An improved implementation scheme for time-optimal commands using symmetric filters

This note presents a new approach of generating time-optimal commands for reducing vibrations in flexible systems with lightly damped modes. Existing schemes for real-time implementation of time-optimal commands requires expensive computations where non-convex parametric optimization problems are solved for different reference moves. For undamped systems, the time-optimal command is known to be symmetric. Based on this, a new design of symmetric filters is proposed that can be computed offline and tabulated for quick lookup. This reduces the on-line computational burden of deriving time-optimal profiles for undamped multi-mode flexible systems. The proposed approach is compared with existing input shaping based schemes in terms of computational requirement and system performance.