A Generalized Model of Nonisolated Multiphase DC–DC Converter Based on Novel Switching Period Averaging Method

The continuously innovated topologies of the nonisolated multiphase dc-dc converter (NMDC) demand generalized and flexible models for the controller design. However, the increased phase number, coupling of inductors, stray circuit parameters, and asymmetric problems make the modeling work difficult. In this paper, a novel switching period averaging method aiming to simplify the modeling process is proposed. The method takes full advantage of the linear characteristic of the circuit differential equations to find out the relationship between averaged state variables and switch duty cycles. Then, the generalized model applicable to several different topologies of the NMDC is derived. The analytical solutions of steady-state model, dynamic model in both time and frequency domain are all approached. In order to verify the results, a MATLAB/Simulink model and the corresponding experimental prototype of a four-phase boost converter with two groups of two-phase coupled inductors are built. Both results coincide with the theoretical derivation, which indicates the effectiveness of the proposed method. Finally, a design process of the H_∞ controller for the NMDC is presented to show the application of this model.