Vibration reduction using time-optimal shaping filters with reduced higher-mode excitations

Vibration reduction in flexible systems can be achieved by shaping the input command using time-delay filters designed for time-optimality, vibration cancellation of characteristic modes, or control robustness. Fast settling time with limited control requires application of bang-bang control which often excite the higher modes of unmodeled dynamics. In this paper an approach is presented to improve the performance by better utilization of the actuator authority. Optimal control formulations are given where the mode excitations in specified bands of frequencies are limited by terminal state inequality constraints while minimizing the settling time. Simulation results are presented comparing the proposed design with other reported solutions.