On frequency-domain and time-domain input shaping for multi-mode flexible structures

The technique of input shaping has been successfully applied to the problem of maneuvering flexible structures without excessive residual vibration. Because a shaper is designed such that vibration is eliminated at the end of the shaped input, a short shaper length means that vibration is eliminated sooner. As different shaper design methods yield different shapers, it is advantageous to know how the shaper lengths of these different methods compare. In this paper we draw comparisons between time-domain input shaping methods and frequency-domain input shaping methods after outlining conditions when non-negative amplitude shapers exist when using frequency-domain methods.