Optimization of fed-batch penicillin fermentation: a case of singular optimal control with state constraints

The determination of the optimal feeding profile of a fed-batch fermentation requires the solution of a singular optimal control problem that is often complicated by constraints imposed on the state variables. Such constraints can be a maximum allowable biomass concentration beyond which oxygen transfer is severely limited or maximum substrate concentration to avoid side reactions. Due to these state constraints and the singular nature of the problem, complete solutions are especially hard to obtain and almost nonexistent in the literature. In this work the feed concentration is employed as the control variable in a solution approach that first determines the optimal reactor substrate concentration and subsequently solves for the feed concentration profile that results in the optimal reactor profile. Calculations for the fed-batch penicillin fermentation indicate sharp increases in productivity over frequently employed strategies.