Practical Identification of Unstructured Growth Kinetics by Application of Optimal Experimental Design

Abstract
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‐monotonickinetics (with the Haldanemodel as a prototype) and monotonickinetics (with the Monodmodel 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 ofprocess performance, is an excellent starting point forfeed rate optimization with respect to estimation of thoseparameters with large influence upon processperformance. 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.