Performance measures and optimization condition for a third-order sampled-data tracker

In a recent paper Benedict and Bordner derived the relationship between α and β for an optimized "
\alpha=\beta
" sampled-data tracker. This note shows how the optimization condition is modified when acceleration terms are included and the tracker becomes an "
\alpha=\beta=\gamma
" tracker. The optimization relationship between
\alpha, \beta, \gamma
is
2\beta - \alpha (\alpha + \beta + \frac{1}{2}\gamma) = 0
.