Rapid Stabilization of Timoshenko Beam by PDE Backstepping

• 成果类型: Article
• 署名作者: Chen, Guangwei; Vazquez, Rafael; Krstic, Miroslav
• 署名单位: Beijing University of Technology; University of Sevilla; University of California System; University of California San Diego
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3276748
• 发表日期: 2024
• 页码: 1141-1148
• 关键词: Boundary control; Distributed parameter systems; hyperbolic systems; PDE backstepping; Timoshenko beam

摘要

In this article, we present rapid boundary stabilization of a Timoshenko beam with antidamping and antistiffness at the uncontrolled boundary, by using infinite-dimensional backstepping. We introduce a Riemann transformation to map the Timoshenko beam states into a set of coordinates that verify a 1-D hyperbolic PIDE-ODE system. Then backstepping is applied to obtain a control law guaranteeing closed-loop stability of the origin in the $L<^>{2}$ sense. Arbitrarily rapid stabilization can be achieved by adjusting control parameters, and has not been achieved in previous results. Finally, a numerical simulation shows the effectiveness of the proposed controller. This result extends a previous work which considered a slender Timoshenko beam with Kelvin-Voigt damping, by allowing destabilizing boundary conditions at the uncontrolled boundary and attaining an arbitrarily rapid convergence rate.