Linear Time Periodic Analysis of Dc-Dc converter

Abstract: Aim of this thesis is to analyze Dc-Dc converters by using the techniques of Linear Periodic Time varying (LTP) systems to estimate the amount of subharmonics injected in the load. Dc-Dc converters are used to transform a Dc input to a Dc output of different voltage. In this thesis we study in particular the so called "switch mode" converters. In this kind of devices the conversion is obtained by using fast commutations of (at least) two switches. Due to the discrete switch-positions these converters are considered a typical example of hybrid systems. Linear models with fixed coefficients (LTI system) give a description of the system inadequate to predict and to analyze harmonic effects, while linear models with coefficients that vary periodically, namely LTP system, can be used effectively to this aim. We use therefore a Linear Time Periodic (LTP) system to describe the converter. This kind of description in much more accurate but the model and the tools used to study it are more complex. In the thesis we first introduce the LTP system theory and its main results. In particular we introduce the concept of Harmonic Transfer Function (HTF). A LTP model for a Dc-Dc converter is then derived and it is shown that this model accurately describes the response of the converter. Furthermore this LTP model is used to analyze the open and closed loop behavior of the system. It is shown that the linear model estimates correctly the amplitude of the subharmonics in the output. The thesis has been developed at the Automatic Control Department, Lund University, Sweden under the supervision of Andreas Wernrud and Anders Rantzer. The Italian supervisor of this thesis is Giorgio Picci, Dipartimento di Ingegneria dell' Informazione, Università degli studi di Padova, Italy