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Journal of Applied Mathematics
Volume 2013, Article ID 354095, 10 pages
http://dx.doi.org/10.1155/2013/354095
Research Article

Impulsive State Feedback Control of Cheese Whey Fermentation for Single-Cell Protein Production

1Science College, Jimei University, Xiamen, Fujian 361021, China
2Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China

Received 22 March 2013; Accepted 18 June 2013

Academic Editor: Yongkun Li

Copyright © 2013 Chunjin Wei 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.

Abstract

The work is the analysis of a mathematical model of cheese whey fermentation for single-cell protein production with impulsive state feedback control. Through the analysis, the sufficient conditions of existence and stability of positive order-1 periodic solution are obtained. It is shown that the system either tends to a stable state or has a periodic solution, which depends on the feedback state, the control parameter of the dilution rate, and the initial concentrate of microorganism and substrate. For some special cases, it is also shown that the system may exist in order-2 periodic solution. Furthermore, our findings are confirmed by means of numerical simulations.