Stabilization of the spatial oscillations of an elastic system model

TL;DR

This paper develops a feedback control method to stabilize the spatial oscillations of an elastic Euler-Bernoulli beam with a tip mass, ensuring strong stability using semigroup theory.

Contribution

It introduces a novel feedback control approach for stabilizing complex elastic systems modeled by PDEs, with a rigorous proof of stability.

Findings

Achieved strong stability of the beam oscillations

Designed a feedback control using Hilbert space methods

Validated the stability through semigroup theory

Abstract

A system of partial differential equations describing the spatial oscillations of an Euler-Bernoulli beam with a tip mass is considered. The linear system considered is actuated by two independent controls and separated into a pair of differential equations in a Hilbert space. A feedback control ensuring strong stability of the equilibrium in the sense of Lyapunov is proposed. The proof of the main result is based on the theory of strongly continuous semigroups.