Sway Reduction of a Pendulum on a Movable Support Using a Delayed Proportional-derivative or Derivative-acceleration Feedback

A pendulum on a movable support has been used widely in the modeling of many mechanical systems, say, as the simplest model of gantry cranes. This paper presents a comparison study of the stability of the controlled pendulum with a delayed proportional- derivative feedback controller or a delayed derivative-acceleration feedback controller for sway reduction. Numerical calculation shows that the delay combinations and the sign combinations of the gains have important impact on the stability of the controlled pendulum. Although acceleration feedback is used few in applications compared with the widely used proportional-derivative feedback, the case when the delay in the acceleration feedback is double of the one in the derivative feedback can be particularly useful in enlarging the stable region in the gain plane, or in enlarging the stable delay interval if the feedback gains are fixed.