Nonlinear stabilizing control of an uncertain bioprocess model

Neli Dimitrova; Mikhail Krastanov

International Journal of Applied Mathematics and Computer Science (2009)

  • Volume: 19, Issue: 3, page 441-454
  • ISSN: 1641-876X

Abstract

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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.

How to cite

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Neli Dimitrova, and Mikhail Krastanov. "Nonlinear stabilizing control of an uncertain bioprocess model." International Journal of Applied Mathematics and Computer Science 19.3 (2009): 441-454. <http://eudml.org/doc/207947>.

@article{NeliDimitrova2009,
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.},
author = {Neli Dimitrova, Mikhail Krastanov},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {wastewater treatment model; local bifurcations of steady states; asymptotic stabilization; extremum seeking; uncertain data},
language = {eng},
number = {3},
pages = {441-454},
title = {Nonlinear stabilizing control of an uncertain bioprocess model},
url = {http://eudml.org/doc/207947},
volume = {19},
year = {2009},
}

TY - JOUR
AU - Neli Dimitrova
AU - Mikhail Krastanov
TI - Nonlinear stabilizing control of an uncertain bioprocess model
JO - International Journal of Applied Mathematics and Computer Science
PY - 2009
VL - 19
IS - 3
SP - 441
EP - 454
AB - 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.
LA - eng
KW - wastewater treatment model; local bifurcations of steady states; asymptotic stabilization; extremum seeking; uncertain data
UR - http://eudml.org/doc/207947
ER -

References

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