Time-Optimal Negative Input Shapers

Input shaping reduces residual vibration in computer controlled machines by convolving a sequence of impulses with a desired system command. The resulting shaped input is then used to drive the system. The impulse sequence has traditionally contained only positively valued impulses. However, when the impulses are allowed to have negative amplitudes, the rise time can be improved. Unfortunately, excitation of unmodeled high modes and overcurrenting of the actuators may accompany the improved rise time. Solutions to the problem of high-mode excitation and overcurrenting are presented. Furthermore, a simple look-up method is presented that facilitates the design of negative input shapers. The performance of negative shapers is evaluated experimentally on two systems; one driven by a piezo actuator and the other equipped with DC motors.