Direct Adaptive Input Shaping Using On-Line Frequency Domain Information and Extremum-Seeking Optimization

Abstract

The input shaping technique convolves the reference command with a properly designed impulse sequence, creating a shaped reference command that avoids exciting the under-damped vibratory system to achieve zero residual vibration on a point-to-point maneuver. The input shaper needs to know the natural frequencies and damping ratios of the vibratory system to design such an impulse sequence. When system configurations change, the natural frequencies and damping ratios also change, and the input shaper must be updated with this new information. In this paper, a point-by-point discrete Fourier transform (DFT) algorithm was used to compute the frequency content of the vibratory signal. The identified natural frequencies were directly updated into the input shaper. Extremum-seeking optimization was used to further adjust the damping ratios for minimal vibration. The proposed technique was applied to a flexible-link robot manipulator. The manipulator was commanded to have a point-to-point maneuver with changing payload. The experimental results, based on cases with or without DFT and extremum seeking, showed that with the proposed technique, minimum residual vibration was obtained even when the payload changed, without having to know the amount of payload.