Rapid Stabilization of Timoshenko Beam by PDE Backstepping
Abstract
In this paper, we present a rapid boundary stabilization of a Timoshenko beam with anti-damping and anti-stiffness at the uncontrolled boundary, by using PDE backstepping. We introduce a transformation to map the Timoshenko beam states into a (2+2) x (2+2) hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the H^1 sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters. Finally, a numerical simulation shows that the proposed controller can rapidly stabilize the Timoshenko beam. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate.
Keywords
Cite
@article{arxiv.2207.04746,
title = {Rapid Stabilization of Timoshenko Beam by PDE Backstepping},
author = {Guangwei Chen and Rafael Vazquez and Miroslav Krstic},
journal= {arXiv preprint arXiv:2207.04746},
year = {2022}
}
Comments
paper submitted to IEEE Transactions on Automatic Control