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

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.