一类由饱和引起的非线性现象

A class of nonlinear phenomena resulting from saturation

以一个功率因数校正boost变换器为例,描述了当系统在饱和与非饱和状态间不断切换时出现的一类非线性现象,分析了这些现象的特点和产生原因.推导了考虑饱和的分段微分方程,并据此进行了仿真,结果表明,系统一方面会出现倍周期分岔和混沌等传统的非线性现象,另一方面由于整流输入电流碰到饱和边界,系统的定性行为发生突变,会出现边界碰撞分岔,还能从混沌直接变为周期1.这类由饱和引起的非线性现象及相关分析得到了实验验证.

Based on a power-factor-correction （PFC） boost converter, a class of nonlinear phenomena arc described when the system switches between saturated and non-saturated states alternately. Their characteristics and origination are analyzed. According the piecewise differential equations derived, we simulate the system＇s dynamical behavior. The simulating results demonstrate that period-doubling bifurcation and chaos may occur in this system. Moreover, border-collision bifurcation and transition from chaos to period-1 may also appear. These nonlinear phenomena result from the abrupt change of the system＇ s qualitative behavior when the rectified input current runs into its saturation border. The nonlinear phenomena caused by saturation and the rclated analysis arc verified by the experimental results.