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.
Type de document :
Article dans une revue
Nonlinear Analysis: Real World Applications, Elsevier, 2010, 12, pp.487-500. 〈10.1016/j.nonrwa.2010.06.034〉
Liste complète des métadonnées

https://hal.inria.fr/hal-00847303
Contributeur : Jean-Luc Gouzé <>
Soumis le : mardi 23 juillet 2013 - 11:23:44
Dernière modification le : vendredi 12 janvier 2018 - 01:49:34

Identifiants

Collections

Citation

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

Partager

Métriques

Consultations de la notice

198