电压控制不连续导电模式DC-DC变换器的熵特性研究

Entropy in voltage mode controlled discontinuous conducting mode DC-DC converters

结合DC-DC变换器非线性特性随反馈增益k变化的关系,以及熵能够反映序列总体统计特征的特点,提出一种基于熵估计DC-DC变换器非线性行为的新方法.以一阶电压反馈不连续导电模式DCM Buck和Boost变换器为例,详细分析了不同反馈增益k和初值x0形成的数值序列及熵的分布情况.研究结果表明:DC-DC变换器的熵由反馈增益k决定,与初值x0无关,最终小于理论极大值log2N(N为统计区间个数);熵能够准确区分DC-DC变换器的倍周期分岔和混沌行为,从而得到一种新的可量化的DC-DC变换器非线性动力学行为指标;完善了该类变换器非线性动力学分析的理论和方法.

Considering that the variation of nonlinear characteristics of DC-DC converter with parameter k and the fact that entropy can re- flect the statistical characteristic of numerical sequence, in this paper we propose a new method to estimate the nonlinear characteristics of DC-DC converter based on the information about entropy. In this study, taking one-order DCM Buck and Boost converter for ex- ample, the distributions of numerical sequences and entropies are analysed under different values of feedback gain k and initial values of x0. The results prove that the entropy of DC-DC converter is determined by feedback gain k and irrelevant to initial value x0, and its final value is smaller than the theoretical maximum value log 2 N（N is the number of partition）, and that entropy can discriminate the period-doubling bifurcation and chaos. So a quantifiable nonlinear dynamical behavior index is obtained which can provide theoretical basis for understanding chaos characteristic and chaos control, and perfect the theoretical analysis method in DC-DC converters.