The LLC resonant converter constitutes a high-order switching system characterized by multiple operational modes and region-dependent switching sequences. This complexity poses significant challenges to system modeling and dynamic analysis. Furthermore, its inherent high-order nonlinearity tends to induce detrimental nonlinear phenomena, including bifurcation and chaos, which are particularly undesirable in power electronic systems that demand the utmost priority for stability and reliability. To address these concerns, this work focuses on investigating the dynamic behaviors and stability of LLC resonant converter control systems. This study aims to elucidate the origins and evolution of these nonlinear characteristics, thereby facilitating the design of higher-performance power electronic systems. First, a continuous-time model of the closed-loop controlled LLC resonant converter system was established using the sigmoid function modeling method. This model allows direct application of continuous system theory to analyze dynamic behavior, significantly reducing analytical complexity. Second, the system’s bifurcation characteristics and stability were comprehensively investigated through Floquet theory, bifurcation diagrams, and Lyapunov exponent spectra. Results reveal that PFM-controlled LLC resonant converters exhibit rich nonlinear dynamics under variations in key parameters. Experiments successfully captured the observed nonlinear phenomena, validating the evolution of system dynamics and stability. This work provides a novel perspective for stability analysis and parameter design in multi-resonant converter systems.
Wei et al. (Fri,) studied this question.