Robust Kalman-filter-based frequency-shaping optimal active vibration control of uncertain flexible mechanical systems

This paper presents a time-domain control methodology, which is named as th e robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) c ontrol method, to treat the active vibration control (or active vibration s uppression) problem of flexible mechanical systems under simultaneously hig h frequencies unmodelled dynamics, residual modes, linear time-varying para meter perturbations in both the controlled and residual parts, noises (inpu t noise and measurement noise), and noise uncertainties. Two robust stabili ty conditions are proposed for the flexible mechanical system, which is con trolled by a KFBFSOF controller and subject to mode truncation, noise uncer tainties, and linear structured time-varying parameter perturbations simult aneously. The advantage of the presented KFBFSOF control methodology is tha t it can make the controlled closed-loop system to obtain both good robustn ess at high frequencies and good performance at low frequencies. Besides, t he proposed robust stability criteria guarantee that the designed KFBFSOF c ontroller can make the controlled flexible mechanical system to avoid the p ossibilities of both spillover-induced instability and time-varying-paramet er-perturbation-induced instability. Two examples are given to illustrate t he application of the presented control methodology to the active vibration control problems of a simply supported flexible beam and of a flexible rot or system.