Sigmoid Function Model and Dynamic Characteristics Analysis for Inductive Wireless Power Transmission Control System

In this article, an inductive wireless power transmission (IWPT) system is a high-order nonlinear switching system with multiple operating modes. It is challenging to analyze the dynamic characteristics of such a system using the extended describing function, generalized state-space averaging, or other existing modeling methods. To address this challenge, this study proposes a modeling and dynamic characteristics analysis method for a closed-loop IWPT control system based on a sigmoid function model. A sigmoid function with a large steepness factor is adopted to approximate the switching process of the switch and a unified smooth continuous dynamic model is established for a phase-shift controlled IWPT system. Because this model is infinitely differentiable, a stability theory of continuous systems, such as the Floquet theory, can be directly applied to analyze the bifurcation type of the system and stability of periodic solutions. Analysis results reveal the transition of the phase-shift-controlled IWPT system from periodic behavior to chaotic behavior through saddle-node bifurcation and Neimark–Sacker bifurcation. A stable domain in the two-parameter space of the controller proportional coefficient and load is also obtained. Both simulation and experimental results validate the accuracy of the proposed model and theoretical analysis method, which can significantly reduce the difficulty of analyzing IWPT system dynamics.