Application of Filippov method for the analysis of subharmonic instability in dc-dc converters

Abstract

We propose a method of estimating the fast-scale stability margin of dc-dc converters based on Filippov's theory-originally developed for mechanical systems with impacts and stick-slip motion. In this method one calculates the state transition matrix over a complete clock cycle, and the eigenvalues of this matrix indicate the stability margin. Important components of this matrix are the state transition matrices across the switching events, called saltation matrices. We applied this method to estimate the stability margins of a few commonly used converter and control schemes. Finally, we show that the form of the saltation matrix suggests new control strategies to increase the stability margin, which we experimentally demonstrate using a voltage-mode-controlled buck converter. Copyright © 2008 John Wiley and Sons, Ltd.