Improved linear model of self oscillating systems such as relay feedback current controllers

In this paper, some analytical tools for the study of self-oscillating systems such as current-controlled static converters using pulse-width modulators are presented. These tools, based on the Tsypkin locus, concern the prediction of the switching frequency of the power stage and the characterization of its input–output behavior by an equivalent linear model. These first results, that can be used for any value of the duty cycle, are extended to the construction of the frequency response of the closed-loop system, where the power stage is replaced by a constant gain, associated with a constant time delay. This study is validated by experiments using a classical hysteresis current controller and a recent current controller without hysteresis. The obtained results are particularly useful for applications such as active filtering or high precision power supplies, where the frequency of the signal to follow can be close to one fifth of the switching frequency.