Vibration reduction with specified-swing input shapers

Residual vibration of flexible structures can be greatly reduced by generating specially-shaped command signals. Input shaping is a type of command generation scheme that is implemented by convolving a sequence of impulses with any desired system command. The resulting shaped input is used as the reference command. Many types of useful impulse sequences have been proposed. Most of these have contained only positively valued impulses. However, when some of the impulses are allowed to have negative amplitudes, the system rise time can be improved. The improved rise time comes with the potential drawback of actuator saturation. New types of impulse sequences containing negative impulses are proposed. These sequences allow the designer to specify the swing in amplitude between successive impulses. This in turn allows the actuator effort to be controlled