Comments on “Design of $\varvec{\alpha }$-filter based UDE controllers considering finite control bandwidth”

Abstract

In the paper “Design of $\alpha$-filter based UDE controllers considering finite control bandwidth” by A. Kuperman (Nonlinear Dynamics, vol. 81, no. 1, July. 2015), performances of a new first-order $\alpha$-filter for uncertainty and disturbance estimator (UDE)-based control and a classical first-order UDE filter where examined. It was shown that performance superiority of the $\alpha$-filter is not straightforward and takes place for limited operating region only in case practical implementation issues of the filters are taken into account. The purpose of this note is complementing (Kuperman in Nonlinear Dyn 81:411–416, 2015) by proving that in case practical implementation restrictions are extended to the overall control system and classical UDE-filter-based controller would always outperform the $\alpha$-filter-based controller in terms of disturbance and noise rejection, while the $\alpha$-filter-based controller would be superior in terms of stability.