Choice of control variable for optimization of fed-batch fermentation

The optimization problem for fed-batch fermentation is formulated in a framework which allows comparison of optimal operating policies with four different control variables. These variables include the original control variable, namely the substrate feed rate, and three transformed control variables, i.e. the substrate concentration in the fermenter, the substrate concentration in the feed and the mass flow rate of substrate. The optimality conditions for the three transformed control variables are identical but are generally different from the optimality condition for the original control variables. The optimality condition for the transformed control variables does not take into account (i) the dependence of the specific rates on the concentrations of cell mass and product and (ii) the substrate consumption dynamics.