脉冲序列控制双断续导电模式BIFRED变换器的动力学建模与多周期行为∗

摘要

According to four different operating modes of a BIFRED converter, a piecewise smooth linear time-varying model for pulse train (PT)-controlled BIFRED converter operating in dual discontinuous conduction modes (DCM-DCM) is established, from which time-domain waveforms and phase portraits under different loads are obtained by numerical simulations. By analyzing the variation of the charge of an output capacitor in a switching period, a one-dimensional approximate discrete mapping model for PT-controlled DCM-DCM BIFRED converter is derived, in which the multi-periodic behaviors with the variations of the load resistance and the input voltage are studied, and the stability analysis and the estimations of the load resistance ranges are performed. Research findings indicate that the dynamical behaviors depicted by the one-dimensional approximate discrete mapping model are in good agreement with those described by the piecewise smooth linear time-varying model, well revealing the complicated multi-periodic behaviors existing in the PT-controlled DCM-DCM BIFRED converter. By PSIM circuit simulations and physical circuit experimental measurements, the waveforms obtained are consistent with the results of theoretical analysis, effectively validating the feasibility of the two dynamical models.%根据BIFRED变换器四种不同的工作模式，建立了脉冲序列(PT)控制双断续导电模式(DCM-DCM) BIFRED变换器的分段光滑线性时变模型，数值仿真得到了负载不同时的时域波形和相轨图。通过分析在一个开关周期内输出电容的电荷变化量，导出了PT控制DCM-DCM BIFRED变换器的一维近似离散映射模型，研究了随负载电阻和输入电压变化的多周期行为，并进行了稳定性分析和负载取阻范围估算。研究发现，一维近似离散映射模型刻画的动力学行为与分段光滑线性时变模型描述的完全一致，均较好地揭示了PT控制DCM-DCM BIFRED变换器所存在的复杂多周期行为。 PSIM电路仿真和物理电路实验测量获得了与理论分析结果所一致的波形，有效验证了两种动力学模型的正确性。