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Nonlinear modelling of ethanol inhibition with the state feedback control

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Abstract

Considering the ethanol fermentation is a typical product-inhibiting process, a mathematical model of the ethanol fermentation with the state feedback control is proposed in this paper. The sufficient conditions for existence of the positive period-1 solution and period-2 solution are obtained based on the theory of the impulsive semi-dynamical system and the qualitative properties of the corresponding continuous system. We prove that ethanol fermentation with impulsive state feedback control tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the fermentation. Furthermore, mathematical results are justified by some numerical simulations.

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Authors and Affiliations

  1. Department of Mathematics, Huanghuai University, Zhumadian , 463000, Henan, People’s Republic of China

    Zhong Zhao, Junyi Zhang, Liuyong Pang & Ying Chen

Authors
  1. Zhong Zhao
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  2. Junyi Zhang
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  3. Liuyong Pang
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  4. Ying Chen
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Corresponding author

Correspondence to Zhong Zhao.

Additional information

This work is supported by the National Natural Science Foundation of China (No. 11371164), NSFC-Talent Training Fund of Henan(U1304104) and the young backbone teachers of Henan (No. 2013GGJS-214).

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Zhao, Z., Zhang, J., Pang, L. et al. Nonlinear modelling of ethanol inhibition with the state feedback control. J. Appl. Math. Comput. 48, 205–219 (2015). https://doi.org/10.1007/s12190-014-0799-9

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  • DOI: https://doi.org/10.1007/s12190-014-0799-9

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