Research on the Nonlinear Dynamic Characteristics of Fractional-Order Flyback Converter Based on Generalized Euler Method

The nonlinear dynamic characteristics of a peak current regulation fractional-order (FO) flyback converter, considering the fractional nature of inductance and capacitance, are investigated in detail. First, the discrete iterative model of the fractional-order (FO) flyback converter under 10 kHz operating conditions is accomplished using the application of the Generalized Euler Method (GEM). On this basis, bifurcation diagrams, phase diagrams, and simulated time domain diagrams are used to describe the nonlinear dynamic behavior of the converter. The nonlinear dynamics of the converter are investigated through bifurcation and phase diagram analyses. A comprehensive examination is conducted to evaluate the impact of key parameters, including input voltage, reference current, and the fractional orders of inductance and capacitance, on the system’s stability. Furthermore, a comparative analysis is performed with conventional integer-order (IO) flyback converters to highlight the distinctive characteristics. The findings demonstrate that the FO converter manifests distinct nonlinear characteristics, including period-doubling bifurcation and chaotic behavior. Moreover, for identical parameter sets, the FO flyback converter is found to possess a smaller stability domain but a larger parameter region for bifurcation and chaos compared to its IO counterpart. This behavior allows the FO converter to more accurately capture the nonlinear dynamic characteristics of the flyback converter. Simulation results further substantiate the theoretical predictions.