脉冲序列控制电流断续模式Buck变换器的动力学建模与边界碰撞分岔

通过建立一个开关周期内输出电容电荷变化量对应的输出电压变化量, 建立了工作于电感电流断续模式(discontinuous conduction mode, DCM)的脉冲序列(pulse train, PT)控制Buck变换器的近似离散时间模型, 研究了负载电阻及输入电压变化时PT控制DCM Buck变换器的边界碰撞分岔行为. 通过构造相应的迭代映射曲线, 分别分析了不同负载电阻时PT控制DCM Buck变换器的周期1、周期2和周期3运行轨迹的不动点稳定性, 揭示了PT控制DCM Buck变换器在不同周期态时的边界碰撞分岔的形成机理. 研究结果表明, 随参数变化, PT控制DCM Buck变换器始终运行在不同的周期态, 各周期态的切换由边界碰撞分岔引起, 李雅谱诺夫指数始终小于零. 利用PSIM电路仿真软件, 给出了不同负载电阻时的时域波形和相轨图. 实验结果验证了理论分析和仿真结果的正确性, 同时说明了本文动力学建模的可行性.

Dynamical modeling and border collision bifurcation in pulse train controlled discontinuous conduction mode buck converter

According to the charge variation of output capacitor in a switching cycle, the output voltage variation in a switching cycle can be obtained, from which an approximate discrete-time model of pulse train (PT) controlled buck converter operating in discontinuous conduction mode (DCM) is established. Based on the model, the border-collision bifurcations of the PT controlled DCM buck converter with the variations of the load resistance and the input voltage are studied. By constructing the corresponding iterative map curves, the stabilities of the fixed points, formed by the orbits of period-1, period-2, period-3 and so on, are analyzed, and the mechanisms of border-collision bifurcations of the converter under different operation states are revealed. The analysis results indicate that with the variation of parameters, the PT controlled DCM buck converter always operates in different periodic states, in which the change of the operation mode with periodic state is caused by the border-collision bifurcation and the lyapunov exponent is always less than zero. By using PSIM circuit simulation software, the time domain waveforms and phase portraits under different load resistances are obtained. Experimental results are provided to verify the correctnesses of theoretical analyses and circuit simulations and the feasibility of dynamical modelling.