The Direct Piece-Wise Affine Modeling of LLC Resonant Converter

Resonant converters are hard nonlinear systems which are comprised of both continuous and discontinuous nonlinearities. Many nonlinear modeling approaches lead to a very awkward, unsystematic stability analysis and controller design. Hence, stability analysis and stabilizing controller design of the popular LLC resonant converter still remain challenging as direct consequences of the absence of a “systematic modeling”. In this paper, the LLC resonant converter is modeled in the form of Piece-Wise Affine (PWA) systems and a Direct Piece-Wise Affine (DPWA) model of the DC-DC LLC resonant converter is proposed. No dynamic is omitted in the modeling approach, and accordingly, the proposed “systematic model” is exact and can be utilized in a precise, systematic stability analysis and controler design. In addition, using the method, no voltage controlled oscillator is needed to control the resonant converter.