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Indexed by:Journal Papers

Date of Publication:2020-07-01

Journal:JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS

Included Journals:SCIE

Volume:357

Issue:11

Page Number:6571-6594

ISSN No.:0016-0032

Key Words:Optimal control computation; Nonlinear dynamical system; Total variation; Parallel optimization; Fed-batch fermentation

Abstract:In this paper, an optimal minimal variation control in the fed-batch fermentation of glycerol bio-conversion 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. (C) 2020 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.