Modeling and control of batch fermentation processes under conditions of uncertainty

An approach of model-based control design of batch biotechnological processes combining the advantages of two different analytical descriptions (deterministic and fuzzy model) is proposed. The approach uses the kinetic unstructured model accounting for the basic process dependencies. Using the fuzzy optimal decomposition of the physiological space into fuzzy regions, a new model is derived as a fuzzy weighted sum of distinct subsystems with unstructured models describing the process dynamics in the respective region. The proposed model can be considered as a compromise between the simple fuzzy model (input-output process description) which does not take into account the analytical process characteristics and the unstructured deterministic model that is not suitable for the control design purpose. On-line linearizing control law on the basis of the developed model is also proposed. The theoretical results are illustrated for the example of batch xanthan gum fermentation of strain Xanthomonas campestris ITS-342

Modelling of continuous microbial cultivation taking into account the memory effects

The problem of chemostat dynamics modelling for the purpose of control is considered. The "memory" of the culture is explicitly taken into account. Two possibilities for improving the quality of the proposed modelling approaches are discussed. A general model that accounts for the culture 'memory' by means of different 'memory' functions in the expressions of the specific growth rate and of the specific consumption rate and a polynomial function of the substrate concentration for the yield factor is proposed. The case where the maintenance energy is taken into account is also discussed. Two modifications of the general model (mu-type and S-type) are presented. A zero-order 'memory' function and a S-function with delay are applied in order to describe the 'memory' effects. Continuous growth of the strain Saccharomyces cerevisiae on a glucose limited medium is considered as a case study. Detailed investigations of the variety of models, derived from the general model by applying different 'memory' functions and different assumptions are carried out. The results are compared with those previously reported for the same process. It is shown that a significant improvement in predicting the substrate dynamics (not accompanied by any decrease in the quality of the model with respect to the biomass concentration) could be achieved, involving a first- or second-order polynomial function for the yield factor. It is also shown that the quality of the model mainly depends on the way that 'memory' function is incorporated. The detailed investigations give priority to the mu-type models. In this case past values of both biomass and substrate variables are considered. The time delay models with pure (constant) delay and those which account for the culture 'memory' by zero-order 'memory' function (adaptability parameter) are compared with respect to their utilization for the purpose of model-based control

Biochem. Eng. J.

The unstructured mathematical model was developed in the present investigation for the mixed culture, where the metabolites produced by one microorganism is assimilated by the other microorganism. For this, we specifically employed such model system in which sugars such as glucose were converted to lactate by Lactobacillus delbrueckii and the lactate was converted in turn to poly-beta-hydroxybutyrate (PHB) by Ralstonia eutropha in one fermentor. Several batch and fed-batch culture experiments were conducted using each microorganism at different dissolved oxygen (DO) concentrations. Those experimental data were then fitted to the mathematical model, which can describe the dynamics of a mixed culture. Some of the model parameters were expressed as functions of DO concentrations, and some of the other model parameters were tuned based on the mixed culture experiments. The model developed describes the effects of such concentrations of glucose, lactate, DO, and NH3 on the dynamic behavior of such concentrations as both microorganisms, glucose, lactate, and PHB. Optimal operating condition was then investigated using the model developed, It was found that the periodic change in DO concentration improved such performance as PHB yield, and it was verified by experiments. The optimal NH3 concentration profile was also obtained for the efficient PHB production by the application of the maximum principle, (C) 2002 Elsevier Science B.V. All rights reserved.The unstructured mathematical model was developed in the present investigation for the mixed culture, where the metabolites produced by one microorganism is assimilated by the other microorganism. For this, we specifically employed such model system in which sugars such as glucose were converted to lactate by Lactobacillus delbrueckii and the lactate was converted in turn to poly-beta-hydroxybutyrate (PHB) by Ralstonia eutropha in one fermentor. Several batch and fed-batch culture experiments were conducted using each microorganism at different dissolved oxygen (DO) concentrations. Those experimental data were then fitted to the mathematical model, which can describe the dynamics of a mixed culture. Some of the model parameters were expressed as functions of DO concentrations, and some of the other model parameters were tuned based on the mixed culture experiments. The model developed describes the effects of such concentrations of glucose, lactate, DO, and NH3 on the dynamic behavior of such concentrations as both microorganisms, glucose, lactate, and PHB. Optimal operating condition was then investigated using the model developed, It was found that the periodic change in DO concentration improved such performance as PHB yield, and it was verified by experiments. The optimal NH3 concentration profile was also obtained for the efficient PHB production by the application of the maximum principle, (C) 2002 Elsevier Science B.V. All rights reserved