Vibration control of an axially moving beam attached to a translating base

In this paper, the control problem of an Euler-Bernoulli beam attached to a translating base is addressed, in which the beam’s length is varying, and the large-amplitude vibration is considered. Based on the extended Hamilton principle, the mathematical model describing the system’s dynamic is established. A boundary control law is proposed to control the base’s position and simultaneously suppress the beam’s vibration. Analysis of the Lyapunov function candidate proved that the closed-loop system with the designed control law is stable exponentially. Finally, the impressive effectiveness of the designed control law is shown via numerical simulations.