Vibration control of a flexible varying-length beam attached to a translating base under an unknown boundary disturbance

This paper develops a robust adaptive boundary control scheme for a flexible varying-length beam attached to a translating base in the existence of an unknown boundary disturbance. A mathematical model of the flexible beam systems established via the extended Hamilton principle is introduced. Based on this model, a robust adaptive boundary control is designed by using the Lyapunov design method, wherein the unknown boundary disturbance is estimated by an adaptation law. The control law guarantees that the base approaches to the desired position and the transverse vibration of the beam is suppressed simultaneously. Finally, the superior control performance of the designed control law is shown via simulation results.