Limiting excitation of unmodeled high modes with negative input shapers

Vibration of flexible structures can be greatly reduced by using properly shaped reference commands. Input shaping is a command generation scheme that filters the reference command in real time by convolving it with a sequence of impulses, called the input shaper. The resulting shaped command has a slower rise time than the unfiltered command. The rise time is increased by the time duration of the input shaper, so it is desirable to keep the duration as short as possible. To achieve very short durations, the shaper must contain negatively valued impulses. The improved rise time of negative input shapers comes with the potential drawbacks of actuator saturation, increased sensitivity to modeling errors, and excitation of unmodeled high modes. A method for controlling the potential excitation of unmodeled high modes is presented. Characteristics of the impulse sequence as a function of the limitation on high-mode excitation are presented. Simulations of a linear system with unmodeled high modes are used to demonstrate the important features of this approach