Design of input shapers using modal cost for multi-mode systems

This paper presents two techniques for the determination of modal weights for the design of robust input shapers for multi-mode systems. The weights for the first technique are derived based on the scaling factor for the potential energy in each mode, such that the modal displacement is the same. The second technique exploits the modal cost analysis which uses the angle between the right eigenvectors and the row vectors of the output matrix to determine the contribution of each mode to the output. Two examples are used to illustrate the improvement in performance of the modal weighted minimax shapers compared to the traditional minimax shaper which equally weights all the modes.