Following an Optimal Batch Bioreactor Operations Model

The problem of following an optimal batch operation model for a bioreactor in the presence of uncertainties is studied. The optimal batch bioreactor operation model (OBBOM) refers to the bioreactor trajectory for nominal cultivation to be optimal. A multiple-variable dynamic optimization of fed-batch reactor for biomass production is studied using a differential geometry approach.

The maximization problem is solved by handling both the optimal filling policy and substrate concentration in the inlet stream. In order to follow the OBBOM, a master–slave synchronization is used. The OBBOM is considered as the master system which includes the optimal cultivation trajectory for the feed flow rate and the substrate concentration.

The “real” bioreactor, the one with unknown dynamics and perturbations, is considered as the slave system. Finally, the controller is designed such that the real bioreactor is synchronized with the optimized one in spite of bounded unknown dynamics and perturbations. It is formally proven that the inclusion of an additional inlet stream, free of the limiting substrate, enables global controllability and thereby provides the solution to the controllability problems pointed out by Szederkényi et al. [30], fact that have not been reported previously.

The scheme is applied to a nonlinear fed-batch fermentation process.