General characteristics of optimal feed rate profiles for various fed-batch fermentation processes.

General Characteristics of the optimal feed rate profiles have been deduced for various fed-batch fermentation processes by analyzing singular controls and singular arcs. The optimal control sequences depend on the shapes of the specific growth and product formation rates, mu andpi, and the initial conditions. For fed-batch processes described by four mass balance equations, the most general optimal control sequence consists of a period of maximum feed rate, a period of minimum feed rate (a batch period), a period of singular feed rate (variable and intermediate), and a batch period. Degenerate sequences in which one or more periods are missing can result with a particular set of initial conditions. If the fermentation time is not critical, the singular control maximizes the net yield of product and only when the time is also important, it balances a trade off between the yield of product and the specific growth rate which dictates the fermentation time. With the sequence of optimal control known, the optimal feed rate profile determination is reduced to a problem of determining switching times.