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.