Stabilization of an Euler-Bernoulli beam system with a tip mass subject to non-uniform bounded disturbance

We consider the stabilization problem of an Euler-Bernoulli beam with tip mass, which undergoes non-uniform bounded disturbance. We employ the idea of active disturbance rejection control to design a disturbance estimator that has a time-varying gain of exponential-type, and design a feedback controller, in which the estimate of disturbance is used to cancel the effect of disturbance. We apply the semigroup theory to prove the well-posedness of the resulting closed system. We prove the exponential stability of the closed loop system by the Lyapunov function approach. Some numerical simulations are given to support these results.