Stabilization of a string with two rigid loads: application of optimal feedback gain based on a finite difference approximation

Authors:
Hideki Sano
Affiliations:
Kagoshima University, Computing and Communications Center, Korimoto, Kagoshima, Japan
Venue:
MATH'08 Proceedings of the 13th WSEAS international conference on Applied mathematics
Year:
2008

Citing 4
Cited 0

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Abstract

This paper is concerned with the problem of stabilizing a string with two rigid loads which is described by two kinds of hyperbolic equations. In our previous work, a control law that made an energy function of the system non-increasing was derived, and the asymptotic stability of the closed-loop system with the controller was proved by using the LaSalle's invariance principle. Moreover, a simplified lumped parameter model was considered in connection with the string with two rigid loads, and the design method to determine an optimal feedback gain for the model was proposed. In this paper, it is shown that the controller with an optimal gain based on a finite differnce approximation works more effectively for the original system through numerical simulations.