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Mathematical Problems in Engineering
Volume 2009, Article ID 179724, 11 pages
Research Article

PD Control for Vibration Attenuation in a Physical Pendulum with Moving Mass

1Centro de Investigación en Computación del IPN, Apartado Postal 75-476, 07700 México, DF, Mexico
2Departamento de Control Automático, Centro de Investigación y de Estudios Avanzados del IPN, Apartado Postal 14-740, 07300 México, DF, Mexico

Received 8 December 2008; Accepted 22 May 2009

Academic Editor: John Burns

Copyright © 2009 Oscar Octavio Gutiérrez-Frias 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 proposes a Proportional Derivative controller plus gravity compensation to damp out the oscillations of a frictionless physical pendulum with moving mass. A mass slides along the pendulum main axis and operates as an active vibration-damping element. The Lyapunov method together with the LaSalle's theorem allows concluding closed-loop asymptotic stability. The proposed approach only uses measurements of the moving mass position and velocity and it does not require synchronization of the pendulum and moving mass movements. Numerical simulations assess the performance of the closed-loop system.