带恒功率负载DC-DC变换器的Lyapunov指数计算和动力学特性分析

摘要

The Lyapunov exponents of a DC-DC converter with constant power load cannot be calculated at the switching points because of the inexistence of Jacobi matrixes at these points. Aiming at this problem, this paper studies the Lyapunov exponent algorithm of such system using the local maps to construct the system compound Poincaré mapping. Thus, the piece-wise smooth nonlinear dynamic properties of the system can be analyzed according to the Lyapunov exponents. The calculating process is illustrated by the example of a Buck converter with constant power load. Both the local maps of non-switching and switching stage are deduced in detail. Then compound Poincaré mapping of system is constructed based on these two local maps. The theoretical results are verified by the numerical and circuit simulations. It is shown that the accuracy of Lyapunov exponents is improved by introducing the local mapping of load switching. The proposed method can also be extended to the other kind of switching power converters with nonlinear load or nonlinear source.%针对带恒功率负载的DC-DC变换器在切换点处不存在Jacobi矩阵而无法计算系统的Lyapunov指数的问题,利用局部映射构成系统的复合Poincaré 映射的方法研究该类系统的Lyapunov指数的计算方法,并据此分析系统的动力学特性.以带恒功率负载的电流模式Buck变换器为例,首先推导系统非切换阶段的局部映射和在不同模态下发生负载切换时的零时间不连续映射;然后利用局部映射构成系统的复合Poincaré 映射,从而推导出系统Lyapunov指数的计算方法;最后通过数值模拟及电路仿真证明了算法的正确性.负载切换映射的引入使Lyapunov指数的计算精度得到进一步提高,本文的研究结果可为分析电力电子级联系统的非线性分段光滑动力学特性提供依据.