Remote Vibration Control for Flexible Beams Subject to Harmonic Disturbances

Abstract

A low-order control algorithm is developed to regulate an infinitely dimensional flexible beam subject to nondecaying, harmonic disturbances of known frequency. The control input is applied at the boundary while the output of concern is at the opposite end of the flexible structure. Only local displacement and velocity at the boundary are required in the control algorithm, which emulates the behavior of a set of mechanical spring, mass, and damper. A virtual spring is integrated with the structure flexibility to establish an internal model for the external disturbance. Such a virtual passive algorithm ensures stability in the presence of structural and parameter uncertainties. It is shown that, by properly choosing the control gains, the output tends to a standstill while the other parts of the system oscillate in such a way as to counteract the harmonic disturbance.