In this paper, we present a time-domain control methodology, called the robust Kalman-filter-based frequency-shaping optimal feedback (KFBFSOF) control method. Using this method, we treat the active vibration control (or active vibration suppression) problem of flexible mechanical systems under simultaneously high-frequency unmodeled dynamics, residual modes, linear time-varying parameter perturbations in both the controlled and residual parts, noises (input noise and measurement noise), noise uncertainties and actuator nonlinearities. 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, actuator nonlinearities 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 have 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 avoid the possibilities of instability induced by both spillover and time-varying parameter perturbations. 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.
