Optimal substrate feeding policy for a fed batch fermentation with substrate and product inhibition kinetics

The optimal substrate feeding policy for the fed batch fermentation which is governed by product and substrate inhibited kinetics is presented. The conjunction point between nonsingular and singular arcs and the feeding policy along the singular arc are derived analytically in terms of the concentrations of substrate and product and the liquid volume. Thus, it is possible to determine the feeding rate by monitoring the state variables (i.e., closed loop control). As a specific example, an optimization study of the fed batch fermentation for ethanol production by Saccharomyces cerevisiae is presented. It is shown that the optimal feeding patterns are heavily dependent upon the initial conditions. The point selectivity provides the guideline for predicting the optimal feeding patterns and explaining the results of rigorous mathematical analysis.