Takagi-Sugeno fuzzy-based approach for modeling and control of an activated sludge process

Wastewater treatment systems have recently taken on new trends resulting from the growing awareness of health and environmental risks. New strategies aimed at the recovery of treated water are increasingly being proposed. Given its better performance, biological treatment via an activated sludge process (ASP) represents the key phase in the overall treatment chain. In this work, a Takagi-Sugeno (TS) fuzzy-based modeling and control approach of an ASP is proposed and successfully carried out for the carbon removal. Using the formalism of linear parameter-varying state-space representation and convex polytopic transformation, a TS fuzzy model of the studied ASP is firstly established. Such a fuzzy model is then used to design advanced control laws that maintain the considered state variables, i.e., volume of the effluent and concentrations of the heterotrophic biomass, biodegradable substrate and dissolved oxygen, at the set-point values. Two stabilization control approaches, namely parallel distributed compensation and static output parallel distributed compensation, are proposed and successfully applied. All these control problems are reformulated as Lyapunov quadratic stability conditions and linear matrix inequality constraints. Demonstrative results are carried out and compared to show the effectiveness and superiority of the proposed TS fuzzy-based control approach of such complex and nonlinear biochemical processes.