Research on Nonlinear Dynamic Characteristics of Fractional Order Resonant DC-DC Converter Based on Sigmoid Function

Resonant DC-DC converters are a class of strongly nonlinear systems with rich nonlinear phenomena. In order to describe the dynamic behavior of resonant DC-DC converters more accurately, the nonlinear dynamic behavior of fractional order (FO) resonant DC-DC converters is studied deeply, based on the fractional order nature of inductance and capacitance. Firstly, a Sigmoid function state model of the fractional order resonant converter is established and integrated with phase shift control. A discrete model of the converter is established by using an estimation correction algorithm. Secondly, the mathematical and equivalent circuit models of the fractional order converter are constructed in MATLAB. The circuit simulations and the experimental results verified the correctness of the Sigmoid function model. Thirdly, the effect of circuit parameters on the converter’s nonlinear dynamics is analyzed using bifurcation diagrams, time-domain waveforms, and phase diagrams. Finally, an experimental platform is established to validate the theoretical analysis. The results demonstrate that increasing the proportional coefficient and load resistance destabilizes the system, leading to rich nonlinear phenomena such as bifurcation and chaos. Compared to integer order converters, fractional order converters offer a broader stable operating range. Fractional order models can more accurately reflect the nonlinear dynamic characteristics of resonant DC-DC converters.