Nonlinear stabilizing control of an uncertain bioprocess model

• Autorzy: Neli Dimitrova , Mikhail Krastanov
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.

Słowa kluczowe

EN

wastewater treatment model; local bifurcations of steady states; asymptotic stabilization; extremum seeking; uncertain data

• Wydawca: University of Zielona Gora Press
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2009
• Tom: 19
• Numer: 3
• Strony: 441-454

Daty

wydano

2009

otrzymano

2008-09-11

poprawiono

2009-02-09

Twórcy

autor

Neli Dimitrova

• Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria

autor

Mikhail Krastanov

• Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria

Bibliografia

• Alcaraz-González, V., Harmand, J., Rapaport, A., Steyer, J.-P. and Pelayo-Ortiz, C. (2002). Software sensors for highly uncertain WWTPs: A new apprach based on interval observers, Water Research 36(10): 2515-2524.
• Antonelli, R., Harmand, J., Steyer, J.-P. and Astolfi, A. (2003). Set-point regulation of an anaerobic digestion process with bounded output feedback, IEEE Transactions on Control Systems Technology 11(4): 495-504.
• Bastin, G. and Dochain, D. (1990). On-line Estimation and Adaptive Control of Bioreactors, Elsevier Science, New York, NY.
• Bernard, O., Hadj-Sadok, Z. and Dochain, D. (2000). Advanced monitoring and control of anaerobic wastewater treatment plants: Dynamic model development and identification, Proceedings of the 5th IWA International Symposium WATERMATEX 2000, Gent, Belgium, pp. 3.57-3.64.
• Bernard, O., Hadj-Sadok, Z., Dochain, D., Genovesi, A. and Steyer, J.-P. (2001). Dynamical model development and parameter identification for an anaerobic wastewater treatment process, Biotechnology and Bioengineering 75(4): 424-438.
• Carr, J. (1981). Applications of Centre Manifold Theory, Applied Mathematical Science, Vol. 35, Springer, New York, NY, Heidelberg/Berlin.
• Clarke, F., Ledyaev, Yu., Stern, R. and Wolenski P. (1998). Nonsmooth Analysis and Control Theory, Graduate Text in Mathematics, Vol. 178, Springer, Berlin.
• Dimitrova, N. and Krastanov, M. I. (2006). Nonlinear adaptive control of an uncertain wastewater treatment model, IEEE Proceedings of the 12th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, Duisburg, Germany, p.11.
• Filippov, A. F. (1988). Differential Equations with Discontinuous Right-hand Sides, Mathematics and Its Applications: Soviet Series, Vol. 18, Kluwer Academic Publishers, Dordrecht.
• Grognard, F. and Bernard, O. (2006). Stability analysis of a wastewater treatment plant with saturated control, Water Science Technology 53(1): 149-157.
• Harmand, J., Rapaport, A. and Trofino, A. (2003). Optimal design of a series of two reactors-Some new results, American Institute of Chemical Engineering Journal 49(6): 1433-1450.
• Heinzle, E., Dunn, I. J. and Ryhiner, G. B. (1993). Modelling and control for anaerobic wastewater treatment, Advances in Biochemical Engineering and Biotechnology 48: 79-114.
• Hess, J. and Bernard, O. (2008). Design and study of a risk management criterion for an unstable anaerobic wastewater treatment process, Journal of Process Control 18(1):71-79.
• Karmanov, V. (2000). Mathematical Programming, FIZMATLIT, Moscow, (in Russian).
• Khalil, H. K. (1992). Nonlinear Systems, Macmillan Publishing Company, New York, NY.
• Maillert, L., Bernard, O. and Steyer, J.-P. (2004). Nonlinear adaptive control for bioreactors with unknown kinetics, Automatica 40(8): 1379-1385.
• Marcos, N. I., Guay, M., Dochain, D. and Zhang, T. (2004). Adaptive extremum-seeking control of a continuous stirred tank bioreactor with Haldane's kinetics, Journal of Process Control 14(3): 317-328.
• Schoefs, O., Dochain, D., Fibrianto, H. and Steyer, J.-P. (2003). Modelling and identification of a distributedparameter system for an anaerobic wastewater treatment process, Chemical Engineering Research and Design 81(A9): 1279-1288.
• Simeonov, I. (1994). Modelling and control of anaerobic digestion of organic waste, Chemical and Biochemical Engineering Quaterly 8(2): 45-52.
• Simeonov, I. (1999). Mathematical modelling and parameter estimation of anaerobic fermentation processes, Bioprocess Engineering 21(4): 377-381.
• Simeonov, I., Noykova, N. and Stoyanov, S. (2004). Modelling and extremum seeking control of the anaerobic digestion, Proceedings of the International IFAC Workshop DECOMTT, Bansko, Bulgaria, pp. 289-294.
• Simeonov, I., Noykova, N. and Gyllenberg, M. (2007). Identification and extremum seeking control of the anaerobic digestion of organic wastes, Cybernetics and Information Technologies 7(2): 73-84.
• Wang, H.-H., Krstic, M. and Bastin, G. (1999). Optimizing bioreactors by extremum seeking, International Journal of Adaptive Control and Signal Processing 13(8): 651-669.
• Wiggins, S. (1990). Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, New York, NY.

Identyfikatory

DOI

10.2478/v10006-009-0036-0