An analysis of frequency-domain input shaping designs for three-mode flexible systems

The technique of input shaping has recently been successfully applied to the problem of manoeuvring flexible structures without excessive residual vibration. In the method of input shaping, positive impulses are often desired because they can be used with any arbitrary (unshaped) commands and do not cause actuator saturation (if these original unshaped commands do not cause actuator saturation). In this paper, we outline conditions when nonnegative amplitude shapers will result when using frequency-domain methods of input shaping, and we draw comparisons with conventional time-domain input shaping in terms of shaper length (speed) and number of impulses (ease of implementation).