基于符号动力学的开关变换器时间不可逆性分析*

摘要

A new method based on symbobic dynamics and relative entropy theory is proposed to examine the nonlinear behaviours of converters. Firstly, the discrete numerical sequence is obtained from iteration map, which is then transferred to a symbol-time series according to the topological conjugation, and the relative entropy is calculated by means of forward and backward probabilities. This paper takes a first one-order voltage feedback DCM Boost converter as an example, and the result shows that the relative entropy, which can measure quantitatively the distance apart from equilibrium when converter lies in a chaotic state, is a new and quantified nonlinear dynamic behaviours which has not been used in converters yet.%本文提出了一种采用符号动力学和相对熵理论分析开关变换器非线性特性的新方法。根据迭代映射描述的开关变换器非线性系统得到离散数值序列，基于拓扑共轭理论将其转化为符号序列，通过前向序列和后向序列概率计算该符号序列的相对熵。文中以一阶电压反馈DCM Boost变换器为例，研究结果表明，开关变换器存在时间不可逆性，相对熵数值能够量化开关变换器处于混沌状态时离开平衡点的距离，从而得到一种新的可量化的开关变换器非线性动力学行为指标。