A note on the optimality criteria for maximum biomass production in a fed‐batch fermentor

Abstract

The objective of this is to complement studies by establishing the optimal startup and final phase procedure in a fed-batch reactor through the formulation of the corresponding optimal control problem and the use of the maximum principle for its solution. Furthermore, useful criteria which signal the entrance of the optimal startup trajectory to the singular arc are established. Also some intuitive notions about the nature of the conditions which must be satisfied along the singular arc and which have been employed in previous studies without justification are placed in the right perspective. The maximization of cell biomass produced in a fed-batch fermentor is used as a vehicle for presenting the above results and ideas. However, the same methodology can be applied to different performance indices that would be considered more appropriate in other fermentations. If the biomass growth kinetics is of the Monod type, the optimal feeding strategy for the optimization of the final biomass produced in a fed-batch reactor is to fill the reactor after inoculation at the fastest possible rate and then run it in the batch mode until condition (24) is satisfied. If the biomass growth kinetics exhibits a maximum, the optimal startup feeding strategy is nomore » flow if the initial substrate concentration is to the right of the maximum, and maximum flow if it is to the left. In both cases, the substrate concentration tends towards the maximum.« less