Optimal robust extra insensitive time-delayed filter to eliminate residual vibrations of slight-damping flexible systems

For the flexible systems with varying frequencies in a larger range, based on the optimization theory and vector graph method, an optimal robust extra insensitive time-delayed filter is designed, for which the magnitude-frequency performance under the condition of zero vibration is taken as objective function. The characteristics of the filter include that the parameter variation ranges are taken into account, and within the parameter variation range each maximum magnitude of the residual vibrations is set to be equal. Thus, if the system parameters vary in lager ranges, the filter is more robust and the residual vibrations can be effectively eliminated. This technique was used in the experiment system of gantry crane and can effectively restrain the residual oscillations of payload.