Robust Fuzzy Tracking Control For An Activated Sludge Process

Abstract

In this work we are interested in a tracking problem with reference model. A robust fuzzy controller is designed for the regulation of the pollutant substrate and the dissolved oxygen concentrations inside an activated sludge process. The process is described by Takagie-Sugeno fuzzy model obtained from the nonlinear mass-balance model. An observer is considered for the on-line estimation of the unavailable biological states using the dissolved oxygen concentration as unique measurable. The control law is based on the Parallel Distributed Compensation formulation and is combined with a robust Takagie-Sugeno fuzzy observer. The stability of the entire system for both the observer and the controller is then discussed using Lyapunov theory to guarantee tracking performance of the closed loop system. Using the $H_{\infty}$ norm, new sufficient conditions to develop the fuzzy controller is obtained and given in terms of linear matrix inequalities. The efficiency and the robustness of the control scheme is demonstrated via simulations.