Optimization of a Primary Metabolite Fermentation Process: Effect of Cost Factor on the Optimal Feed Rate Control

Optimization of a fed-batch fermentation process is usually done using the calculus of variations to determine an optimal feed rate profile. The obtained optimal feed rate profile consists of sequences of maximum, minimum and singular feed rates. The optimal feed rate control of a primary metabolite process was studied and a biomass production was used as an example. A simple material balance model was used to describe the chosen fermentation process. The problem was then formulated as a free final time problem in the optimal control literature where the control objective was to maximise biomass at the end of the batch. It was shown mathematically that a cost factor per unit of operating time is needed in formulating the objective function. Otherwise the optimal feed rate can not be specified. This is explained by the fact that without cost factor, the optimization algorithm does not take the importance of operating time into account and might result in longer operating time than necessary. This also indicates the essential of using fermentation model on the optimal control problem.