Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

Authors:
Neli Dimitrova;Mikhail Krastanov
Affiliations:
Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria;Department of Biomathematics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Acad. G. Bonchev str., bl. 8, 1113 Sofia, Bulgaria
Venue:
International Journal of Applied Mathematics and Computer Science - Verified Methods: Applications in Medicine and Engineering
Year:
2009

Citing 4
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Abstract

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.