Mixed Kalman-Fuzzy Sliding Mode State Observer in Disturbance Rejection Control of a Vibrating Smart Structure

Abstract

In the controllers that are synthesized on a nominal model of a nonlinear plant, the parametric matched uncertainties and nonlinear/unmodelled dynamics of the high order nature can significantly affect the performance of the closed-loop system. On this note, owing to the robust characteristic of the sliding mode observer against modelling perturbations, measurement noise, and unknown disturbances and due to the non-fragile behaviour of the Kalman filter against process noise, a mixed Kalman sliding mode state-observer is proposed and later enhanced by the addition of an intelligent fuzzy agent. In light of the proposed technique, the chattering phenomena and the conservative boundary neighboring layer of the high gain sliding mode observer are addressed. Then, a robust active disturbance rejection controller is developed by using the static feedback of the estimated states using a~direct Lyapunov quadratic stability theorem. The reduced order plant for control design purposes is subjected to some simulated square-integrable disturbances and is assumed to have mismatched uncertainties in the system matrices. Finally, the robust performance of the closed-loop scheme with respect to the mentioned perturbation signals and modelling imperfections is tested by implementing the control system on a mechanical vibrating smart cantilever beam.