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Journal of Applied Mathematics
Volume 2012, Article ID 245315, 13 pages
Research Article

Optimal Control of a Fed-Batch Fermentation Involving Multiple Feeds

1School of Mathematics and Information Science, Shandong Institute of Business and Technology, Yantai 264005, Shandong, China
2School of Energy and Power Engineering, Dalian University of Technology, Dalian, Liaoning 116024, China
3School of Mathematical Science, Huaiyin Normal University, Huai'an 223300, Jiangsu, China

Received 19 May 2011; Accepted 14 November 2011

Academic Editor: Pablo González-Vera

Copyright © 2012 Chongyang Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A nonlinear dynamical system, in which the feed rates of glycerol and alkali are taken as the control functions, is first proposed to formulate the fed-batch culture of 1,3-propanediol (1,3-PD) production. To maximize the 1,3-PD concentration at the terminal time, a constrained optimal control model is then presented. A solution approach is developed to seek the optimal feed rates based on control vector parametrization method and improved differential evolution algorithm. The proposed methodology yielded an increase by 32.17% of 1,3-PD concentration at the terminal time.