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

✍ Scribed by Erwin Hernández; Dante Kalise; Enrique Otárola

Publisher
Elsevier Science
Year
2011
Tongue
English
Weight
515 KB
Volume
235
Category
Article
ISSN
0377-0427

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✦ Synopsis

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.

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