Modelling of continuous microbial cultivation taking into account the memory effects

The problem of chemostat dynamics modelling for the purpose of control is c onsidered. The "memory" of the culture is explicitly taken into account. Tw o possibilities for improving the quality of the proposed modelling approac hes are discussed. A general model that accounts for the culture 'memory' b y 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 w here the maintenance energy is taken into account is also discussed. Two mo difications 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 t o describe the 'memory' effects. Continuous growth of the strain Saccharomy ces cerevisiae on a glucose limited medium is considered as a case study. D etailed investigations of the variety of models, derived from the general m odel by applying different 'memory' functions and different assumptions are carried out. The results are compared with those previously reported for t he same process. It is shown that a significant improvement in predicting t he substrate dynamics (not accompanied by any decrease in the quality of th e model with respect to the biomass concentration) could be achieved, invol ving 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 priorit y to the mu-type models. In this case past values of both biomass and subst rate variables are considered. The time delay models with pure (constant) d elay and those which account for the culture 'memory' by zero-order 'memory ' function (adaptability parameter) are compared with respect to their util ization for the purpose of model-based control.