STUDY OF CHAOTIC BEHAVIOR BASED ON DISCRETE ITERATIVE MAPPING FOR DC-DC BOOST AND SEPIC CONVERTERS

Abstract

Power electronic systems in switched-mode DC-DC converters exhibit complex behaviors such as rapid adjustments, bifurcation and chaotic performance. These unexpected behaviors are often attributed to random external influences, leading to issues like sensor failure, electromagnetic interference and reduced efficiency and in the worst cases it leads to converter failure. The growing demand for affordable DC-DC power conversion requires reliable operation in all loading conditions, including extreme scenarios. In the past decade, researchers have focused on studying these boundary conditions in power electronic converters, employing various analytical and theoretical approaches. However, the most intriguing findings are based on abstract mathematical structures that cannot be directly applied to the development of practical industrial applications. In this thesis utilizes the discrete time Iterative mapping method to investigate the dynamics of non-linear behavior in DC-DC Boost and SEPIC converters. By establishing a state space and discrete iterative mapping, the stability of the system can be demonstrated incorporating comprehensive information about closed-loop control and DC converter parameters. The discrete iterative mapping technique enables further analysis of stability considering the impact of nonlinear loads and potential extensions to different types of converters. Based on the findings, modern control algorithms can be developed to ensure the converter's proper functionality and prevent complex behaviors, including rapid and slow-scale bifurcations. The Boost and SEPIC converters are both theoretically derived and analyzed with simulation results focusing on doublet and chaotic bifurcations.