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Journal Articles Nonlinear Analysis: Real World Applications Year : 2010

Dynamical study and robustness for a nonlinear wastewater treatment model

Abstract

In this work we deal with a wastewater treatment by using the activated sludge process. The problem is formulated as a nonlinear dynamical system. Firstly, we develop the dynamical study of the model when all parameters are well known. Hence, basic properties of invariance and dissipation are established and, under a suitable condition on parameters, a globally asymptotically stable equilibrium point occurs. Secondly, when the bacterium growth function and the substrate concentration in the feed stream are not well known, the robustness analysis provides the existence of an attractor domain to which all trajectories of the system converge. Finally, we prove that we can reduce the size (volume) of this attractor domain by increasing the recycle rate to a maximum fixed level.In this work we deal with a wastewater treatment by using the activated sludge process. The problem is formulated as a nonlinear dynamical system. Firstly, we develop the dynamical study of the model when all parameters are well known. Hence, basic properties of invariance and dissipation are established and, under a suitable condition on parameters, a globally asymptotically stable equilibrium point occurs. Secondly, when the bacterium growth function and the substrate concentration in the feed stream are not well known, the robustness analysis provides the existence of an attractor domain to which all trajectories of the system converge. Finally, we prove that we can reduce the size (volume) of this attractor domain by increasing the recycle rate to a maximum fixed level.

Dates and versions

hal-00847303 , version 1 (23-07-2013)

Identifiers

Cite

Mustapha Serhani, Jean-Luc Gouzé, Nadia Raissi. Dynamical study and robustness for a nonlinear wastewater treatment model. Nonlinear Analysis: Real World Applications, 2010, 12, pp.487-500. ⟨10.1016/j.nonrwa.2010.06.034⟩. ⟨hal-00847303⟩
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