Optimal control of a fed-batch fermentation process

Abstract

Optimisation of fed-batch fermentation processes usually employs the calculus of variations to determine optimal feed-rate profiles that will maximise a given objective function. This results in a two-point boundary-value problem and because of the nonlinear nature of the pro cesses, the optimal solution usually falls out as an open-loop control algorithm. One advantage of this approach is that it does not need measurements of state variables which are often difficult to obtain on-line. Instead it assumes that the state variables are proceeding along known paths a-priori determined by models. However, the disadvantage of such an approach is that the performance will severely deteriorate in the presence of process disturbances or plant-model mismatch. Recently, on-line estimation of state variables has been successfully developed and used in the industry and therefore a method which operates the fed-batch fermentation in a closed-loop control scheme using state feedback is proposed. This is achieved by a two-step method. First, the optimal substrate concentration profile which governs the biochemical reactions in the fermentation process is determined. Then a controller is designed in closed-loop form to track this desired profile. Simulation studies for both primary and secondary metabolite production processes show that better performance is obtained by this closed-loop aptifaaal control method than by the open- loop optimal feed rate profile method. This is due to the self-correcting property of the proposed method, which proves to be advantageous when there are disturbances or plant-model mismatch.