-16-260-8266. E-mail address: [email protected] (P.I.F. Almeida).

Y Greek letters D

scope interval of the output linguistic variable increment

2. Introduction Cephalosporin C (CPC) is a b-lactam antibiotic produced industrially through a bioprocess making use of a strictly aerobic fungus, Cephalosporium acremonium. Its importance is derived from the fact that CPC is the raw material for obtaining antibiotics widely used in the treatment of bacterial disease [1]. The CPC production process in fed-batch culture, carried out for approximately 170 h, is divided into two stages defined as trophophase and idiophase, where distinct metabolic activities are identified. In the first stage, lasting from 35 to 70 h, rapid growth of the microorganism is observed propitiated by the consumption of the glucose that is fed at the start of the process. The CPC produc-

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tion rates are low because of the catabolite repression of the synthesis of a specific enzymic complex, the b-lactam synthetase [2,3]. Once the glucose is consumed, the idiophase begins. During this stage, continuous inverted sucrose feeding is done, CPC accumulates in the fermentation medium and a low increment of cellular concentration is observed. The present work seeks to implement a system that can automatically select the moment when the feeding of inverted sucrose should start. Fuzzy methodology was used for this task. The quantities of sugars, cell mass and CPC correspond to variables not monitored continually, but quantified through the analysis of samples taken periodically from the bioreactor. For this reason, it would be difficult to use these directly to reach the above-mentioned objective. However, there is another variable, monitored continually, which can be used: the percentage of carbonic gas in the outflow gases. Takagi et al. [4] investigated a strategy for controlling sugar feeding by monitoring the CO2 production rate in a culture for Cephalosporin C production. It proved effective in tracking the cell growth profile. Silva et al. [5] used a methodology based on the microorganism growth phase to determine the proper time of sucrose addition to the Cephalosporin C production bioprocess where high levels of CO2 are produced reaching its maximum when glucose depletion occurs. Fig. 1 shows this variable for one experiment [5], where the end of the trophophase was characterized by a maximum CO2 percentage at 35 h of cultivation. In two studies reported in the literature, Kwong et al. [6,7] suggest the use of the filtered derivative of an on-line signal for driving fed-batch fermentations and the development of feeding strategies. In that approach,

before a low-pass filtering was used, the quality and quantity of the interferences were estimated using Fast Fourier Transformations and spectral analysis. In a different route, the present work plans to design a fuzzy system and implement it in C, trying to detect the point of maximum CO2 percentage associated with the starting point for inverted sucrose feeding just imitating the observations and decisions usually taken by a skilled process operator. Two experiments monitored in realtime were carried out. The data collected during the first run, in addition to those previously obtained by the research group at the Department of Chemical Engineering of Federal University of Sa˜ o Carlos (DEQUFSCar), allowed the definition of the membership functions and the rule base of the controller. The second experiment was accomplished to test the feasibility and robustness of the algorithm. 3. Fuzzy methodology In two-valued logic, a specific element is in (1) or out (0) of a set. In the fuzzy sets theory established by Zadeh [8,9], the element is allowed a degree of membership in relation to the set, which will be a numeric value between zero and one (membership limit values). When all the elements of a set are considered, it is defined a membership function, through which it is possible to obtain the degree of membership of each element. Another concept of fundamental importance regarding fuzzy sets is that of linguistic variable. The fuzzy logic variables described correspond, in a first analysis, to qualitative expressions such as slow, fast, high, low, etc., which in turn correspond to the linguistic values of the linguistic variable.

Fig. 1. CO2 percentages for the CPC production process.

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More formally: A fuzzy set A (linguistic value) defined in a universe of discourse X (the scope interval of the linguistic variable) is expressed by its membership function: A:X “[0,1]

(1)

where A(x) expresses the extent to which x (input value) matches the category specified by A. A very useful form to A(x) is an isosceles triangle, which was utilized in this work. The basic concept of fuzzy control is to explore the expertise gained through several hours of observation. With analysis of this data, a suitable synthesis of this knowledge is established and the subsequent development of the control algorithm can be made [10]. When one asks a person who has been controlling a system for a long time about the methods that were used, the answer is frequently in a fuzzy rule form, such as: ‘If the temperature is very high, I then increase the flow rate of the refrigeration fluid.’ The ‘If –then’ rule corresponds to the Cartesian product Ai ×Bi of two fuzzy sets. R = Ai ×Bi would be the fuzzy relationship generated from all the fuzzy rules supplied by the specialist. Given an input value of the controller, the computation of the control action (inference) is derived from the scheme of modus ponens: X is A (X, Y) is SAi × Bi == == == == == == == Y is B

(2)

In this work, the antecedent set (A) are fuzzy sets and the consequent one (B) are singleton spikes (zero-order Sugeno approach, [11]). The main difference between the Mamdani method of inference [12] and the Sugeno approach is that the output membership functions are constant or linear for the Sugeno method. When the output of each rule is a constant (zero order), the degree of similarity with the Mamdani approach is very high. The only distinction is that all output membership functions are singleton spikes. Initially, it is necessary to fuzzyficate the input (x). Basically, there are two fuzzyfication ways. The first one is associated with datum disturbed by random noise. In this case, the fuzzyfication incorporates the uncertainty at the acquisition level. In the other approach, the input is treated as a crisp value. In the present work, inputs were treated as crisp values because, under usual operating conditions, significant random noise was not observed in the direct readings of variables of interest. The only significant interfer-

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ence is associated with an operational problem (it is not random noise) and cannot be filtered out only through traditional fuzzyfication: The CO2 analyzer gets two silica columns, which remove the moisture of the outflow gases before they reach the analyzer. During the process run, some exchanges of the silica column are performed. During those exchanges the metabolic activity does not change. However, the readings done by the analyzer correspond to smaller percentages of CO2. In the usual representation, the control originates from the individual control actions, each one being activated at a certain level by comparing the actual state of the process and the ith rule: B =%min (mi, Bi )

(3)

where mi = sup (ASAi ). Once the consequent is calculated, it is necessary to defuzzyficate it to find out the output value y. There are different ways to do it [13]. In the case of consequent sets being constant spikes (zero-order Sugeno approach), the method most used is the weighted average calculation, which returns the value y corresponding to the average of the singleton outputs weighted by their degrees of membership. In this work, due to the intrinsic dichotomy associated with the consequent singletons (feed vs. do not feed, for example), there was no sense in applying any kind of average. Pre-determined criterion values were therefore used as an alternative, as in Kitsuta and Kishimoto’s study [14]. Shioya et al. [15] present an important review of studies where knowledge-based (KB) approaches, like fuzzy logic, were used in the design and operation of various bioprocesses. Regarding process control, KB approaches can be classified into two categories: direct and supervisory control. In the direct scheme, expert knowledge is used in the synthesis of controllers to maintain particular variables, replacing the standard ones. In the supervisory scheme, expert knowledge is concentrated in a separate KB module, which analyzes the process, assays its state, detects particular events and issues supervisory commands that tell the direct system or the process operator when to do what [16]. Shioya et al. cite fuzzy control of sake mashing processes [17] and enzyme production processes using a recombinant gene [18] as some of the most typical examples of the direct use of fuzzy methodology. They also cite several applications of fuzzy supervisory control based on the recognition of physiological states or cultivation phase changes [19–21]. In the present work, we apply a fuzzy supervisory control strategy based on the detection of a specific event, the transition of culture phase from trophophase to idiophase.

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4. Materials and methods The fungus used in the two experiments was obtained from cryotubes conditioned in a ultrafreezer at the temperature of −50 °C. This material was prepared previously in the Laboratory of Biochemistry at DEQUFSCar. With this procedure a germination stage was eliminated. This reduced the time to prepare the fermentation. Eight cryotubes (5 ml) were used for each experiment. The contents of the cryotubes were added (divided) into two Erlenmeyer flasks containing 150 ml of prepared medium. They were maintained for 36 h (60 h in the second experiment) in a shaker at 26 °C and 250 rev./min. The first experiment was carried out in the bioreactor BIOFLO II-C (New Brunswick Scientific Co.®), in fedbatch culture, for approximately 150 h (there was a delay of 30 h to the initial cellular growth period). The temperature was maintained at 26 °C, the air flow rate at 3 l/min and the dissolved oxygen at 35%. The feeding of the supplemental medium was promoted after the end of the growth phase. When all the glucose was consumed, after 66.71 h, the continuous addition of the supplemental medium was initiated for 85 h. A peristaltic pump was used working at a flow rate of 10 ml/h. Samples were periodically withdrawn for analysis of sugars, CPC and cellular concentration. The second experiment was carried out in fed-batch culture for 147 h in a procedure equivalent to the previous one. The bioreactor was set up with complete instrumentation for process control and data acquisition for pH, temperature, DO, CO2, etc. [22]. The equipment for CO2 measurement is an infrared analytical (Rosemount Analytical®, model 880A) with maximum noise of 0.05% and 0.5–20 s of response time (application dependent). In the present work, the whole apparatus was used with an industrial GE-Fanuc® Automation series 90-30 PLC (Programmable Logic Controller). The Supervisory System used consisted of a 486 DX4-100 MHz microcomputer, with 16 K RAM, using UniSoft® supervision software in Windows® 3.11. An algorithm coded in C to accomplish a specific task, such as selecting the starting point for inverted sucrose feeding, could be easily coupled to the control system. For this implementation, the adopted sampling interval was 6 s.

5. Fuzzy system definition In Fig. 1, it is possible to observe a point of maximum CO2 percentage at the end of trophophase, at which the CO2 level begins to drop perceptibly. Therefore, the moment when the feeding of the supplemental medium should start can be characterized by a transition from increasing CO2 percentages (positive varia-

tions) to decreasing ones (negative variations). However, in long bioreactor runs, the operator is not interested in tracking the percentages of CO2 to detect the point of maximum percentage since the beginning of the process. Therefore, the idea was conceived to build a fuzzy control system that would operate on two reasoning levels. The first one, called attention level, acts only to determine the moment when the CO2 percentage is considered sufficiently high to begin tracking the percentages of CO2 to detect the point of maximum percentage specifically. The second one, called action level, acts by tracking variations of the CO2 percentage (DCO2) seeking to detect the point of maximum percentage at which the supplemental medium feeding will begin. The rules of the attention level proposed were: 1) If (time is EARLY) and (CO2% is LOW) then DO NOT activate the action level (activate the action level= 0) 2) If (time is LATE) and (CO2% is LOW) then DO NOT activate the action level (activate the action level= 0) 3) If (time is EARLY) and (CO2% is HIGH) then activate the action level (activate the action level=1) 4) If (time is LATE) and (CO2% is HIGH) then activate the action level (activate the action level=1) Note that there are two different possibilities of localizing the point of maximum percentage. The first one corresponds to the experiment pattern using the pre-processing procedure (shaker) via germination, through which larger initial growth rates were obtained (Fig. 1). The second possibility concerns pre-processing via cryotube, through which a delay in the response of the process was observed (as will be shown in Fig. 2). The attention system seems to present a degree of freedom, which can be used to advantage to characterize a different procedure that comes to be necessary (a different flow rate of the supplemental medium, for example). The action level is activated after the degree of membership of ‘activate’ is equal to the predetermined value 0.8 and the degree of membership of ‘DO NOT activate’ is 0.2 (80% of certainty). Kitsuta and Kishimoto [14] also used a predetermined criterion value. Regarding the action level, it is important to indicate that the available experimental data, sampled at a time interval of about 8 h (discreet), were inaccurate for a precise characterization of the transition from the increasing CO2 percentages to the decreasing ones. The sampled data did not determine if the transition occurs due to a zone of constant CO2 percentages (zero variation), or if such a transition occurs abruptly due to the presence of an inflection point. The Supervisory Control and Data Acquisition System, constituted by the PLC and the supervisory software, executes the start-up procedure of the process, the definition of operational

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Fig. 2. Cultivation time intervals of CO2 percentage (1st experiment).

Fig. 3. Detail for the CO2 percentages (1st experiment).

parameters and the continuous monitoring of the process variables. A first experiment in fed-batch culture for the production of CPC was then run with real time supervision. Fig. 2 shows the time intervals of CO2 percentage for this run. In Fig. 2, the divisions between the areas indicate points where the degree of membership in relation to each one of the classes is 0.5. Points close to a division certainly will present degree of membership greater than zero not only in the linguistic area where they are found, but also in the neighboring area. The abrupt drops observed in the CO2 percentages shown in this figure correspond to the exchanges of the silica column in operation, and are the unique signifi-

cant interferences in the CO2 readings in the usual operating conditions. Detail for the CO2 percentages close to the point of maximum CO2 percentage associated with the end of trophophase can be seen in Fig. 3. Fig. 3 shows the time intervals of CO2 percentages where a maximum point was perfectly determined based on a zone of constant percentage of CO2 (zero variation, not a point of inflection, as shown in Fig. 1). The high quality of the CO2 signal under the usual conditions, may be seen in this figure. With the maximum zone characterized, it was possible to define the appropriate membership functions and rules associated with the action level, based on variations of CO2 percentages (DCO2) defined as:

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DCO2(k)= CO2(k)− CO2(k − 100)

(4)

where k is the kth reading performed by the acquisition system. Although the CO2 readings can be treated as crisp values, the calculation of DCO2 taking into account successive readings of CO2 results in a significant amount of random noise. Eq. (4) characterizes a linear low-pass filter for (DCO2) estimation, smoothing the calculation results in an adequate way. Kwong et al. [6,7] also had to filter only the derivative of the on-line signal. The two rules proposed for the action level were: 5) If (variation of CO2 (DCO2) is ZERO or POSITIVE) then DO NOT feed (feed= 0) 6) If (variation of CO2 (DCO2) is NEGATIVE) then feed (feed=1) The membership functions for (DCO2) are presented in Fig. 4. The parameter VC1 defines variations of the CO2 percentages that are certainly negative. The beginning of the feeding should take place after the degree of membership of ‘feed’ is equal to 1 and the degree of membership of ‘DO NOT feed’ is equal to 0 (variations of the CO2 percentages that are certainly negative). An important point to be noted is that if (DCO2) was tracked from the beginning of the process (without an attention level), the response for the approximation of the zone of the end of the trophophase would be incorrect. This is because at the start of the process (DCO2) is positive but small, turning into high positive values as it approximates the end of the growth phase. The fuzzy controller would have as response a decrease in the degree of membership of ‘feed’ as it approximates the end of the growth phase, which would be incorrect. It is possible to verify that misinterpretation could occur in relation to the detection of the end of the trophophase due to the drops in the percentage of CO2

read during the silica column exchanges. It could be identified as the maximum point associated with the starting point of inverted sucrose feeding. Therefore, it is possible to verify that the operation of silica column exchange can constitute an error source for the performance of the fuzzy control system. This, in turn, makes it necessary to define an appropriate protection routine to prevent possible errors during the silica column exchanges. It is possible to verify a fundamental difference in the behaviour of the variables for the column exchange and at the end of the trophophase. In the column exchange, after a minor time interval, fast recovery of the CO2 percentage is observed. This difference allows the appropriate characterization of a protection system (a third reasoning level), defined through four proposed rules. Proposed protection rules: 7) If (time is EARLY) and (CO2 variation is NEGATIVE) then wait (wait=1) 8) If (time is LATE) and (CO2 variation is NEGATIVE) then CONFIRM feeding (feeding=1) 9) If (time is EARLY) and (CO2 variation is POSITIVE) then CANCEL feeding (feeding= 0) 10) If (time is LATE) and (CO2 variation is POSITIVE) then CANCEL feeding (feeding= 0) The protection level can confirm or cancel the feeding taking into account the predetermined criterion value corresponding to degree of membership of ‘CANCEL’ or ‘CONFIRM’ greater than 0.5.

6. Results and discussion To test the application and robustness of the proposed algorithm, the second experiment was carried out in fed-batch culture with automatic data acquisition

Fig. 4. Membership functions for (DCO2).

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Fig. 5. Cultivation time intervals of CO2 percentage (2nd experiment).

Fig. 6. Detail for the CO2 percentages (2nd experiment).

(Fig. 5). It can be noticed that this was an unusual experiment due to the existence of other interferences (not only the interferences generated by the silica column exchanges) in the percentages of CO2 measured during the cultivation. Initially (between 10 and 50 h), systematic oscillations of low amplitude were observed (Fig. 6). The amplitude of these systematic oscillations is about 0.20% and the corresponding period, in turn, is about 1 h. This kind of oscillation is not associated with the CO2 measurement equipment, which is much more accurate. These unexpected oscillations appeared because of the presence of a periodic variation in the air pressure at the reactor entrance during the above-men-

tioned interval. The problem was worked out at 50 h of cultivation. The equipment for CO2 measurement could precisely detect the interference due to its fast response time. Due to the unexpected low amplitude systematic oscillations in the CO2 percentages, it is clear that misinterpretation could occur in relation to the detection of the end of the trophophase. When the action level was turned on, the low amplitude oscillations could be identified as the maximum point associated with the beginning of the inverted sucrose feeding. But the problem can be solved by choosing an adequate value for the parameter VC1 (the degree of tolerance to uncertainties). In this implementation, VC1= −0.20%

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Fig. 7. Fuzzy controller response.

was adopted. It is important to note that the use of only a derivative method with a low-pass filter could misinterpret the maxima of these oscillations as the starting point for inverted sucrose feeding. Concerning the interferences that occurred after 50 h of cultivation, these appeared because of a lack of efficacy of the automatic dissolved oxygen PID control and occurred after the beginning of the supplemental medium feeding. Going on the analysis of the experimental results, it is also possible to notice that the maximum in the CO2 percentages associated with the beginning of the inverted sucrose feeding occurred in a cultivation time between time early and time late. Such occurrence is completely coherent with the experimental procedure. Although the pre-processing had made use of cryotubes (feeding of the supplemental medium in time late), these were left for 60 h in the shakers, 24 h further than usually made. Therefore, common growth delay associated with cryotubes was reduced. The response of the control algorithm (Fig. 7) shows that, in such a case, the idealized fuzzy system activates the action level appropriately at 38.47 h of cultivation. This was possible because of the fuzziness between the two zones (early and late). It is also possible to verify (Fig. 7) that the protection level cancels the feeding in the case of column exchange (40.42 h). To the end of the trophophase, the feeding of the supplemental medium is confirmed at 42.68 h. The devised system not only detects points of maximum, but can also distinguish different events that occur during the fermentation process.

7. Conclusions A fuzzy controller was designed that operates on three reasoning levels, attention, action and protection. The corresponding algorithm was implemented in C. These results indicate that the algorithm is robust for the conditions tested, allowing a safe automatic operation. The protection level must be coupled to the designed controller to prevent possible errors due to the silica column exchanges. We have suggested an alternative to the filtered derivative technique for the development of feeding strategies based on the recognition of specific events using fuzzy logic. Acknowledgements The authors thank CNPq and Capes for their financial support. References [1] Arau´ jo MLGC, Oliveira RP, Giordano RC, Hokka CO. Comparative studies on Cephalosporin C production process with free and immobilized cells of Cephalosporium acremonium ATCC 48272. Chemical Engineering Science 1996;51:2835 – 40. [2] Zanca DM, Martin JF. Carbon catabolite regulation of the conversion of penicillin N into cephalosporin C. Journal of Antibiotics 1983;36:700 – 8. [3] Behmer CJ, Demain AL. Further studies on carbon catabolite regulation of b-lactam antibiotic synthesis in Cephalosporium acremonium. Current Microbiology 1983;8:107 – 14.

R. Sousa, Jr, P.I.F. Almeida / Process Biochemistry 37 (2001) 461–469 [4] Takagi M, Ishimura F, Fujimatsu I. Control of cell growth rate by sugar feeding based on CO2 production rate. Journal of Fermentation and Bioengineering 1998;85:354 –7. [5] Silva AS, Cruz AJG, Arau´ jo MLGC, Hokka CO. Determinac¸ a˜ o do Inı´cio de Suplementac¸ a˜ o no Processo de Produc¸ a˜ o de Cefalosporina C em Batelada Alimentada. Paper presented at the 12th Brazilian Congress of Chemical Engineering, Porto Alegre, Brazil, 1998. [6] Kwong SCW, Rao G. Metabolic monitoring by using the rate of change of NAD(P)H fluorescence. Biotechnology and Bioengineering 1994;44:453 –9. [7] Kwong SCW, Randers L, Rao G. On-line detection of substrate exhaustion by using NAD(P)H fluorescence. Applied and Environmental Microbiology 1993;59:604 –6. [8] Zadeh LA. Fuzzy sets. Information and Control 1965;8:338 – 53. [9] Zadeh LA. Outline of a new approach to the analysis of complex systems and decision processes. IEEE Transactions on Systems, Man and Cybernetics 1973;SMC-3:28 –44. [10] Munakata T, Jani Y. Fuzzy systems: An overview. Communications of the ACM 1994;37:69 –76. [11] Sugeno M. Industrial applications of fuzzy control. Amsterdam: Elsevier, 1985. [12] Mamdani EH, Assilian S. An experiment in linguistic synthesis with a fuzzy logic controller. International Journal of Man-Machine Studies 1975;7:1 –13. [13] Lee CC. Fuzzy logic in control systems: fuzzy logic controller — Part I & Part II. IEEE Transactions on Systems, Man and Cybernetics 1990;20:404 –35. [14] Kitsuta Y, Kishimoto M. Fuzzy supervisory control of glutamic acid production. Biotechnology and Bioengineering 1994;44:87 – 94.

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[15] Shioya S, Shimizu K, Yoshida T. Knowledge-based design and operation of bioprocess systems. Journal of Bioscience and Bioengineering 1999;87:261 – 6. [16] Konstantinov KB, Yoshida T. Knowledge-based control of fermentation processes. Biotechnology and Bioengineering 1992;39:479 – 86. [17] Oishi K, Tominaga M, Kawato A, Abe Y, Imayasu S, Nanba A. Application of fuzzy control theory to the sake brewing process. Journal of Fermentation and Bioengineering 1991;72:115 –21. [18] Shiba S, Nishida Y, Park YS, Iijima S, Kobayashi T. Improvement of cloned a-amylase gene expression in fed-batch culture of recombinant Saccharomyces cere6isiae by regulating both glucose and ethanol concentrations using a fuzzy controller. Biotechnology and Bioengineering 1994;44:1055 – 63. [19] Kishimoto M, Kitta Y, Takeuchi S, Nakajima M, Yoshida T. Computer control of glutamic acid production based on fuzzy clusterization of culture phases. Journal of Fermentation and Bioengineering 1991;72:110 – 4. [20] Alfafara CG, Miura K, Shimizu H, Shioya S, Suga K, Suzuki K. Fuzzy control of ethanol concentration and its application to maximum glutathione production in yeast fed-batch culture. Biotechnology and Bioengineering 1993;41:493 – 501. [21] Von Numers C, Nakajima M, Asama H, Linko P, Endo I. A knowledge-based system using fuzzy inference for supervisory control of bioprocesses. Journal of Biotechnology 1994;34:109 – 18. [22] Cruz AJG, Arau´ jo MLGC, Giordano RC, Almeida PIF, Hokka CO. Implementation of a data acquisition system in a bioreactor utilizing a programmable logic controller. Paper presented at the 2nd European Symposium on Biochemical Engineering Science, Porto, Portugal, 1998.