Optimization of Single Cycle and Repeated Fed-Batch Fermentations

Optimization of single cycle and repeated fed-batch operations of a broad class of fermentations described by three key rate processes is considered within the frame-work of optimal control theory. The three key rate processes are described in terms of three key concentration variables. The necessary and sufficient conditions for admissibility of singular control are obtained analytically, with the control policy (feed rate profile) during the singular control interval being obtained exclusively in terms of the three concentration variables. Singular surfaces are identified in the three-dimensional concentration space. Existence of at least one limit point (singular inflection point) on the singular surface is necessary for admissibility of singular control in a steady cyclic operation. Uniqueness of a singular inflection point for given feed conditions guarantees its accessibility in the singular control operation. For fermentation processes involving multiple limit points for given feed conditions, accessibility of each limit point is decided by its local stability characteristics.