幂次指数趋近律滑模控制逆变器的分岔与混沌

Bifurcation and chaos in power exponential reaching law sliding mode controlled inverter

中文关键词  逆变器  滑模控制  幂次指数趋近律  分岔  混沌控制  Washout滤波器

英文关键词  inverter  sliding mode  power exponential reaching law  bifurcation  chaos control  Washout filter

中文摘要

      针对滑模控制逆变器频发的分岔与混沌现象, 本文基于滑动模态的存在和到达条件, 构造了幂次指数趋近律滑模控制逆变器系统. 运用频闪映射理论推导其离散数学模型, 采用折叠图、频谱图和分岔图等详细分析此逆变器的复杂动力学演变规律, 基于快变稳定性定理探究系统控制系数的平稳运行域. 发现分别随控制系数和内部电路参数在一定范围内变化, 系统会出现周期分岔、切分岔、阵发性混沌和多种周期状态共存现象, 以及存在控制系数稳定域较窄的缺陷, 不利于该逆变器的平稳有序运行. 为克服参数变化带来的系统不稳定性隐患, 将Washout滤波器混沌抑制方式引入到幂次指数滑模控制逆变器中. 该方法利用分岔反控制原理改善系统非线性特性, 具有易于实现和控制简单的优点. 数值仿真结果验证了此混沌控制策略的可行性和有效性. 为幂次指数趋近滑模控制逆变器的优化设计、动态调试和稳态作业提供可参考价值.

英文摘要

      Aiming at the frequent bifurcation and chaos in sliding mode controlled inverters, the power exponential reaching law sliding mode controlled inverter system was constructed based on the existence and arrival conditions of sliding modes in this paper. A discrete mathematical model was derived using stroboscopic mapping theory, the complex dynamic evolution of this inverter was analyzed in detail using folding diagrams, spectrum diagrams and bifurcation diagrams, and the stability working domain of system’s control coefficients was explored based on the fast-scale stability theorem. It was found that period-doubling bifurcation, tangential bifurcation, paroxysmal chaos and coexistence of multiple period-doubling states as the control coefficients and internal circuit parameters vary within a certain range respectively,as well as a narrow stability domain of the control coefficient, which affects the system’s stability seriously. In order to overcome the hidden issues of system’s instability caused by parameters vary, the chaos suppression method of Washout filter was introduced into the power exponential reaching law sliding mode controlled inverter. The proposed method not only improves the system’s nonlinear characteristics based on the bifurcation inverse control principle, but also has the advantages of being easy to implement and simple to control. The numerical simulation results verified the feasibility and effectiveness of this chaos control strategy. The findings can be used to provide some reference for the optimal design,dynamic debugging and steady-state operation of power exponential reaching law sliding mode controlled inverter.