中文

Operations Research Transactions >

2017 , Vol. 21 >Issue 2: 46 - 56

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2017.02.006

Nonlinear dynamic system of batch fermentation with the function as parameters and identification

Expand
  • 1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, Liaoning, China; 2. School of Energy and Power Engineering, Dalian University of Technology, Dalian 116024, Liaoning, China;
    3.School of Environmental and Biological Science and Technology, Dalian University of Technology, Dalian 116024, Liaoning, China

Received date: 2016-09-12

  Online published: 2017-06-15

Fold

Abstract

In this paper, we propose a nonlinear dynamical system of batch fermentation with the continuous piecewise linear functions as parameters, and investigate the existence of solution about the nonlinear dynamical system. Based on a smooth curve which is fitted to the experimental data, a new identifiable model was established by using the continuous piecewise linear function as optimization parameters. According to the relationship between the state variables and identification function, an efficient algorithm is developed to solve the identification system, and the convergence of optimization algorithm is also analysed. Finally, numerical results are discussed to illustrate the validity of the present model.

Key words： nonlinear dynamic system; continuous piecewise linear function; identification; batch fermentation

Cite this article

YANG Qi, JIANG Zhigang, FENG Enmin, YIN Hongchao, XIU Zhilong .

Nonlinear dynamic system of batch fermentation with the function as parameters and identification
[J]. Operations Research Transactions, 2017 , 21(2) : 46 -56 . DOI: 10.15960/j.cnki.issn.1007-6093.2017.02.006

References

[1] Hermann B G, Patel M. Today's and tomorrow's bio-based bulk chemicals from white biotechnology: a techno-economic analysis [J]. Applied Biochemistry and Biotechnology, 2007, 136(3): 361-388.
[2] Eiteman M A, Lee S A, Altman E. A co-fermentation strategy to consume sugar mixtures effectively [J]. Journal of Biological Engineering, 2008, 2(1): 3.
[3] 修志龙. 微生物发酵法生产1,3-丙二醇的研究进展 [J]. 微生物学通报, 2000, 27(4): 300-302.
[4] 修志龙, 曾安平, 安利佳. 甘油生物歧化过程动力学数学模型和多态研究 [J]. 大连理工大学学报, 2000, 46(4): 428-433.
[5] Sun Y Q, Qi W T, Teng H, et al. Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: Concerning enzyme-catalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane [J]. Biochemical Engineering Journal, 2008, 38(1): 22-32.
[6] Sun Y Q, Ye J X, Mu X J, et al. Nonlinear mathematical simulation and analysis of Dha Regulon for glycerol metabolism in Klebsiella pneumonia [J]. Chinese Journal of Chemical Engineering, 2012, 20(5): 958-970.
[7] 高彩霞, 王宗涛, 冯恩民. 微生物间歇发酵生产1,3-丙二醇过程的辨识与优化 [J]. 大连理工大学学报, 2006, 46(5): 771-774.
[8] 袁金龙, 冯殊伦, 冯恩民. 甘油间歇发酵酶催化非线性动力系统的强稳定性 [J]. 控制与决策, 2014, 29(08): 1505-1508.
[9] Lian H S, Feng E M, Li X F. Oscillatory behavior in microbial continuous culture with discrete time delay [J]. Nonlinear Analysis: Real World Applications, 2009, 10(5): 2749-2757.
[10] Wang J, Ye J X, Yin H C, et al. Sensitivity analysis and identification of kinetic parameters
in batch fermentation of glycerol [J]. Journal of Computational and Applied Mathematics, 2012, 236(9): 2268-2276.
[11] Zhai J G, Ye J X, Wang L, et al. Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture [J]. Nonlinear Analysis: Real World Applications, 2011, 12(5): 2730-2741.
[12] Wang G, Feng E M, Xiu Z L. Modeling and parameter identification of microbial bioconversion in fed-batch cultures [J]. Journal of Process Control, 2008, 18(5): 458- 464.
[13] Liu C Y, Gong Z H, Feng E M. Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture [J]. Journal of Industrial and Management Optimization, 2009, 5(4): 835-850.
[14] 李晓红, 冯恩民, 修志龙. 微生物间歇发酵非线性动力系统的性质及最优控制 [J]. 运筹学学报, 2005, 9(4):89-96.
[15] Elijah P. Optimization: Algorithms  and Consistent Approximations [M]. New York: Springer, 1997.
Options
Outlines

/

〈 〉