基于自适应滑模控制的分数阶蔡氏电路系统动力学分析与控制  

Dynamic Analysis and Control of Fractional-Order Chua's Circuit System Based on Adaptive Sliding Mode Control

作　　者：朱伟 陈坤[2,3] 王谦 朱弘钊[2,3] ZHU Wei;CHEN Kun;WANG Qian;ZHU Hongzhao(Hunan Provincial Power Transmission and Maintenance Branch, Hengyang 421000, China;Electric Power Research Institute, Wuhan South Company LTD, Wuhan 430074, China;Hubei Key Laboratory of Power Grid Lightning Risk Prevention, Wuhan 430074, China)

机构地区：[1]国网湖南省输电检修分公司,湖南衡阳421000 [2]国网电力科学研究院武汉南瑞有限责任公司,武汉430074 [3]电网雷击风险预防湖北省重点实验室,武汉430074

出　　处：《复杂系统与复杂性科学》2018年第2期88-94,共7页Complex Systems and Complexity Science

摘　　要：为了研究整数阶电路系统的动态行为,国内外学者做了非常巨大的努力,得出了许多重要的结论。然而,在现实生活中,更多的系统是分数阶系统。因此,研究分数阶蔡氏电路系统的动力学行为就变得非常的前沿和有意义。这篇文章主要研究对象是三阶分数阶蔡氏电路系统,通过分数阶劳斯-赫尔维兹判据,李雅普诺夫稳定性判断方法以及矩阵理论等推导出分数阶蔡氏电路系统的渐近稳定性的充分条件以及自适应控制器的选取条件。最后通过数值模拟的方法,验证了理论的有效性和合理性。In order to study the dynamic behavior of integer order system,scholars both in china and abroad have made great efforts and reached many important conclusions.However,in real life,the more existence is the fractional-order system.Therefore,The study of dynamic behavior of fractional-order Chua's circuit system becomes very forward and meaningful.The main research object of this paper is the three dimensional fractional-order chua's circuit system,through the Routh-Hurwitz criterion,Lyapunov stability judgment method and matrix theory derived the sufficient condition of the asymptotic stability of the Chua's circuit system and the selection of adaptive controller condition.Finally,the validity and rationality of the theory are verified by nu-merical simulation.

关 键 词：分数阶 稳定性 自适应滑模控制 蔡氏电路系统 

分 类 号：N94[自然科学总论—系统科学]