An Analysis of the Total Insensitivityof Input

An Analysis of the Total Insensitivity of Input Shaping Designs Lucy Y. Pao Electrical and Computer Engineering Department University of Colorado Boulder, Colorado 80309{0425 Abstract In the modeling of exible 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 studies, however, have addressed only frequency modeling errors. We consider modeling errors in damping as well and de ne a total insensitivity measure that incorporates both frequency and damping modeling errors. An analysis of several types of input shapers shows a di erent ordering of shaper types in terms of their total insensitivity to frequency and damping modeling errors compared to previous studies and comparisons of these shaper types in terms of uncertainty in frequency alone.