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.

Abstract: A repetitive controller scheme with positive 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 controller more selective, in the sense that; the original overlapping (appearing at the valleys in a simple positive feedback repetitive controller) 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 repetitive controller includes a simple Low Pass Filter (LPF). This modification restricts the bandwidth of the controller and at the same time reinforces stability when the controller is inserted in the closed-loop system.

Abstract: An n-buck cascade converter, where the DC conversion ratio is Un where U is the duty ratio. The converter comprises n inductors, n capacitors, (2n-1) diodes and a MOSFET transistor. The cascading configuration uses the minimum number of active switches while avoiding complex control circuitry. It is assumed that this converter operates in continuous condition mode, i.e., all the inductor currents never decay to zero. The corresponding formulae for the ripples in the capacitor voltages and the inductor currents are given. This allows designing in principle a specific converter following some specifications.