A simple output-feedback controller for fed-batch cultures of microbial strains with overflow metabolism

Abstract

An output-feedback controller is proposed for fed-batch cultures of microbial strains exhibiting overflow metabolism, i.e., cultures where cell strains may produce inhibiting metabolites when excess substrate is fed. The control objective is therefore to control the substrate feed rate in order to remain near the optimal substrate concentration during the whole culture. The proposed controller uses measurements of an output signal that can be calculated from on-line process data and determines the necessary dilution rate to maintain the output near its local, time-varying, maximum at all times. The controller is hybrid, combining a proportional plus integral controller with antiwindup, modified so that the error signal used in the feedback may change its sign according to a state machine which keeps track of whether the control action should be positive or negative. The transition is made smoothly to avoid chattering and based on an auxiliary variable which follows the local output maximum. Partial proof of convergence is given and simulations of the model of a yeast production system show the applicability of the proposed strategy.