Rapid Boundary Stabilization of Two-Dimensional Elastic Plates with In-Domain Aeroelastic Instabilities

TL;DR

This paper develops a rapid boundary stabilization method for 2D elastic plates with in-domain aeroelastic instabilities, enabling arbitrary decay rates and effective suppression of flow-induced vibrations through PDE backstepping and observer design.

Contribution

It introduces a novel boundary control and observer design for 2D PDE models of elastic plates with aeroelastic instabilities, allowing arbitrary decay rate tuning.

Findings

Exponential stability achieved with tunable decay rate.

Effective suppression of flow-induced vibrations demonstrated.

Boundary feedback control successfully stabilizes the 2D elastic plate.

Abstract

Motivated by active wing flutter suppression in high-Mach-number flight, this paper presents a rapid boundary stabilization strategy for a two-dimensional PDE-modeled elastic plate with in-domain instabilities, where the exponential stability is achieved with a decay rate that can be arbitrarily assigned by the users. First, the aeroelastic system is modeled as two-dimensional coupled wave PDEs with internal anti-damping terms, derived by Piston theory and Hamilton's principle. Using Fourier series expansion, the 2-D problem is decomposed into a large-scale 1-D system, based on which full-state boundary feedback control is designed via PDE backstepping transformation. To enable output-feedback implementation, a state observer is further designed to estimate the distributed states over the two-dimensional spatial domain using the available boundary measurements. Through Lyapunov analysis, the exponential stability of the 2-D elastic plate PDE under the proposed boundary control is established with a designer-tunable decay rate. Numerical simulations verify the effectiveness of the control strategy in suppressing flow-induced vibrations in a 2-D elastic plate.