Deflection vector diagrams for a mass under PD control

This paper documents a new tool for both eliminating the residual vibration and reducing the transient deflection of a flexible system. A deflection vector diagram has been developed to graphically predict both the residual vibration and the transient deflection for a mass under PD control, or equivalently, a mass-printing-damper system with position input. The deflection vector diagram 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 unshaped command for an arbitrary reference command.