Symmetric computation of regularized inverse dynamics for high-speed flexible beams

A high speed flexible beam system, a simple but typical nonminimum phase system with ill posed noncausal inversion, is considered. Regularization based inverse dynamics can be used for recovering output trajectory tracking of a nonminimum phase system with the ill posed noncausal inversion. In the course of deriving the preimage of the output, high computational efficiency is always sought to meet increasingly stringent performance requirements in practical applications. The article addresses the symmetric computation issue for the regularization based preshaping of the inverse dynamics of a high speed flexible beam system. Regularization based preshaping filter in the time domain is presented for recovering the ill posed inverse dynamics satisfying the torque constraint. Also, the symmetric acausal/causal decoupled form of the preshaping filter is developed, and the symmetry computation scheme is proposed for computational efficiency.