optimal shaped command is better than the unshaped
command but not superior to the ZVD shaping since
the error range considered in the cost function is
½ 0:75!d, 1:25!d .
Figure 10 plots numerous trials based on various
frequency errors. In Figure 10, the abscissa denotes
the frequency ratio expressed as !o=!d, the ordinate is
the pitch angle when the movement has settled. The
optimal input shapers offer better performance than
the ZVD shapers when !o 2 ½ 0:75!d, 1:25!d , but at
!o 50:75!d or !o 41:25!d the performance of the
optimal input shapers is poorer than that of the ZVD
shapers. This result suggests that the improvement of
the performance at 0:75!d !o 1:25!d comes at the
deteriorating performance when the operating frequency
!o is beyond this range. Such deterioration
can be expected since there is no factor in the cost function
to reflect the performance of the optimal shapers in