Robustness analysis of input shaping commands for two-mode flexible systems

A robustness evaluation of input-shaping techniques to reduce residual vibration of two-mode flexible systems is presented. Using a benchmark two-mode system, the robustness problem is illustrated by first applying input shapers designed for only one mode. These simple shapers are effective for a wide array of two-mode systems because the amplitude of the second mode is often small, perhaps near the noise level. However, single-mode shapers are ineffective when the second mode contributes substantial oscillation amplitude. Therefore the robustness analysis for both single- and two-mode input shapers reveals an inherent compromise between shaper robustness to parameter uncertainties and rise time of the command. A specified-insensitivity shaper can result in command profiles that are significantly more robust to modelling errors than profiles produced with alternative input shapers. The robustness evaluation is verified with a numerical simulation of double-pendulum dynamics and experimentally validated on a 10 ton industrial bridge crane.