Robust Kalman-Filter-Based Frequency-Shaping Optimal Active Vibration Control of Uncertain Flexible Mechanical Systems

Abstract

ABSTRACTThis paper presents a time-domain control methodology, which is named as the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method, to treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high frequencies unmodelled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise),and noise uncertainties. Two robust stability conditions are proposed for the flexible mechanical system, which is controlled by a KFBFSOF controller and subject to mode truncation, noise uncertainties, and linear structured time-varying parameter perturbations simultaneously. The advantage of the presented KFBFSOF 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, the proposed robust stability criteria guarantee that the designed KFBFSOF controller can make the controlled flexible mechanical system to avoid the possibilities of both spillover-induced instability and time-varying-parameter-perturbation-induced instability. Two examples are given to illustrate the application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rotor system.