永磁同步电机混沌模型的拓扑马蹄分析与FPGA设计
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摘要
深入分析永磁同步电机PMSM(pormoment magnet synchronous motor)的混沌特性以便进一步研究如何消除或利用其混沌特性。针对气隙均匀永磁同步电机混沌模型进行了深入分析,通过绘制该混沌模型相图、Ly-apunov指数谱图和分岔图等,对其动力学特性进行仿真分析。借助拓扑马蹄引理严格判定其混沌吸引子存在,用Housetool找出该PMSM混沌模型在Poincaré截面映射下的马蹄。此外,还给出该模型的现场可编程门阵列FPGA(field programmable gate array)设计与实现,为其在实际中的应用提供一定的理论基础和技术支持。
In this paper,the chaotic characteristics of apermanent magnet synchronous motor(PMSM)are analyzed in depth to study how to eliminate or utilize its chaotic characteristics. A chaos model of a PMSM with uniform air gapis analyzed,and its dynamic behaviors are simulated and analyzed by drawing its phase trajectory,Lyapunov spectrum,andbifurcation diagram,etc. The existence of chaotic attractors in the PMSM model is strictly proved using the HorseshoeLemma,and its topological horseshoe under the mapping of Poincaré section is found by Housetool. In addition,thefield programmable gate array(FPGA)design and therealization of the proposed modelare given,which provides a theoretical basis and technical support for its practical applications.
In this paper,the chaotic characteristics of apermanent magnet synchronous motor(PMSM)are analyzed in depth to study how to eliminate or utilize its chaotic characteristics. A chaos model of a PMSM with uniform air gapis analyzed,and its dynamic behaviors are simulated and analyzed by drawing its phase trajectory,Lyapunov spectrum,andbifurcation diagram,etc. The existence of chaotic attractors in the PMSM model is strictly proved using the HorseshoeLemma,and its topological horseshoe under the mapping of Poincaré section is found by Housetool. In addition,thefield programmable gate array(FPGA)design and therealization of the proposed modelare given,which provides a theoretical basis and technical support for its practical applications.
引文
[1]刘婷婷,谭彧,吴刚,等(Liu Tingting,Tan Yu,Wu Gang,et al).基于SVPWM的高转速永磁同步电机控制系统的研究(Simulating of high speed PMSM control system based on SVPWM)[J].电力系统保护与控制(Power System Protection and Control),2009,37(12):11-14,19.
[2]祝晓辉,李颖晖,陈玉峰(Zhu Xiaohui,Li Yinghui,Chen Yufeng).永磁同步电机转子位置及速度提取灰色预测法(Extraction of rotor position and speed for PMSM using grey system prediction)[J].电机与控制学报(Electric Machines and Control),2009,13(2):184-189.
[3]Jing Zhujun,Yu Chang,Chen Guanrong.Complex dynamics in a permanent-magnet synchronous motor model[J].Chaos,Solitons and Fractals,2004,22(4):831-848.
[4]张波,李忠,毛宗源,等(Zhang Bo,Li Zhong,Mao Zongyuan,et al).一类永磁同步电动机混沌模型与霍夫分叉(The chaotic model and Hopf bifurcation of a type of permanent-magnet synchronous motor)[J].中国电机工程学报(Proceedings of the CSEE),2001,21(9):13-17.
[5]Krishan R,Bharadwaj A S.A review of parameter sensitivity and adaptation in indirect vector controlled induction motor drive systems[J].IEEE Trans on Power Electronics,1991,6(4):695-703.
[6]Pichot M A,Kajs J P,Murphy B R,et al.Active magnetic bearings for energy storage systems for combat vehicles[J].IEEE Trans on Magnetics,2001,37(1):318-323.
[7]邹国棠,王政.混沌电机驱动及其应用[M].北京:科学出版社,2009.
[8]Kennedy J,Kocak S,Yorke J A.A chaos lemma[J].Amer Math Monthly,2001,108(5):411-423.
[9]Yang Xiao-Song,Tang Yun.Horseshoes in piecewise continuous maps[J].Chaos,Solitons and Fractals,2004,19(4):841-845.
[10]Yang Xiaosong,Li Qingdu.Existence of horseshoe in a foodweb model[J].International Journal of Bifurcation and Chaos in Science and Engineering,2004,14(5):1847-1852.
[11]杨晓松,李清都,唐云(Yang Xiaosong,Li Qingdu,Tang Yun).双摆系统的拓扑马蹄与混沌(Topological horseshoe and chaos in a double pendulum system)[J].力学季刊(Chinese Quarterly of Mechanics),2009,30(1):149-153.
[12]Yang Xiaosong,Li Qingdu.On entropy of Chuas circuits[J].International Journal of Bifurcation and Chaos,2005,15(5):1823-1828.
[13]Li Qingdu,Yang Xiaosong.A simple method for finding topological horseshoes[J].International Journal of Bifurcation and Chaos,2010,20(2):467-478.
[14]薛薇,郭彦岭,陈增强(Xue Wei,Guo Yanling,Chen Zengqiang).永磁同步电机的混沌分析及其电路实现(Analysis of chaos and circuit implementation of a permanent magnet synchronous motor)[J].物理学报(Acta Physica Sinica),2009,58(12):8146-8151.
[15]Yang Xiaosong.Topological horseshoes and computer assisted verification of chaotic dynamics[J].International Journal of Bifurcation and Chaos,2009,19(4):1127-1145.
[16]田浩(Tian Hao).MATLAB在电机教学中的应用(Applications of MATLAB in the teaching of electric machinery)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2006,18(2):108-112.
[17]殷丽娟,赵熙临,梅真(Yin Lijuan,Zhao Xilin,Mei Zhen).基于混沌粒子群优化算法的微电网优化运行技术(Optimizing technology for micro grid operation based on chaos particle swarm optimization algorithm)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2016,28(5):55-61.
[18]Yang Xiaosong,Li Huimin,Huang Yan.A planar topological horseshoe theory with applications to computer verifications of chaos[J].Journal of Physics A,2005,38(19):4175-4185.
[19]李清都,唐宋(Li Qingdu,Tang Song).三维超混沌映射拓扑马蹄寻找算法及应用(Algorithm for finding horseshoes in three-dimensional hyperchaotic maps and its application)[J].物理学报(Acta Physica Sinica),2013,62(2):020510-1-8.
[20]禹思敏.混沌系统与混沌电路:原理、设计及其在通信中的应用[M].西安:西安电子科学出版社,2011.
[21]陈春光,禹思敏(Chen Chunguang,Yu Simin).基于混沌序列的视频保密通信(Video secure communications based on chaotic sequences)[J].电视技术(Video Engineering),2014,38(23):97-99,163.
[2]祝晓辉,李颖晖,陈玉峰(Zhu Xiaohui,Li Yinghui,Chen Yufeng).永磁同步电机转子位置及速度提取灰色预测法(Extraction of rotor position and speed for PMSM using grey system prediction)[J].电机与控制学报(Electric Machines and Control),2009,13(2):184-189.
[3]Jing Zhujun,Yu Chang,Chen Guanrong.Complex dynamics in a permanent-magnet synchronous motor model[J].Chaos,Solitons and Fractals,2004,22(4):831-848.
[4]张波,李忠,毛宗源,等(Zhang Bo,Li Zhong,Mao Zongyuan,et al).一类永磁同步电动机混沌模型与霍夫分叉(The chaotic model and Hopf bifurcation of a type of permanent-magnet synchronous motor)[J].中国电机工程学报(Proceedings of the CSEE),2001,21(9):13-17.
[5]Krishan R,Bharadwaj A S.A review of parameter sensitivity and adaptation in indirect vector controlled induction motor drive systems[J].IEEE Trans on Power Electronics,1991,6(4):695-703.
[6]Pichot M A,Kajs J P,Murphy B R,et al.Active magnetic bearings for energy storage systems for combat vehicles[J].IEEE Trans on Magnetics,2001,37(1):318-323.
[7]邹国棠,王政.混沌电机驱动及其应用[M].北京:科学出版社,2009.
[8]Kennedy J,Kocak S,Yorke J A.A chaos lemma[J].Amer Math Monthly,2001,108(5):411-423.
[9]Yang Xiao-Song,Tang Yun.Horseshoes in piecewise continuous maps[J].Chaos,Solitons and Fractals,2004,19(4):841-845.
[10]Yang Xiaosong,Li Qingdu.Existence of horseshoe in a foodweb model[J].International Journal of Bifurcation and Chaos in Science and Engineering,2004,14(5):1847-1852.
[11]杨晓松,李清都,唐云(Yang Xiaosong,Li Qingdu,Tang Yun).双摆系统的拓扑马蹄与混沌(Topological horseshoe and chaos in a double pendulum system)[J].力学季刊(Chinese Quarterly of Mechanics),2009,30(1):149-153.
[12]Yang Xiaosong,Li Qingdu.On entropy of Chuas circuits[J].International Journal of Bifurcation and Chaos,2005,15(5):1823-1828.
[13]Li Qingdu,Yang Xiaosong.A simple method for finding topological horseshoes[J].International Journal of Bifurcation and Chaos,2010,20(2):467-478.
[14]薛薇,郭彦岭,陈增强(Xue Wei,Guo Yanling,Chen Zengqiang).永磁同步电机的混沌分析及其电路实现(Analysis of chaos and circuit implementation of a permanent magnet synchronous motor)[J].物理学报(Acta Physica Sinica),2009,58(12):8146-8151.
[15]Yang Xiaosong.Topological horseshoes and computer assisted verification of chaotic dynamics[J].International Journal of Bifurcation and Chaos,2009,19(4):1127-1145.
[16]田浩(Tian Hao).MATLAB在电机教学中的应用(Applications of MATLAB in the teaching of electric machinery)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2006,18(2):108-112.
[17]殷丽娟,赵熙临,梅真(Yin Lijuan,Zhao Xilin,Mei Zhen).基于混沌粒子群优化算法的微电网优化运行技术(Optimizing technology for micro grid operation based on chaos particle swarm optimization algorithm)[J].电力系统及其自动化学报(Proceedings of the CSU-EPSA),2016,28(5):55-61.
[18]Yang Xiaosong,Li Huimin,Huang Yan.A planar topological horseshoe theory with applications to computer verifications of chaos[J].Journal of Physics A,2005,38(19):4175-4185.
[19]李清都,唐宋(Li Qingdu,Tang Song).三维超混沌映射拓扑马蹄寻找算法及应用(Algorithm for finding horseshoes in three-dimensional hyperchaotic maps and its application)[J].物理学报(Acta Physica Sinica),2013,62(2):020510-1-8.
[20]禹思敏.混沌系统与混沌电路:原理、设计及其在通信中的应用[M].西安:西安电子科学出版社,2011.
[21]陈春光,禹思敏(Chen Chunguang,Yu Simin).基于混沌序列的视频保密通信(Video secure communications based on chaotic sequences)[J].电视技术(Video Engineering),2014,38(23):97-99,163.