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

Carlos Aguilar-Ibanez; Miguel S. Suarez-Castanon; Jose de Jesus Rubio

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

机译：用逆李雅普诺夫方法稳定球在横梁系统上的稳定性

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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.

机译：一种新颖的逆Lyapunov方法与能量整形技术相结合，可以得出光束在横梁系统上的稳定控制器。所提出的策略包括对候选Lyapunov函数进行整形，就好像它是反稳定性问题一样。为此，我们固定了一个合适的未知能量函数的耗散函数，其特性是所选耗散除以候选Lyapunov函数的相应时间导数。之后，直接从已经成形的Lyapunov函数中获得稳定控制器。利用LaSalle不变性定理进行闭环系统的稳定性分析。仿真结果证明了所获得控制器的有效性。

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来源
《Mathematical Problems in Engineering》 |2012年第5期|p.16.1-16.13|共13页
作者
Carlos Aguilar-Ibanez; Miguel S. Suarez-Castanon; Jose de Jesus Rubio;
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CIC-IPN, Unidad Prqfesional Adolfo Lopez Mateos, Avendia Juan de Dios Batiz S/N, Casi Esquire Miguel Othon de Mendizobal, Colonia Nueva Industrial Vallejo, Delegation Gustavo A. Madero, 07738 Mexico City, DF, Mexico;

ESCOM-IPN, 07738 Mexico City, DF, Mexico;

SEPI-ESIME Azcapotzalco, 02250 Mexico City, DF, Mexico;

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

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