Sigmoid Function Model for a PWM DC-DC Converter

Considering the presence of switching devices, a pulse-width modulation (PWM) dc-dc converter is a piecewise smooth switching system that causes difficulties in stability analysis and controller design. Hence, a new modeling method that employs a sigmoid function is proposed to approximate the switching transition of a power device to construct a smooth continuous-time system model for a converter. This study adopts the equivalent circuit modeling method of a three-terminal switch to establish the sigmoid function model of the basic dc-dc converter and zero-current switching quasi-resonant dc-dc converter. The proposed sigmoid function models are simulated and experimentally verified. Furthermore, the simulation speed and accuracy of the proposed model are compared with the state-space averaged model. The results of this study are consistent with the Simulink circuit simulation results and experimental results. In addition, the proposed model improves accuracy and does not result in a significant loss in simulation speed. The model possesses various advantages: first, based on the model, the stability analysis and control theory for smooth continuous-time systems can be directly applied to PWM dc-dc converters; second, the model can present a unified description of the continuous conduction mode and discontinuous conduction mode for converters.