Stabilization of an Axially Moving Elastic Tape Under an External Disturbance

This paper considers the stabilization problem of a hybrid system consisting of a linear Euler-Bernoulli beam equation, which describes the motion of a tape moving axially between two sets of rollers, where the mass of the left rollers is taken into account and subject to an external disturbance. The objective of this work is to propose a nonlinear feedback control law to cancel the effect of the uniformly bounded external disturbance located at the left rollers. The well-posedness of the system is proved by the nonlinear maximal-monotone operators theory and the variational principle. Moreover, the exponential stability is established by the Lyapunov approach. Finally, the article concludes by presenting some numerical simulations to illustrate the validity of the theoretical results.