Control using equal length shaped commands to reduce vibration

Input shaping; a feedforward method used to reduce system vibration, typically lengthens the duration of an input command. This paper considers shaped bang-off-bang commands which do not lengthen the duration of the input command. Analytical expressions are developed to describe the vibration due to shaped commands and unshaped commands of equal length. These are then used to analyze sensitivity to parameter variation. The vibration is analyzed over a range of frequencies, damping factors, and command lengths to show that the equal length shaped inputs often reduce residual vibration even when the actual frequency varies from the modeled frequency and to demonstrate the possible advantages of an equal length shaped bang-off-bang input. Last, an equal length shaped input is applied to a tape drive head system to demonstrate reduced settling time.