输出电容时间常数对V^2控制Buck变换器的动力学特性的影响

Effect of output capacitance time-constant on dynamic characteristics of V^2-controlled buck converter

建立了V2控制Buck变换器的二阶离散迭代映射模型,在其基础上绘制了输出电容及其等效串联电阻(equivalent series resistance,ESR)变化时的分岔图,研究了输出电容时间常数对V2控制Buck变换器的动力学特性的影响.研究结果表明,随着输出电容时间常数的逐渐减小,V2控制Buck变换器具有从稳定的连续导电模式(continuous conduction mode,CCM)周期1态逐渐演变到CCM周期2态、CCM周期4态、CCM周期8态、CCM混沌态、断续导电模式(discontinuous conduction mode,DCM)混沌态的动力学行为.推导了不动点处的雅可比矩阵,利用特征值和最大Lyapunov指数对系统进行了稳定性分析,并验证了分岔分析的正确性.最后,搭建了仿真和实验电路,用仿真和实验结果验证了文中理论分析的正确性.

The second-order discrete iterative map model of V2-controlled Buck converter is established, based on which, the bifurcation diagrams with variation of output capacitance and its equivalent series resistance （ESR） are obtained, and the effect of output capacitance time-constant on the dynamic characteristics of V2-controlled Buck converter is investigated. It is found that with gradual reduction of output capacitance time-constant, the V2-controlled Buck converter shows the evolutive dynamic behavior from continuous conduction mode （CCM） period-1 to CCM period-2, CCM period-4, CCM period-8, CCM chaos, and discontinuous conduction mode （DCM） chaos. Jacobi matrix at a fixed point is also derived. According to this, the converter stability is analyzed by using characteristic values and maximum Lyapunov exponent, which validates the correctness of bifurcation analysis. Finally, the simulation and experimental circuits are set up, and the correctness of the theoretical analysis is verified by simulation and experimental results.