Optimal minimal variation control with quality constraint for fed-batch fermentation processes involving multiple feeds

Abstract

In this paper, an optimal minimal variation control in the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD) caused by Klebsiella pneumonia (K. pneumonia) is considered. In fed-batch process, it is required for the concentration of 1,3-PD to satisfy a quality constraint (i.e., the concentration of 1,3-PD at the terminal time is to reach a critical value), and furthermore, the cost associated with the change of the control signal must also be taken into account. It is formulated as an optimal control problem in which the total variation of the control signal is taken as the cost function, while the feeding rates of glycerol and alkali and the switching instants are taken as decision variables. The optimal control problem is subject to the quality constraint and certain continuous state inequality constraints. To handle the continuous state inequality constraints, the optimal control problem is approximated as a sequence of nonlinear programming subproblems. Because of the nature of the optimal control problem, which is highly complicated, a parallel algorithm is proposed to solve these subproblems based on genetic algorithm and the gradients of the constraint functions with respect to decision variables. From extensive simulation studies, it is observed that the obtained optimal feeding rates and switching instants are highly satisfactory.