Mathematical Problems in Engineering
Volume 2010 (2010), Article ID 162875, 12 pages
Research Article

Lyapunov-Based PD Linear Control of the Oscillatory Behavior of a Nonlinear Mechanical System: The Inverted Physical Pendulum with Moving Mass Case

1Centro de Investigación en Computación, Instituto Politécnico Nacional, A. P. 75-476, 07700 México, DF, Mexico
2Departamento de Control Automático, Instituto Politécnico Nacional, A. P. 14-740, 07300 México, DF, Mexico
3CANDE-INGENIEROS, Clemente Orozco No. 18, 03710 México, DF, Mexico

Received 2 December 2009; Accepted 3 April 2010

Academic Editor: Oleg V. Gendelman

Copyright © 2010 Carlos Fernando 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.


This paper concerns active vibration damping of a frictionless physical inverted pendulum with a radially moving mass. The motion of the inverted pendulum is restricted to an admissible set. The proposed Proportional Derivative linear controller damps the inverted pendulum (which is anchored by a torsion spring to keep it in a stable upright position), exerting a force on the radially moving mass. The controller design procedure, which follows a traditional Lyapunov-based approach, tailors the energy behavior of the system described in Euler-Lagrange terms.