Dynamical study and robustness for a nonlinear wastewater treatment model (Q611272)

The paper considers a nonlinear dynamical system which is used to model the wastewater treatment by using the activated sludge process in a depuration station. The principle of the model is as follows: the wastewater is discharged into an aerator. Here, the oxidation of the polluted water (considered as being the substrate in the model) begins by blending a bacterial population in an aerobic reaction consuming the oxygen. Due to gravity, the solid components will settle down and will concentrate at the bottom. The sedimentation of the soluble organic matter is neglected. A part of the bacteria biomass is recycled into the aerator in order to stimulate the oxidation. By using reaction kinetics, the authors derive a system of ODEs that models this process and perform a dynamical study of this system in two cases: when all the parameters of the model are known and the case when some of them are not a priori known. In the case when all the parameters of the model are known, a positively invariant set is obtained. Also, the existence and local stability of equilibria is investigated, showing that, under some condition upon the parameters, there exists a global asymptotically stable equilibrium point. If some of the parameters of the model are not known (e.g., the bacterium growth function and the substrate concentration in the feed stream), then a robustness analysis is performed, providing the existence of an attractor domain for the trajectories of the dynamical system. In the final part of the paper it is shown that the size of the attractor domain can be reduced through the increase of the recycle rate to a maximum fixed level.