Repetitive controller to compensate for (61+-1) harmonics

Abstract

"A repetitive controller scheme with two feedbacks one negative and one positive plus a negative feedforward introduces infinitely many poles on the imaginary axis located at j(6l+-1)omegao (l=0,1,2, . . . ,[infinity]) which produces resonant peaks tuned at 6l+-1 (l=0,1,2, . . . ,[infinity]) multiples of the fundamental frequency omegao. The feedforward introduces zeros, which produce notches located at 3lomegao (l=0,1,2, . . . ,[infinity]), that is, in between two consecutive resonance 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. The proposed compensator composed of a negative and a positive feedback plus feedforward is especially useful when only the compensation of 6l+-1 (l=0,1,2, . . . ,[infinity]) harmonics is required, but not all harmonics, like in many power electronic systems. In contrast, the positive feedback controller or the negative feedback controller would try to reinject, and indeed amplify, any small noise, which has components on the even frequencies or frequencies 3(2l+1)omegao (l=0,1,2, . . . ,[infinity])."