Active Vibration Control of the Axially Moving String by Wave Cancellation

Abstract

Active vibration control of an axially moving string by wave cancellation is presented. The control problem is formulated in the frequency domain. An exact, closed-form expression for the transfer function of the controlled system, consisting of the flexible structure, a feedback control law and the dynamics of the sensing and actuation devices, is derived. It is shown that all vibration modes can be stabilized and that the controlled system has no resonance. Moreover, the designed controller is applicable to the control of the string transverse vibration under various kinds of loading and constraint conditions. Results for the response of the controlled string under different excitations are presented and discussed along with the wave propagation and cancellation characteristics.