Vibration control of a spinning disk

Abstract

An active control scheme based on the transfer function model is proposed to suppress the vibration of a disk spinning both in the sub- and super-critical speed ranges. The feedback controller consists of a space-fixed point sensor and a point actuator, which are not on any nodal circle of the freely spinning disk. The point sensor can measure both the displacement and the pitching slope of the spinning disk. In the sub-critical speed range, a controller measuring the displacement information alone works well in suppressing the disk vibration. However, such a controller is not only unable to suppress the disk vibration in the super-critical speed range, it may destabilize the spinning disk instead. In order to control a disk in the super-critical speed range, a controller using both the displacement and slope information is proposed. The range of the control gain parameter which renders the spinning disk asymptotically stable can be determined by a stability analysis. The success of such a controller is demonstrated via numerical simulations.