A locking-free scheme for the LQR control of a Timoshenko beam

作者：Hernandez Erwin^*; Kalise Dante; Otarola Enrique

来源：Journal of Computational and Applied Mathematics, 2011, 235(5): 1383-1393.

DOI：10.1016/j.cam.2010.08.025

• Optimal control
• Finite element method
• Timoshenko beam
• Error estimates
• Feedback control

In this paper we analyze a locking-free numerical scheme for the LQR control of a Timoshenko beam. We consider a non-conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension. To solve the LQR problem we seek a feedback control which depends on the solution of an algebraic Riccati equation. An optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems. This estimate is valid with constants that do not depend on the thickness of the beam, which leads to the conclusion that the method is locking-free. In order to assess the performance of the method, numerical tests are reported and discussed.

• 出版日期2011-1-1