Fuzzy logic control of a fed-batch fermentor

A rule-based fuzzy logic control is developed for control of penicillin concentration in a fed-batch bioreactor. The membership functions, fuzzy ranges for the error and for the controller output are defined. A fuzzy rule base is constructed relating error to the control output based on operators' knowledge. The performance of the fuzzy-logic controller is evaluated by simulating a mathematical model of the fed-batch bioreactor.     

Genetic algorithm based fuzzy logic control of a fed-batch fermentor

In the normal fuzzy logic control (FLC) system, both the membership functions and the rule sets are usually decided upon subjectively, case by case. The application of Genetic Algorithm(GA) could lead to proper selection of membership functions and rule base objectively. In this paper, the optimisation of membership functions of a FLC for a fed-batch fermentor is carried out with help of Genetic Algorithm (GA). Results are found to be satisfactory.     

Dynamic reoptimization of a fed-batch fermentor

Traditionally, fed-batch biochemical process optimization and control use complicated models and off-line optimizers with no on-line model adaptation and re-optimization. This work demonstrates the applicability, effectiveness, and economic potential, of a simple phenomenological model for modeling, and a novel optimizer for on-line re-optimization and control of an aerobic fed-batch fermentor.     

Fuzzy supervisory control of fed-batch baker's yeast process

Summary A fuzzy supervisory system for bioprocess control was developed, and applied to baker's yeast fermentation. The system was based on hierarchical bioprocess control with fuzzy phase recognition and separate fuzzy control of each process phase. A two-level knowledge base included rules both for the phase recognition and control. The system was tested by using experimental data of fed-batch baker's yeast cultivations and by process simulations.     

An algorithm for operating a fed-batch fermentor at optimum specific-growth rate

An algorithm for operating a fed-batch fermentor at an optimum specific fermentation rate is proposed. It does not require on-line measurement of nutrient concentration in the culture medium. An on-line estimate of the specific fermentation rate is sufficient for implementation of this scheme. The algorithm is model independent and works well even with poor estimates of the product yields and the specific fermentation rate. Results of a detailed simulation study are presented for a simple case of optimization of cell-mass production in a fed-batch fermentor. The results clearly demonstrate the efficacy of this algorithm under a wide range of fermentation situations.     

Fuzzy logic control of an unstable bioreactor

A rule based fuzzy controller (FLC) is developed for stabilization of an unstable continuous stirred tank bioreactor (CSTBR) from various start-up conditions. The output variable is the reactor substrate concentration and the manipulated variable is the dilution rate. The performance of the FLC is evaluated by simulating a mathematical model of an unstable CSTBR. FLC is robust to perturbations in the specific growth rate, specific consumption rate and also to a disturbance in the feed substrate concentration. The performance of the FLC is superior to that of a conventional proportional controller.     

A fuzzy logic controller to control nutrient dosage in a fed-batch baker's yeast process

A fuzzy logic controller designed to control glucose feeding in a fed-batch baker's yeast process is presented. Feeding is carried out in portions and the controller determines the time at which glucose should be added and computes the size of the portion to provide the maximum glucose uptake rate. Moreover, the controller detects and prevents the occurrence of overdosage. The experimental results indicate that yield and specific growth rate obtained with the controller approached 55% and 0.13 h^–1, respectively.     

Robust pole placement control of a fermentor

This paper deals with robust pole placement control of a continuous flow alcoholic fermention process. The strain used for experiments is Saccharomyces cerevisae UG5. The fermentor is subject to changs in pH, temperature, mixing, etc. The regularized pole placement adaptive control algorithm is used for regulation and tracking purposes. The substrate concentration and the dilution rate have been respectively selected as controlled and control variables. The eliminant matrix associated to the pole placement problem is non-singular if the identified input-output model has common poles and zeros. Two solutions have been adopted to deal with this ill-conditioning problem. The first solution consists of monitoring the determinant of the eliminant matrix and the second consists of adding a correction term to the highest degree coefficient of either the numerator or denominator of the process transfer function. A robust recursive identification scheme is used for parameters estimation. The fermentor was interfaced with PC computer using a multitasking operating system. Experiments carried out with the fermentor, illustrate the use of the regularized pole placement adaptive control algorithm.     

Automation of glucose measurement in fermentor broths

Summary A semi-on-line automated analysis for fermentation is presented. The system consists of a modified commercial biosensor analyser YSI 27 and a Gilson dilutor injector. The results of direct glucose monitoring in fermentation broths are presented. Measurements, calibrations and washes are completely automated, with a maximum analysis frequency of 16 per hour with dilutions. The detection limits are 50 mg/1 and 41 g/1 with good linearity and a precision of ±5%.Offprint requests to: J. M. Cavalie     

Repeated fed-batch lactic acid production in a packed bed-stirred fermentor system using a pH feedback feeding method

Lactic acid production by repeated fed-batch fermentation using free and immobilized cells of Lactobacillus lactis-11 in a packed bed-stirred fermentor (PBSF) system filled with different support materials including ceramic beads, macro-activated carbon cylinders and glass fiber balls was investigated. The results showed that the optimal support materials were the ceramic beads with diameters of 1–2 mm. Compared with the free cell fermentation system, lactic acid production and volumetric productivity in the PBSF system increased by 16.6 and 12.5%, respectively. Though the concentration of free cells decreased sharply, lactic acid production remained stable in five consecutive fed-batch runs using the PBSF system. pH gradients, immobilized cell concentration and mass diffusion in the packed bed were all affected by the recirculation rate of the culture broth. Maximum lactic acid production, productivity and yield occurred at a recirculation rate of 50 mL min⁻¹.     

Calorimetric control of fed-batch fermentations

Measurements of the heat produced by Saccharomyces cerevisiae CBS 426 were used in conjunction with elemental and enthalpic balances to control fed-batch fermentations. A proportional control using the ratio of carbon dioxide evolution rate to heat production resulted in high biomass yields and minimal ethanol production. For the special case where the carbon source contains no nitrogen, biomass production estimated from heat measurements agreed well with measured values. When the controller gain was set below the maximum specific cellular growth rate, stable control was achieved, even in response to large upsets in feed concentrations.     

Fuzzy control of ethanol concentration its application to maximum glutathione production in yeast fed-batch culture

A fuzzy logic controller (FLC) for the control of ethanol concentration was developed and utilized to realize the maximum production of glutathione (GSH) in yeast fedbatch culture. A conventional fuzzy controller, which uses the control error and its rate of change in the premise part of the linguistic rules, worked well when the initial error of ethanol concentration was small. However, when the initial error was large, controller overreaction resulted in an overshoot.An improved fuzzy controller was obtained to avoid controller overreaction by diagnostic determination of "glucose emergency states" (i.e., glucose accumulation or deficiency), and then appropriate emergency control action was obtained by the use of weight coefficients and modification of linguistic rules to decrease the overreaction of the controller when the fermentation was in the emergency state. The improved fuzzy controller was able to control a constant ethanol concentration under conditions of large initial error.The improved fuzzy control system was used in the GSH production phase of the optimal operation to indirectly control the specific growth rate mu to its critical value mu(c). In the GSH production phase of the fed-batch culture, the optimal solution was to control mu to mu(c) in order to maintain a maximum specific GSH production rate. The value of mu(c) also coincided with the critical specific growth rate at which no ethanol formation occurs. Therefore, the control of mu to mu(c) could be done indirectly by maintaining a constant ethanol concentration, that is, zero net ethanol formation, through proper manipulation of the glucose feed rate. Maximum production of GSH was realized using the developed FLC; maximum production was a consequence of the substrate feeding strategy and cysteine addition, and the FLC was a simple way to realize the strategy. (c) 1993 John Wiley & Sons, Inc.     

A ternary logic model for recurrent neuromime networks with delay

 In contrast to popular recurrent artificial neural network (RANN) models, biological neural networks have unsymmetric structures and incorporate significant delays as a result of axonal propagation. Consequently, biologically inspired neural network models are more accurately described by nonlinear differential-delay equations rather than nonlinear ordinary differential equations (ODEs), and the standard techniques for studying the dynamics of RANNs are wholly inadequate for these models. This paper develops a ternary-logic based method for analyzing these networks. Key to the technique is the realization that a nonzero delay produces a bounded stability region. This result significantly simplifies the construction of sufficient conditions for characterizing the network equilibria. If the network gain is large enough, each equilibrium can be classified as either asymptotically stable or unstable. To illustrate the analysis technique, the swim central pattern generator (CPG) of the sea slug Tritonia diomedea is examined. For wide range of reasonable parameter values, the ternary analysis shows that none of the network equilibria are stable, and thus the network must oscillate. The results show that complex synaptic dynamics are not necessary for pattern generation. Received: 15 June 1994/Accepted in revised form: 10 February 1995     

Minimal time control of fed-batch bioreactor with product inhibition

This paper is devoted to the minimal time control problem for fed-batch bioreactors, in presence of an inhibitory product, which is released by the biomass proportionally to its growth. We first consider a growth rate with substrate saturation and product inhibition, and we prove that the optimal strategy is fill and wait (bang-bang). We then investigate the case of the Jin growth rate which takes into account substrate and product inhibition. For this type of growth function, we can prove the existence of singular arc paths defining singular strategies. Several configurations are addressed depending on the parameter set. For each case, we provide an optimal feedback control of the problem (of type bang-bang or bang-singular-bang). These results are obtained gathering the initial system into a planar one by using conservation laws. Thanks to Pontryagin maximum principle, Green’s theorem, and properties of the switching function, we obtain the optimal synthesis. A methodology is also proposed in order to implement the optimal feeding strategies.     

Optimal nonsingular control of fed-batch fermentation

Presented is a new simple method for multidimensional optimization of fed-batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau-Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.The method is applied for a homogeneous model of fermentation with volume, substrate, biomass, and product concentrations as the state variables. Computer study shows considerable simplicity of the method, its high accuracy for low order of approximation, and efficient convergence.     

On-line adaptive control of a fed-batch fermentation of Saccharomyces cerevisiae

The feasibility of applying an adaptive control technique to a fermentation process is investigated. The nonlinear, time-variant parameters of a fermentation process were estimated on-line as a series of linearized describing matrices. The matrices were used to update a suboptimal feedback law which controlled the process in real time over the linear region. Experiments were performed on a small-scale fully instrumented fermenter with the online, real-time adaptive control package. Results are presented for both single- and multivariable control, and indicate successful control of yeast cell growth.     

The control of glucose concentration during yeast fed-batch cultivation using a fast measurement complemented by an extended Kalman filter

In this contribution results are presented from the control of glucose during a yeast fed-batch cultivation. For glucose measurements a special flow injection analysis (FIA) system was employed, which uses a glucose oxidase solution instead of immobilized enzymes. To avoid the large delay time caused by probing systems samples containing cells, i.e., samples containing the ordinary culture broth, are injected into the FIA system. Based on a special evaluation method the glucose concentration can be measured with a delay time of about 60 s. Employing an extended Kalman filter, the biomass, the glucose concentration as well as the w_max (Monod model) are estimated. Based on the estimation a feed forward and a PI-control with a set point of 0.5 g/l was carried out. The mean deviation of the set point and the estimated value as well as the set point and the measured value were 0.05 and 0.11 g/l respectively for a control period of 8 h producing a cell dry mass of more than 6 g/l.     

Profile control scheme in a Bakers' yeast fed-batch culture

This article develops and discusses a practical and useful computer control scheme so that the biomass concentration or the specific growth rate will as accurately as possible follow a desired profile specified in advance. Many computer simulations certified the validity of the proposed control scheme. The control scheme proposed, called "programmed-controller/feedback-compensator (PF) system," consists of a programmed controller that will follow the desired profile unless there is noise or disturbance and a feedback compensator that will compensate the noise and correct error in the model parameters. As the feedback compensator, the model reference adaptive control (MRAC) algorithm was also proposed. The PF system with MRAC, named PF-MRAC, could be used sufficiently for the profile control of the specific growth rate. For the profile control of the cell concentration, "predictive control algorithm" should be added to the PF system, and the consequent control scheme was named as the PFP system. Many numerical examples showed that the PFP system with MRAC, named PFP-MRAC, proposed here worked sufficiently well.     

On the optimal control of fed-batch reactors with substrate-inhibited kinetics

The optimal feed rate profiles, for fed-batch fermentation that maximizes the biomass production and accounts for time, are analyzed. The solution can be found only if the final arc of the optimal control is a batch arc, since in this case the final concentrations of substrate and biomass can be determined by ulterior conditions on the mass balance and on the final growth rate of biomass and thus it is possible to solve the resulting time optimal problem by using Green's theorem. This evidences the "turnpike property" of the solution, which tries to spend the maximum time on or at least near the singular arc along which the substrate concentration is maintained constant. The optimality of the final batch arc is related to the time operational cost in the performance index. The sequence of the control depends on the initial conditions for which six different regions, with the respective patterns, have been identified, in case the performance index allows the control sequence to have a final batch.