Optimal limited-jerk time-delayed filter for restraining residual vibration of flexible systems

The fact that time-delayed filters used for suppressing residual oscillation of flexible systems are accompanied by a rigid impact motivates to propose an optimal limited-jerk time-delayed filter based on limited-jerk theory and optimization theory. The limited-jerk control commands are designed by fixing on a jerk maximum to limit the varying ratio of the reference orders, then the optimal time delays are solved by minimizing the oscillation energy of flexible modes. It is revealed that the control commands from the filter are composed of a sequence of ramp signals, whose time-ratio of variation never exceeds the permissible value to restrain the excitation to un-modeled harmonic modes. Compared with typical ones, the filter enables to suppress the residual oscillation of flexible systems, weaken the rigid motion impact simultaneously and accelerate the system response by 30%.