Control of uncertain highly nonlinear biological process based on Takagi–Sugeno fuzzy models

This note deals with the control of uncertain highly nonlinear biological processes. Indeed, an adaptive fuzzy control (AFC) scheme is developed for the pre-treatment of wastewater represented by a Takagi–Sugeno (TS) fuzzy model. The proposed approach uses a fuzzy system to approximate the unknown substrate consumption rate in designing the adaptive controller, and then an observer is designed to estimate the concentration in substrate at the outlet bioreactor. The observer is employed to generate an error signal for the adaptive control law which permits to minimize the influence of the measurement noise on the estimation of the substrate concentration. An update of the fuzzy models parameters are obtained using Lyapunov׳s second method. The closed-loop system behavior is then illustrated on a noisy simulation.