Optimal control applications & methods vol:15 issue:1 pages:13-34
This paper presents the application of optimal control theory in determining the optimal feed rate profile for the penicillin G fed-batch fermentation, using a mathematical model based on balancing methods. Since this model does not fulfil all requisites for standard optimal control, we propose a sequence of new models - that converges to the original one in a smooth way - to which the standard techniques are applicable. The unusual optimization of some initial conditions is included. We then state the conjecture that allows us to obtain the optimal control for the original model. The enormous gains in production and the vanishing of the characteristic biphasic behaviour through feed rate profile optimization raise some questions concerning the validity of this model. In this way this optimal control study can prove to be very useful for model discrimination purposes. Furthermore, mathematical and microbial insights lead to the construction of a suboptimal heuristic strategy - which we show to be a limiting case of the optimal scheme - that can serve as a basis for the development of robust, model-independent, optimal adaptive control schemes.