Artículos

Controlling the Strongly Damping Inertia Wheel Pendulum via Nested Saturation Functions

Control del Péndulo con Rueda de Inercia Fuertemente Amortiguado mediante Funciones de Saturación Anidadas

Carlos Aguilar Ibáñez¹, Óscar Octavio Gutiérrez Frías², Miguel Santiago Suárez Castañón³

¹ Centro de Investigación en Computación del Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n Esq. Manuel Othón de M., Unidad Profesional Adolfo López Mateos Col. San Pedro Zacatenco, A.P. 75476, México, D.F. 07700, México Phone: (52–55) 729–6000 ext. 56568, FAX: (52–55) 586–2936, email: caguilar@cic.ipn.mx.

² Centro de Investigación en Computación del Instituto Politécnico Nacional, Av. Juan de Dios Bátiz s/n Esq. Manuel Othón de M., Unidad Profesional Adolfo López Mateos Col. San Pedro Zacatenco, A.P. 75476, México, D.F. 07700, México Phone: (52–55) 729–6000 ext. 56568, FAX: (52–55) 586–2936.

³ Escuela Superior de Cómputo del Instituto Politécnico Nacional Av. Juan de Dios Bátiz s/n Esq. Manuel Othón de M., Unidad Profesional Adolfo López Mateos Col. San Pedro Zacatenco, A.P. 75476, México, D.F. 07700, México Phone: (52–55) 729–6000 ext. 52028, email: sasuarez@prodigy.net.mx.

Article received on January 16, 2008
Accepted on June 03, 2008

Abstract

In this paper we solve the stabilization problem of the strongly damping inertia wheel pendulum around its unstable equilibrium. The stabilization is accomplished by using nested saturation functions. The use of nested saturation function is possible because this system can be rewritten approximately as a chain of integrators with and nonlinear perturbation. The proposed control strategy makes the closed–loop system globally asymptotically and locally exponentially stable around the unstable inverted vertical position, even when the physical damping is presented in the model.

Keywords: Nested saturation functions, Lyapunov function, nonlinear systems.

Resumen

En este artículo resolvemos el problema de estabilización del péndulo con rueda de inercia fuertemente amortiguado alrededor de su punto de equilibrio inestable. La estabilización el lograda mediante el uso de funciones de saturación anidadas. El uso de funciones de saturación anidadas es posible porque se puede escribir una aproximación del sistema como una cadena de integradores con una perturbación no lineal. La estrategia de control que se propone hace que el sistema en lazo cerrado sea asintóticamente estable de forma global y exponencialmente estable de forma local alrededor de la posición vertical inestable, aún cuando el amortiguamiento físico está presente en el modelo.

Palabras Clave: Funciones de saturación anidadas, Función de Lyapunov, Sistemas no lineales.

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Acknowledgements

This research was supported by the Secretaría de Investigación y Posgrado (SIP–IPN) under research grants 20071088, 20082694 and 20082887. Octavio Gutiérrez–Frias is a doctoral student at the CIC–IPN and a scholarship holder of the CONACYT.

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