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.

Abstract

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.