Input shaping is a method of reducing residual vibrations in computer
controlled machines. Vibration is eliminated by convolving a sequence
of impulses with a desired system command to produce a shaped input th
at is then used to drive the system. Techniques for designing the impu
lse sequence for two-mode systems are presented. Properties of the var
ious techniques are compared as a function of the mode ratio. Simulati
ons of a two-mode system demonstrate key results.