开关变换器的仿真建模方法及最大Lyapunov指数计算

提出DC-DC开关变换器的两种建模方法,并对之进行了比较,以便更有效地对变换器中的各种线性、非线性现象进行数值仿真及分析计算。一种建模方法是考虑时间,将时间变量看成为一个状态变量,从而建立非自治系统模型;另一种是不考虑时间,而仅考虑电路状态变量,来建立变换器的自治系统模型。两种模型的数值仿真结果完全一致,但以这两种模型为基础,计算所得到的最大Lyapunov指数的表现是不同的,相比较而言,以自治系统模型为基础,计算所得的最大Lyapunov指数包含更多的信息,它不仅能指示混沌的产生,而且可以指示各次分叉的情况。

Modeling of DC-DC Converter and Calculation of Largest Lyapunov Exponent

Two modeling methods of DC-DC converters were proposed and discussed, for the purpose of carrying out numerical simulation and calculation more effectively. One modeling method is constructing non-autonomous model by considering time, and regarding the time variable as a state variable; the other way is constructing autonomous model by discarding time, and considering only the state variables of circuit. The same results are achieved when simulating these two models. But the calculated largest Lyapunov exponent based on the two models can show the different styles and, by contrast with the occasion of non-autonomous model, the largest Lyapunov exponent calculated with autonomous model contains more information, which can indicate not only the emergence of chaos, but also the locations of bifurcation.