Vibration reduction for flexible systems by command smoothing

A method is presented for limiting vibration in flexible systems by smoothing the original command. The original command is smoothed to drive the flexible systems without inducing vibration. The proposed smoother is designed as a function of system natural frequency and damping ratio. The comparison between the new method and the zero vibration and triple derivative (ZVDDD) shaper for modeling error is explored and quantified. The theoretic analysis shows that the new method is more insensitive at higher frequencies, while the ZVDDD shaper has more insensitivity at lower frequencies. Moreover, the designed smoother benefits vibration reduction for multi-mode systems. Experimental results for single-mode and multi-mode systems validate the simulated dynamic behavior and the effectiveness of the new method.