Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 659685, 11 pages
Research Article

A Flatness-Based Controller for the Stabilization of the Inverted Pendulum

1CIC IPN, Avenida Juan de Dios Bátiz s/n, U.P.A.L.M, Col. San Pedro Zacatenco, A.P. 75476, Mèxico, D.F. 07738, Mexico
2CINVESTAV IPN, Avenida IPN 2508, Col. San Pedro Zacatenco, A.P. 14740, México, D.F. 07700, Mexico
3ESCOM IPN, Mèxico, D.F. 07738, Mexico

Received 2 September 2010; Accepted 30 December 2010

Academic Editor: Elbert Macau

Copyright © 2011 Carlos Aguilar-Ibáñez et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We propose a flatness based approach for controlling the inverted pendulum cart system, under the assumption that the pendulum state is always located on a vicinity of its unstable equilibrium point. This is achieved by representing the original system, as a chain of integrators with an additive nonlinear state dependent perturbation. After discarding the small nonlinear perturbation, we may directly use design tools provided by the the flatness approach. The effectiveness and robustness of the obtained control law, which turned out to have a large domain of attraction, were numerically assessed in the context of stabilization and, also, for a reference oscillatory trajectory tracking task.