Optimal Feeding Trajectories Design for E. coli Fed-batch Fermentations

In this paper optimal control algorithms for two E. coli fed-batch fermentations are developed. Fed-batch fermentation processes of E. coli strain MC4110 and E. coli strain BL21(DE3)pPhyt109 are considered. Simple material balance models are used to describe the E. coli fermentation processes. The optimal feed rate control of a primary metabolite process is studied and a biomass production is used as an example. The optimization of the considered fed-batch fermentation processes is done using the calculus of variations to determine the optimal feed rate profiles. The problem is formulated as a free final time problem where the control objective is to maximize biomass at the end of the process. The obtained optimal feed rate profiles consist of sequences of maximum and minimum feed rates. The resulting profiles are used for optimization of the E. coli fed-batch fermentations. Presented simulations show a good efficiency of the developed optimal feed rate profiles.