Artículo

A Stabilizable Control Laws For a Rotational Pendulum: A Trajectory Planning Approach

Leyes de control Estabilizadoras para un péndulo rotacional: Una Planificación de Trayectorias

Carlos F. Aguilar Ibañez¹ and Oscar Chavoya A.²

¹ Centro de investigación en Computación del IPN. Laboratorio de Metrología y Control. Av. J.de Dios Bátiz s/n; México D.F., C.P. 07738; México. E–mail: caguilar@cic.ipn.mx.

² Camelback High School, Phoenix, AZ85016, U.S.A.

Article received on April 27, 2000
Accepted on May 17, 2004

Abstract

We propose two simple controls for the regulation of an under actuated rotational pendulum. Both controllers are based on the Lyapunov approach; the first is a simple passive control which makes the closed–loop solution converges asymptotically to an equilibrium manifold. The second approach is a combination of the Lyapunov and the off–line trajectory planning approaches to move the pendulum from an equilibrium point to another equilibrium point, both point belonging to an equilibrium manifold. The last task is accomplished in an approximated fashion. The results are illustrated by means of digital computer simulations.

Keywords: Lyapunov–based control, Trajectory Planning and Under Actuated Systems.

Resumen

Se proponen dos controles simples para la regulación de un péndulo rotacional sub–actuado. Ambos controles están basados en el enfoque de Lyapunov, el primero es un control pasivo simple que hace que la solución de lazo cerrado converja asintóticamente a una variedad (manifold) de equilibrio. El segundo enfoque es una combinación de los enfoques de Lyapunov y el de planeación de trayectoria fuera de línea para mover el péndulo de un punto de equilibrio a otro punto de equilibrio, ambos pertenecientes a una variedad (manifold) de equilibrio. La última tarea se logra de forma aproximada. Los resultados se ilustran mediante simulaciones hechas en una computadora digital.

Palabras clave: Control basado en el enfoque de Lyapunov, Planeación de Trayectoria y Sistemas Subactuados.

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Acknowledgments

This work was supported by CIC–IPN, and by the Coordinación General de Posgrado e Investigación (CGPI–IPN) under research Grant 20040877. Also this paper is dedicated in memory of Professor Leopoldo Arostegui (CBTIS 78).

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