# Boundary feedback stabilization of a flexible wing model under unsteady aerodynamic loads

## TL;DR

This paper develops a boundary feedback control method to stabilize a flexible wing model experiencing unsteady aerodynamic loads, ensuring exponential decay of displacements and energy through Lyapunov analysis and simulations.

## Contribution

It introduces a novel boundary stabilization approach for a coupled Euler-Bernoulli and Timoshenko beam model of a flexible wing under unsteady loads.

## Key findings

- System energy decays exponentially under the control scheme
- Boundary control effectively stabilizes bending and twisting displacements
- Simulation results confirm theoretical stability analysis

## Abstract

This paper addresses the boundary stabilization of a flexible wing model, both in bending and twisting displacements, under unsteady aerodynamic loads, and in presence of a store. The wing dynamics is captured by a distributed parameter system as a coupled Euler-Bernoulli and Timoshenko beam model. The problem is tackled in the framework of semigroup theory, and a Lyapunov-based stability analysis is carried out to assess that the system energy, as well as the bending and twisting displacements, decay exponentially to zero. The effectiveness of the proposed boundary control scheme is evaluated based on simulations.