Sigmoid Function Model for a PFM Power Electronic Converter

A power electronic converter is a switching system; the key to modeling it is how to describe the interaction between the discrete switch variables and the continuous state variables in a unified model. A power electronic converter modeling method based on sigmoid functions is proposed. Since the sigmoid function is continuous, smooth, differentiable, and saturated at a certain value, a sigmoid function with a large steepness factor is used to approximate the switching process of the switch; the converter is transformed from a switching system to a continuous system so that nonlinear continuous system analysis and design methods can be directly applied to the converter control system. Sigmoid function equivalent circuit models for several typical inverter and rectifier circuits are provided. A half-bridge LLC resonant converter is selected as an example, and its sigmoid function model is constructed and subsequently validated through simulation and experimentation. The results show that the constructed model is in good agreement with the circuit simulation and experimental results. The mathematical expression of the model has a simple and unified structure and definite physical meaning and is a high-accuracy large-signal continuous model with universal significance.