2015, 5(4): 359-368. doi: 10.3934/naco.2015.5.359

Modeling and identification of hybrid dynamic system in microbial continuous fermentation

1. 

School of Mathematical Sciences, Inner Mongolia University, 235 West Daxue Road, Hohhot 010021, China, China, China, China

Received  January 2015 Revised  October 2015 Published  October 2015

In this paper, a hybrid dynamic model using fuzzy expert system is investigated in the process of glycerol bioconversion to 1,3-PD by Klebsiella pneumoniae(K.pneumoniae). In continuous culture, we assume that 1,3-PD passes the cell membrane of K.pneumoniae by passive diffusion coupling with active transport. To determine the parameters of the proposed system, a parameter identification model is established according to the biological robustness. An optimization algorithm is developed in order to solve the identification model. Numerical simulations indicate that proposed hybrid model adding fuzzy system is more appropriate and the optimization algorithm is effective.
Citation: Yanan Mao, Caixia Gao, Ruidong Yan, Aruna Bai. Modeling and identification of hybrid dynamic system in microbial continuous fermentation. Numerical Algebra, Control & Optimization, 2015, 5 (4) : 359-368. doi: 10.3934/naco.2015.5.359
References:
[1]

G. M. Cheng, L. Wang, R. C. Loxton and Q. Lin, Robust optimal control of a microbial batch culture process,, J. Optim. Theory. Appl., 167 (2015), 342.  doi: 10.1007/s10957-014-0654-z.  Google Scholar

[2]

C. Gao, E. Feng and Z. Wang, Nonlinear dynamical systems of biodissimilation of glycerol to 1,3-propanediol and their optimal controls,, Journal of Industrial and Management Optimization, 1 (2005), 377.  doi: 10.3934/jimo.2005.1.377.  Google Scholar

[3]

C. Gao, E. Feng, Z. Wang and Z. Xiu, Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures,, Applied Mathematics and Computation, 169 (2005), 476.  doi: 10.1016/j.amc.2004.10.048.  Google Scholar

[4]

J. Gao, L. Wang, E. Feng and Z. Xiu, Modeling and identification of microbial batch fermentation using fuzzy expert system,, Applied Mathematical Modelling, 37 (2013), 8079.  doi: 10.1016/j.apm.2013.02.042.  Google Scholar

[5]

C. Liu, Z. Gong, E. Feng and H. Yin, Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture,, J. Ind. Manag. Optim, 5 (2009), 835.  doi: 10.3934/jimo.2009.5.835.  Google Scholar

[6]

C. Liu, Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process,, Applied Mathematical Modelling, 38 (2014), 1448.  doi: 10.1016/j.apm.2013.07.039.  Google Scholar

[7]

Y. Sun, W. Qi, H. Teng, Z. Xiu and A. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: Concerning enzymecatalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane,, Biochemical Engineering Journal, 38 (2008), 22.   Google Scholar

[8]

G. Wang, E. Feng and Z. L. Xiu, Nonlinear hybrid kinetic system of microbial bioconversion in fed-batch culture,, Nonlinear Analysis: Hybrid System, 2 (2008), 65.  doi: 10.1016/j.nahs.2007.01.006.  Google Scholar

[9]

J. Wang, J. Ye, E. Feng, H. C. Yin and B. Tan, Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness,, Nonlinear Analysis: Hybrid System, 5 (2011), 102.  doi: 10.1016/j.nahs.2010.10.002.  Google Scholar

[10]

L. Wang, Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness,, Bioprocess Biosyst. Eng., 36 (2013), 433.   Google Scholar

[11]

L. Wang, G. Cheng, E. Feng, T. Su and Z. Xiu, Analysis and application of biological robustness as performance index in microbial fermentation,, Applied Mathematical Modelling, 39 (2015), 2048.  doi: 10.1016/j.apm.2014.10.022.  Google Scholar

[12]

Z. Xiu, B. Song, Z. Wang, L. Sun, E. Feng and A. Zeng, Optimization of biodissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae in one-stage and two-stage anaerobic cultures,, Biochem. Eng. J., 19 (2004), 189.   Google Scholar

[13]

Z. Xiu, A. Zeng and L. An, Mathematical modelling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol,, Journal of Dalian University of Technology, 40 (2000), 428.   Google Scholar

[14]

J. Ye, E. Feng, L. Wang, Z. Xiu and Y. Sun, Modeling and Robustness Analysis of Biochemical Networks of Glycerol Metabolism by Klebsiella Pneumoniae,, Lecture Notes of the Institute for Computer Sciences, 4 (2009), 446.   Google Scholar

[15]

A. Zeng and W. Deckwer, Kinetic model for substrate and energy consumption of microbial growth under substrate-sufficient condition,, Biotechnology Progress, 11 (1995), 71.   Google Scholar

[16]

A. Zeng, A. Rose, H. Biebl, C. Tag, B. Guenzel and W. D. Deckwer, Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in glycerol fermentation,, Biotechnology and Bioengineering, 44 (1994), 902.   Google Scholar

[17]

J. Zhai and J. Ye, Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture,, Nonlinear Analysis:Real World Applications, 12 (2011), 2730.  doi: 10.1016/j.nonrwa.2011.03.018.  Google Scholar

show all references

References:
[1]

G. M. Cheng, L. Wang, R. C. Loxton and Q. Lin, Robust optimal control of a microbial batch culture process,, J. Optim. Theory. Appl., 167 (2015), 342.  doi: 10.1007/s10957-014-0654-z.  Google Scholar

[2]

C. Gao, E. Feng and Z. Wang, Nonlinear dynamical systems of biodissimilation of glycerol to 1,3-propanediol and their optimal controls,, Journal of Industrial and Management Optimization, 1 (2005), 377.  doi: 10.3934/jimo.2005.1.377.  Google Scholar

[3]

C. Gao, E. Feng, Z. Wang and Z. Xiu, Parameters identification problem of the nonlinear dynamical system in microbial continuous cultures,, Applied Mathematics and Computation, 169 (2005), 476.  doi: 10.1016/j.amc.2004.10.048.  Google Scholar

[4]

J. Gao, L. Wang, E. Feng and Z. Xiu, Modeling and identification of microbial batch fermentation using fuzzy expert system,, Applied Mathematical Modelling, 37 (2013), 8079.  doi: 10.1016/j.apm.2013.02.042.  Google Scholar

[5]

C. Liu, Z. Gong, E. Feng and H. Yin, Modelling and optimal control for nonlinear multistage dynamical system of microbial fed-batch culture,, J. Ind. Manag. Optim, 5 (2009), 835.  doi: 10.3934/jimo.2009.5.835.  Google Scholar

[6]

C. Liu, Sensitivity analysis and parameter identification for a nonlinear time-delay system in microbial fed-batch process,, Applied Mathematical Modelling, 38 (2014), 1448.  doi: 10.1016/j.apm.2013.07.039.  Google Scholar

[7]

Y. Sun, W. Qi, H. Teng, Z. Xiu and A. Zeng, Mathematical modeling of glycerol fermentation by Klebsiella pneumoniae: Concerning enzymecatalytic reductive pathway and transport of glycerol and 1,3-propanediol across cell membrane,, Biochemical Engineering Journal, 38 (2008), 22.   Google Scholar

[8]

G. Wang, E. Feng and Z. L. Xiu, Nonlinear hybrid kinetic system of microbial bioconversion in fed-batch culture,, Nonlinear Analysis: Hybrid System, 2 (2008), 65.  doi: 10.1016/j.nahs.2007.01.006.  Google Scholar

[9]

J. Wang, J. Ye, E. Feng, H. C. Yin and B. Tan, Complex metabolic network of glycerol fermentation by Klebsiella pneumoniae and its system identification via biological robustness,, Nonlinear Analysis: Hybrid System, 5 (2011), 102.  doi: 10.1016/j.nahs.2010.10.002.  Google Scholar

[10]

L. Wang, Determining the transport mechanism of an enzyme-catalytic complex metabolic network based on biological robustness,, Bioprocess Biosyst. Eng., 36 (2013), 433.   Google Scholar

[11]

L. Wang, G. Cheng, E. Feng, T. Su and Z. Xiu, Analysis and application of biological robustness as performance index in microbial fermentation,, Applied Mathematical Modelling, 39 (2015), 2048.  doi: 10.1016/j.apm.2014.10.022.  Google Scholar

[12]

Z. Xiu, B. Song, Z. Wang, L. Sun, E. Feng and A. Zeng, Optimization of biodissimilation of glycerol to 1,3-propanediol by Klebsiella pneumoniae in one-stage and two-stage anaerobic cultures,, Biochem. Eng. J., 19 (2004), 189.   Google Scholar

[13]

Z. Xiu, A. Zeng and L. An, Mathematical modelling of kinetics and research on multiplicity of glycerol bioconversion to 1,3-propanediol,, Journal of Dalian University of Technology, 40 (2000), 428.   Google Scholar

[14]

J. Ye, E. Feng, L. Wang, Z. Xiu and Y. Sun, Modeling and Robustness Analysis of Biochemical Networks of Glycerol Metabolism by Klebsiella Pneumoniae,, Lecture Notes of the Institute for Computer Sciences, 4 (2009), 446.   Google Scholar

[15]

A. Zeng and W. Deckwer, Kinetic model for substrate and energy consumption of microbial growth under substrate-sufficient condition,, Biotechnology Progress, 11 (1995), 71.   Google Scholar

[16]

A. Zeng, A. Rose, H. Biebl, C. Tag, B. Guenzel and W. D. Deckwer, Multiple product inhibition and growth modeling of Clostridium butyricum and Klebsiella pneumoniae in glycerol fermentation,, Biotechnology and Bioengineering, 44 (1994), 902.   Google Scholar

[17]

J. Zhai and J. Ye, Pathway identification using parallel optimization for a complex metabolic system in microbial continuous culture,, Nonlinear Analysis:Real World Applications, 12 (2011), 2730.  doi: 10.1016/j.nonrwa.2011.03.018.  Google Scholar

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