Practical identification of unstructured growth kinetics by application of optimal experimental design

This paper deals with the practical identification of the parameters of unstructured growth kinetics during growth of biomass on one limiting substrate in a fed-batch bioreactor. We consider kinetic models in which the specific growth rate is a function of the substrate concentration only. Two classes of models are distinguished: non-monotonic kinetics (with the Haldane model as a prototype) and monotonic kinetics (with the Monod model as a prototype). The information content of several simulation experiments, each with a different volumetric feed rate profile is evaluated by using the modified E-criterion for optimal experimental design (i.e., ratio of the largest to the smallest eigenvalue of the Fisher information matrix). The main contribution of this paper is to provide theoretical evidence and to present illustrative examples for the following conjecture: A feed rate strategy which is optimal in the sense of process performance, is an excellent starting point for feed rate optimization with respect to estimation of those parameters with large influence upon process performance. For a two degrees of freedom optimization of the feed rate profile, we obtain for the first time a modified E-criterion value equal to 1, which is the optimal value for this criterion.