×

Recursive parameter identification for fermentation processes with the multiple model technique. (English) Zbl 1243.93072

Summary: This paper considers parameter identification problems for a fermentation process. Since the fermentation process is nonlinear, it is difficult to use a single-model for describing such a process and thus we use the multiple model technique to study the identification methods. The basic idea is to establish the model of the fermentation process at each operation point by means of the least squares principle, to obtain multiple models with different points, and then use the weighting functions or interpolation methods to compute the total model or the global model. Finally, a numerical example is provided to test the effectiveness of the proposed algorithm.

MSC:

93C95 Application models in control theory
93E12 Identification in stochastic control theory
92C40 Biochemistry, molecular biology
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Xiao, Y.S.; Ding, F.; Zhou, Y.; Li, M.; Dai, J.Y., On consistency of recursive least squares identification algorithms for controlled auto-regression models, Appl. math. model., 32, 11, 2207-2215, (2008) · Zbl 1156.93411
[2] Ding, J.; Han, L.L.; Chen, X.M., Time series AR modeling with missing observations based on the polynomial transformation, Math. comput. model., 51, 5-6, 527-536, (2010) · Zbl 1190.62157
[3] Zhang, Y.; Cui, G.M., Bias compensation methods for stochastic systems with colored noise, Appl. math. model., 35, 4, 1709-1716, (2011) · Zbl 1217.93163
[4] Han, L.L.; Sheng, J.; Ding, F.; Shi, Y., Auxiliary models based recursive least squares identification for multirate multi-input systems, Math. comput. model., 50, 7-8, 1100-1106, (2009) · Zbl 1185.93139
[5] Kertes, A.S.; King, C.J., Extraction chemistry of fermentation product carboxylic acids, Biotechnol. bioeng., 103, 3, 431-445, (2009)
[6] Stanton, C.; Ross, R.P.; Fitzgerald, G.F.; Sinderen, D.V., Fermented functional foods based on probiotics and their biogenic metabolites, Curr. opinion biotechnol., 16, 2, 198-203, (2005)
[7] Ding, F.; Liu, P.X.; Liu, G., Identification methods for Hammerstein nonlinear systems, Digital signal process., 21, 2, 215-238, (2011)
[8] Wang, D.Q.; Ding, F., Least squares based and gradient based iterative identification for Wiener nonlinear systems, Signal process., 91, 5, 1182-1189, (2011) · Zbl 1219.94052
[9] Ding, F.; Shi, Y.; Chen, T., Auxiliary model based least-squares identification methods for Hammerstein output-error systems, Syst. control lett., 56, 5, 373-380, (2007) · Zbl 1130.93055
[10] Wang, D.Q.; Ding, F., Extended stochastic gradient identification algorithms for hammerstein – wiener ARMAX systems, Comput. math. appl., 56, 12, 3157-3164, (2008) · Zbl 1165.65308
[11] Bailey, J.E.; Ollis, D.F., Biochemical engineering fundamental, (1986), McGraw-Hill New York
[12] Li, C.C., Mathematical models of ethanol inhibition effects during alcohol fermentation, Nonlinear anal. theory methods appl., 71, 12, 1608-1619, (2009)
[13] Phisalaphong, M.; Srirattana, N.; Tanthapanichakoon, W., Mathematical modeling to investigate temperature effect on kinetic parameters of ethanol fermentation, Biochem. eng. J., 28, 1, 36-43, (2006)
[14] Sriyudthsak, K.; Shiraishi, F., Investigation of the performance of fermentation processes using a mathematical model including effects of metabolic bottleneck and toxic product on cells, Math. biosci., 228, 1, 1-9, (2010) · Zbl 1200.92016
[15] Malik, M.B.; Salman, M., State-space least Mean square, Digital signal process., 18, 3, 334-345, (2008)
[16] James, C., Total least squares, matrix enhancement, and signal processing, Digital signal processing, 4, 1, 21-39, (1994)
[17] Smith, R.M., Multiple model approaches to modeling and control, (1997), Taylor and Francis London
[18] Bajpai, R.K.; Reuß, M., A mechanistic model for penicillin production, J. chem. technol. biotechnol., 30, 330-344, (1980)
[19] Nestaas, E.; Wang, D.I.C., Computer control of the penicillin fermentation using the filtration probe in conjunction with a structured process model, Biotechnol. bioeng., 25, 3, 781-796, (1983)
[20] Heijnen, J.J.; Roels, J.A.; Stouthamer, A.H., Application of balancing methods in modeling the penicillin fermentation, Biotechnol. bioeng., 21, 12, 2175-2201, (1979)
[21] Birol, G.; Ündey, C.; Parulekar, S.J.; Cinar, A., A morphologically structured model for penicillin production, Biotechnol. bioeng., 77, 5, 538-552, (2002)
[22] Birol, G.; Ündey, C.; Cinar, A., A modular simulation package for feed-batch fermentation: penicillin production, Comput. chem. eng., 26, 11, 1553-1565, (2002)
[23] Lee, J.M.; Yoo, C.K.; Lee, I.B., On-line batch process monitoring using a consecutively updated multiway principal component analysis model, Comput. chem. eng., 27, 12, 1903-1912, (2003)
[24] Lee, J.M.; Yoo, C.K.; Lee, I.B., Fault detection of batch processes using multiway kernel principal component analysis, Comput. chem. eng., 28, 9, 1837-1847, (2004)
[25] Kadlec, R.; Grbić, R.; Gabrys, B., Review of adaptation mechanisms for data-driven soft sensors, Comput. chem. eng., 35, 1, 1-24, (2011)
[26] Ding, F.; Liu, P.X.; Liu, G., Gradient based and least-squares based iterative identification methods for OE and OEMA systems, Digital signal process., 20, 3, 664-677, (2010)
[27] Ding, F.; Liu, P.X.; Liu, G., Auxiliary model based multi-innovation extended stochastic gradient parameter estimation with colored measurement noises, Signal process., 89, 10, 1883-1890, (2009) · Zbl 1178.94137
[28] Ding, F.; Liu, G.; Liu, X.P., Parameter estimation with scarce measurements, Automatica, 47, 8, 1646-1655, (2011) · Zbl 1232.62043
[29] Ding, F.; Ding, J., Least squares parameter estimation with irregularly missing data, Int. J. adaptive control signal process., 24, 7, 540-553, (2010) · Zbl 1200.93130
[30] Y.C. Zhu, Z.H. Xu, A method of LPV model identification for control, in: 17th IFAC World Congress, July 6-11, Seoul, Korea, 2008, pp. 5018-5023.
[31] Xu, Z.H.; Zhao, J.; Qian, J.X.; Zhu, Y.C., Nonlinear MPC using an identified LPV model, Ind. eng. chem. res., 48, 6, 3043-3051, (2009)
[32] Aguado, D.; Ribes, J.; Montoya, T.; Ferrera, J.; Seco, A., A methodology for sequencing batch reactor identification with artificial neural networks: a case study, Comput. chem. eng., 33, 2, 465-472, (2009)
[33] Gong, Z.H., A multistage system of microbial fed-batch fermentation and its parameter identification, Math. comput. simul., 80, 9, 1903-1910, (2010) · Zbl 1194.37174
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.