Stabilization of the ball on the beam system by means of the inverse Lyapunov approach
type: Item
instance of: scholarly article
title: Stabilization of the ball on the beam system by means of the inverse Lyapunov approach
zbMATH Open document ID: 1264.70060
DOI: 10.1155/2012/810597
published in: Mathematical Problems in Engineering
publication date: 2013-06-11T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 70Q05
Mathematics Subject Classification ID: 93D15
Mathematics Subject Classification ID: 70E17
Mathematics Subject Classification ID: 70E18
zbMATH DE Number: 6173597
author: Carlos Aguilar-Ibañez
author: Miguel S. Suárez-Castañón
author: José De Jesús Rubio
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/810597
OpenAlex ID: W2043064160
Wikidata QID: Q58912043
cites work: Q4848213
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description: scientific article; zbMATH DE number 6173597