Robust observer-based frequency-shaping optimal vibration control of uncertain flexible linkage mechanisms

Abstract

Based on the state-space model of the flexible linkage mechanism equipped with piezoelectric materials, a robust observer-based frequency-shaping optimal feedback (OBFSOF) control methodology is presented for actively suppressing the elastodynamic responses of the high-speed flexible linkage mechanism with linear structured time-varying parameter perturbations. The advantage of the proposed OBFSOF control methodology is that it can make the controlled closed-loop system to obtain both good robustness at high frequencies and good performance at low frequencies. Besides, this paper also presents two robust stability criteria to guarantee that the designed OBFSOF controller can make the controlled flexible linkage mechanism system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Numerical simulation of a slider–crank mechanism example is performed to evaluate the improvement of the elastodynamic responses.