Abstract
We study a nonlinear model of a biological digestion process, involving two microbial populations and two substrates and producing biogas (methane). A feedback control law for asymptotic stabilization of the closed-loop system is proposed. An extremum seeking algorithm is applied to stabilize the system towards the maximum methane flow rate.
This research has been partially supported by the Bulgarian Science Fund under grant Nr. DO 02–359/2008 and by the bilateral project “Variational Analysis and Applications” between the Bulgarian Academy of Sciences and the Izrael Academy of Sciences.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Alcaraz-González, V., Harmand, J., Rapaport, A., Steyer, J., González–Alvarez, V., Pelayo-Ortiz, C.: Software sensors for highly uncertain WWTPs: a new apprach based on interval observers. Water Research 36, 2515–2524 (2002)
Arsie, A., Ebenbauer, C.: Locating omega-limit sets using height functions. Journal of Differential Equations 248(10), 2458–2469 (2010)
Bernard, O., Hadj-Sadok, Z., Dochain, D.: Advanced monitoring and control of anaerobic wastewate treatment plants: dynamic model development and identification. In: Proceedings of Fifth IWA Inter. Symp. WATERMATEX, Gent, Belgium, pp. 3.57–3.64 (2000)
Bernard, O., Hadj-Sadok, Z., Dochain, D., Genovesi, A., Steyer, J.-P.: Dynamical model development and parameter identification for an anaerobic wastewater treatment process. Biotechnology and Bioengineering 75, 424–438 (2001)
Dimitrova, N., Krastanov, M.I.: Nonlinear Adaptive Control of a Model of an Uncertain Fermentation Process. Int. Journ. of Robust and Nonlinear Control 20, 1001–1009 (2010)
El-Hawwary, M.I., Maggiore, M.: A Reduction Principles and the Stabilization of Closed Sets for Passive Systems. arXiv:0907.0686vl [mathOC], 1–25 (2009)
Grognard, F., Bernard, O.: Stability analysis of a wastewater treatment plant with saturated control. Water Science Technology 53, 149–157 (2006)
Hess, J., Bernard, O.: Design and study of a risk management criterion for an unstable anaerobic wastewater treatment process. Journal of Process Control 18(1), 71–79 (2008)
Khalil, H.: Nonlinear Systems. Macmillan Publishing Company, New York (1992)
Maillert, L., Bernard, O.: A simple robust controller to stabilize an anaerobic digestion processes. In: Proc. of the 8th Conference on Computer Applications in Biotechnology, Quebec, pp. 213–218 (2001)
Maillert, L., Bernard, O., Steyer, J.-P.: Robust regulation of anaerobic digestion processes. Water Science and Technology 48(6), 87–94 (2003)
Mischaikow, K., Smith, H., Tieme, H.: Asymptotically autonomous semiflows: chain recurence and Lyapunov functions. TAMS 347(5), 1669–1685 (1995)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dimitrova, N.S., Krastanov, M.I. (2012). On the Asymptotic Stabilization of an Uncertain Bioprocess Model. In: Lirkov, I., Margenov, S., Waśniewski, J. (eds) Large-Scale Scientific Computing. LSSC 2011. Lecture Notes in Computer Science, vol 7116. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29843-1_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-29843-1_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29842-4
Online ISBN: 978-3-642-29843-1
eBook Packages: Computer ScienceComputer Science (R0)