OPTIMUM OPERATING MODE FOR A CLASS OF FERMENTATION

This paper is concerned with optimization of the operating mode of a fermentor. Combining the various modes of operation—batch, semibatch, and continuous—the operating pattern which maximizes the desired metabolic product in a single fermentor is determined by using Kelley's transformation method with Pontryagin's maximum principle. Kelley's transformation method is a device which avoids the singular situation which occurs when the usual procedure of selecting the optimal control function by the maximum principle breaks down. This is the case in the problem considered in this paper. For lysine fermentation, the best operating mode depends on the fermentor capacity and operating time. The results of this study are summarized thus: (i) when the operating time is “long enough,” optimal conditions require that continuous operation follows either semibatch and/or batch operation, and (ii) when the fermentor capacity becomes “large enough,” semibatch operation becomes important. Copyright © 1978 John Wiley & Sons, Inc.