基于安匝和的隔离式开关变换器霍普夫分岔与准周期现象研究  

Hopf Bifurcation and Quasi-Periodicity Phenomena in Isolated Switching Converters Based on Total Ampere-Turns

作　　者：谢帆[1] 张波[1] 杨汝[2] 

机构地区：[1]华南理工大学电力学院,广东广州510640 [2]广州大学物理与电子工程学院,广东广州510006

出　　处：《电子学报》2013年第9期1778-1783,共6页Acta Electronica Sinica

基　　金：国家自然科学基金重点项目(No.50937001);国家自然科学基金(No.51277035);广东省战略性新兴产业(No.2010A081002004)

摘　　要：本文以电压模式控制反激式变换器为例,研究了隔离式开关变换器的霍普夫分岔与准周期现象.基于安匝和建立系统的离散映射,运用频闪采样得到以控制周期为分岔参数的分岔图.在电流连续模式下,运用特征值法判断平衡点的稳定性及其失稳过程中的霍普夫分岔.提出变压器存在时系统自然周期的正确表达,并解释分岔时系统自然周期和控制周期与特征值的关系.分析了准周期和锁频现象的演化过程并运用转数加以区别.数论理论中的法里原理、魔梯现象和准周期转数的连分数表达在反激式变换器分岔过程中的体现也得到研究.最后,实验验证了理论分析的正确性.Considering the voltage mode controlled flyback converter as the example,this paper studies Hopf bifurcation and quasi-periodicity phenomena in isolated switching converters. The discrete map of the system is derived based on total ampere-turns. Using stroboscopic sampling, bifurcation diagram is obtained with the control period as the bifurcation parameter. Hopf bifurcation phenomenon is studied by calculating the eigenvalues of the period-1 orbit as the equilibrium point loses its stability. The correct ex- pression of natural period with the transformer is presented and the relationship between natural period and control period at Hopf bi- furcation point is explained. The rotation number is used to distinguish the evolvement of quasi-periodicity and frequency locking phenomena. The embodiments of the Farey principle,devil＇s staircase and the expression of rotation rmmber of quasi-periodicity are investigated as well. Finally, experimental results show that the theoretical analysis is correct.

关 键 词：安匝和 反激式变换器 霍普夫分岔 准周期 锁频 法里原理 魔梯 连分数 

分 类 号：TM17[电气工程—电工理论与新技术]