Disturbance estimator based output feedback exponential stabilization for Euler–Bernoulli beam equation with boundary control

Abstract

In this paper, we are concerned with the output feedback exponential stabilization problem for a system (plant) described by a one-dimensional Euler–Bernoulli beam equation. The measurements are only the displacement and the angular velocity at the right end. An infinite dimensional estimator is designed to estimate the disturbance. With the estimated disturbance, we propose a state observer that is exponentially convergent to the original system, then design two different kinds of stabilizing controllers: one is based on the velocity feedback, the other is based on the angular velocity feedback. In both cases, by adopting the Riesz basis approach, the exponential stability of the closed-loop systems is built with guaranteeing that all internal systems are uniformly bounded. The numerical experiments are carried out to illustrate the theoretical results.