Specified-Deflection Command Shapers for Second-Order Position Input Systems

This paper documents new command shapers designed to both eliminate the residual vibration and reduce the transient deflection of a flexible system. Equations are derived to predict both the residual vibration and the transient deflection for a mass-spring-damper system with position input, or equivalently, a mass under PD control. The solution of equations containing constraints on both the transient deflection and the residual vibration leads to the creation of specified-deflection, zero-vibration command shapers. These specified-deflection shapers limit the transient deflection to a predetermined ratio of the base line deflection resulting from an arbitrary reference command. Computer simulations and experiments on a bridge crane verify the efficacy of the new command shapers.