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Stabilization of the Ball on the Beam System by Means of the Inverse Lyapunov Approach

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  • Carlos Aguilar-Ibañez
  • Miguel S. Suarez-Castanon
  • José de Jesús Rubio

Abstract

A novel inverse Lyapunov approach in conjunction with the energy shaping technique is applied to derive a stabilizing controller for the ball on the beam system. The proposed strategy consists of shaping a candidate Lyapunov function as if it were an inverse stability problem. To this purpose, we fix a suitable dissipation function of the unknown energy function, with the property that the selected dissipation divides the corresponding time derivative of the candidate Lyapunov function. Afterwards, the stabilizing controller is directly obtained from the already shaped Lyapunov function. The stability analysis of the closed-loop system is carried out by using the invariance theorem of LaSalle. Simulation results to test the effectiveness of the obtained controller are presented.

Suggested Citation

  • Carlos Aguilar-Ibañez & Miguel S. Suarez-Castanon & José de Jesús Rubio, 2012. "Stabilization of the Ball on the Beam System by Means of the Inverse Lyapunov Approach," Mathematical Problems in Engineering, Hindawi, vol. 2012, pages 1-13, April.
    • Handle: RePEc:hin:jnlmpe:810597
    DOI: 10.1155/2012/810597
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