Continuous-Time Sigmoid Modeling of High-Order Power Converters With Smooth Switching Dynamics

High-order power converter models are usually strongly nonlinear due to the presence of switching devices, multiple state variables, and parasitic parameters. In this work, to achieve accurate continuous-time modeling of such converters, we propose a novel Sigmoid function modeling method, which can accurately capture the nonlinear behavior of converters. Considering smooth mode switching (SMS), the proposed modeling method provides a unified mathematical model that can describe all operating modes of a continuous-time converter system, especially the operating modes that occur between switches' ON and OFF states. Following rigorous mathematical derivations, simulation and experimental verification is conducted on the widely used I4SL-Boost converter as an example of high order converter applications. The stability of the SMS model is investigated based on Floquet theory, and its stable parameter region is determined through simulations. This foundational modeling approach enhances the understanding, analysis, and control of high-order converters.