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.