Optimal Control of Fed-Batch Fermentation Processes

Abstract

In this chapter the design ofa substrate feeding rate controller for a class of biotechnological processes in stirred tank bioreactors characterized by a decoupling between biomass growth and product formation is under study. As a typical example, we consider the most common case of monotonic specific growth rate and non-monotonic specific production rate. In general this yields a singular optimal control problem. Due to state inequality constraints -which reflect physical limitations- complete solutions are especially hard to obtain and almost non-existent in the literature.

However, the techniques proposed in the literature to convert the problem into a non-singular one all suffer from problems with respect to practical implementation. Therefore, we adopt the traditional point of view, i.e., singular optimal control with the volumetric substrate feed rate as the manipulated variable. We consider performance indices of both the yield type and the productivity type. The optimization of the initial substrate concentration is included also.

We illustrate that the determination of the switching times in the feed rate profile can be simplified a lot by incorporating as much as possible microbiological knowledge concerning the process under consideration. The results we present here are in this way general that they are written in terms of the specific reaction rates. In other words, an exact analytical expression for these rates is not required a priori. In addition, no assumptions have been made concerning the metabolism involved for biomass survival and possibly product synthesis.

The computational algorithms presented have some marked advantages over algorithms reported in the literature. In addition, we are able to deduce a complete general solution in the realistic case of both substrate and biomass concentration constraints. As an example, simulation results are given for the penicillin G fed-batch fermentation.

It is shown in Chapter 13 how a detailed analysis of the profiles presented here leads in a natural way to the design of model-independent control strategies which combine nearly optimal performance with excellent robustness properties: optimal adaptive control.