Zero-phase velocity tracking of vibratory systems

The focus of this paper is on the development of an input shaper/time-delay filter that permits the precise tracking of a ramp input, while eliminating residual vibrations. Zero phase error velocity tracking is often required in applications where moving parts have to be mated, such as manufacturing lines with high production output. A closed form solution to a pre-filtering technique is presented which achieves the desired characteristics. The performance of this technique is compared with other input shaper designs in current literature, and is shown to achieve smaller settling time and maintain zero steady state phase error without a priori knowledge of the initiation and termination of ramp profiles. The technique is then physically applied to a rotary pendulum to demonstrate the consistency of its ramp tracking and vibration reduction capabilities.