Repetitive controller to compensate for odd harmonics

Abstract

"A repetitive controller scheme with negative feedback and feedforward introduces infinitely many poles on the imaginary axis located at the resonant peaks. The feedforward introduces zeros, which produce notches located in between two consecutive resonant peaks. The latter has the advantage of making the controllers more selective, in the sense that the original overlapping (appearing at the valleys) or interaction between consecutive resonant peaks is removed by the notches. This would allow, in principle, peaks of higher gains and slightly wider bandwidth, avoiding, at the same time, the excitation of harmonics located in between two consecutive peaks. A negative feedback compensator with feedforward is especially useful when only the compensation of odd harmonics is required, but not the even harmonics, like in many power electronic systems.; In contrast, the positive feedback controller would try to reinject, and indeed amplify, any small noise, which has components on the even frequencies. The negative feedback repetitive controller includes a simple Low Pass Filter (LPF). This modification restricts the bandwidth of the controller, and at the same time reinforces the stability when the controller is inserted in a closed-loop system."