Asymptotic Stabilization of a Flexible Beam with an Attached Mass

TL;DR

This paper analyzes the long-term stability of a flexible beam with an attached mass controlled by piezo actuators, establishing conditions for asymptotic stability using a mathematical model and feedback control.

Contribution

It provides a mathematical framework and sufficient conditions for the asymptotic stability of a beam-mass system with distributed control.

Findings

Precompactness of trajectories established

Sufficient conditions for strong asymptotic stability derived

Mathematical model validated for stability analysis

Abstract

A mathematical model of a simply supported Euler-Bernoulli beam with attached spring-mass system is considered. The model is controlled by distributed piezo actuators and lumped force. We address the issue of asymptotic behavior of solutions of this system driven by a linear feedback law. The precompactness of trajectories is established for the operator formulation of the closed-loop dynamics. Sufficient conditions for strong asymptotic stability of the trivial equilibrium are obtained.