Optimal operation of fed-batch bioreactors with two control variables

Abstract

The optimal operating policies for a fed-batch bioreactor with two manipulated variables is developed. The optimization problem with two control variables is viewed as an extension of a single control variable problem. The necessary conditions of optimality of the control variables are developed using the results of the singular control theory and Pontryagin's maximum principle. An algorithm, which utilizes the computational techniques reported previously for single control variable problems, is extended to handle the problems with two control variables. The solution strategy is demonstrated for determining the optimal operating conditions for a fed-batch bioreactor by controlling (i) the substrate feed rate and the bioreactor temperature and (ii) the feed rates of two growth limiting substrates.