Vibration attenuation of a flexible beam mounted on a rotating compliant hub

This study considers the problem of attenuating the vibration of a slender flexible beam mounted on a compliant rotating hub without the need for sensor(s) placement at the beam. A modal state-space model of the beam-hub system dynamics is constructed from the first ten modes of vibration of the system. A reduced-order optimal observer is utilized to estimate the deflection of the beam tip from measurements of the horizontal and vertical deflections of the hub. Two orthogonal actuators are used to manipulate the hub such that the relative motion between the hub and the tip of the beam is minimized. Hence, the demand on the control effort is to force the beam tip and the hub to vibrate as a rigid body. The horizontal control effort is a function of the difference between the measured horizontal hub deflection and the estimated horizontal tip deflection, and the same is true for the vertical control effort. Simulation of the proposed control strategy is carried out and the results are presented.