# Study of Chaotic Pulse-Width Modulation Methods in Power Electronics Supervisor:
Dr. Sütő Zoltán

Chaotic and non-linear phenomena can be found in all fields of natural science. However in engineering practices they are often avoided, because it can be difficult to deal with them. Engineers take special care to avoid discontinuity induced chaos in everyday power electronics converters, such as mobile and laptop chargers.

The purpose of this project is to study nonlinear power electronics systems that can exhibit chaotic behavior. The project also includes an investigation of a specific chaotic system, namely a Buck converter fed voltage mode controlled brushed DC motor.

Various numerical methods, suited for discontinuous differential equations, and bifurcation theory are used to simulate the system on a computer, in Matlab/Simulink, Wolfram Mathematica environments, as well as using open source C++ libraries directly. Then the results are compared with a real system.

The measured system was found to agree with the simulation results with varying accuracy. The simulation predicted similar results for steady state operation and it deviated when the system and the simulation were in chaotic state, which can be explained by the nature of chaotic systems, their sensitivity on initial conditions and parameters.

The aim of the first chapter is to put chaotic power electronics systems into historical context, and to show why it is worth investigating chaos from a practical aspect.

Chapter 2 aims to systematically introduce the mathematical tools needed to analyze the chaotic systems that appear in power electronics. This includes the general definitions of differential equations, the methods used in non-linear dynamics, an intuitive introduction to piecewise continuous systems, and an overview of the numerical methods needed to simulate them and the problems that can arise during simulations.

The chapter ends with discrete dynamical systems and a brief description of bifurcations. Since both discrete and continuous time systems can exhibit bifurcations, rather than dealing with their respective bifurcations separately, the last part of the second chapter deals with the bifurcations of both type of system.

Chapter 3 deals with the study of the specific system. This chapter is divided into three main parts. The first introduces the mathematical equations describing the system, and the second presents the simulation results. Lastly, the third part contains the description of the measurements and the comparison with the simulation.

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