Input shaping designs to account for uncertainty in both frequency and damping in flexible structures

In the modeling of flexible structures, there is generally uncertainty in both the frequencies and damping constants, and it is thus important that the control methods for such systems be robust to these uncertainties. Input shapers have been shown to yield good performance while being insensitive to modeling errors. Most previous input shaping studies, however, have addressed only frequency modeling errors and do not take into account the distributions of the parameter variations. We extend a recently proposed input shaping method (Pao et al. (1997)), that allows the ranges of system parameter values to be weighted according to the expected modeling errors, for designing shapers that accommodate both frequency and damping uncertainty