Stabilization for a Flexible Beam with Tip Mass and Control Matched Disturbance

TL;DR

This paper develops an output feedback control method for stabilizing a flexible beam with tip mass, using minimal measurements and disturbance estimation, improving previous results by reducing measurement requirements and handling disturbances.

Contribution

It introduces an infinite-dimensional observer and disturbance estimator for exponential stabilization with fewer measurements and disturbance handling.

Findings

Exponential stabilization with one measurement without disturbance.

Effective disturbance estimation and compensation in real-time.

Simulation results demonstrating stabilization performance.

Abstract

This paper is concerned with the output feedback exponential stabilization for a flexible beam with tip mass. When there is no disturbance, it is shown that only one non-collocated measurement is enough to exponentially stabilize the original system by constructing an infinite-dimensional Luenberger state observer to track the state and designing an estimated state based output feedback control law. This essentially improves the existence result in [F. Conrad and O. M\"{o}rg\"{u}l, SIAM J. Control Optim., 36 (1998), 1962-1986] where two collocated measurements including high order feedback were adopted. In the case that boundary internal uncertainty and external disturbance are considered, an infinite-dimensional disturbance estimator is constructed to estimate the state and total disturbance in real time. By virtue of the estimated state and estimated total disturbance, an output feedback control law is designed to exponentially stabilize the original system while guaranteeing the boundedness of the closed-loop system. Some illustration simulations are presented.