永磁同步电机混沌运动机理分析
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摘要
永磁同步电机的参数变化会使系统的稳定性发生改变,主要表现为电机转速的失稳和电流的不规则振荡,针对此问题,提出一种基于轨迹保稳降维的永磁同步电机混沌运动机理分析方法。首先,利用Lyapunov稳定性理论和分岔图研究不同参数条件下永磁同步电机的动力学特性,从宏观角度分析该系统的稳定性;然后,采用平面坐标投影法对永磁同步电机混沌运动的微观机理进行深入解析,分析系统平衡点在混沌运动过程中性态的变化规律,从而进一步揭示永磁同步电机混沌吸引子的特性;最后,利用电子电路对永磁同步电机进行物理构建,并验证理论分析的正确性。
Changes in parameters of permanent magnet synchronous motors may influence its stability,such as the instability of motors speed and the irregular oscillation of current. To solve this problem,a novel method was proposed to analyze chaotic motion mechanism of permanent magnet synchronous motors which is based on trajectory stability-preserving dimension-reduction. Firstly,Lyapunov stability theory and bifurcation diagram was adopted to study the dynamic characteristics of permanent magnet synchronous motors under different parameters,which analyzes the stability of the system in a macroscopic perspective. Then,the lane coordinate projection method was proposed to explore the micro mechanism of chaotic motion of permanent magnet synchronous motors and the varying rule of equilibrium point was analyzed during the chaotic motion,which reveals the characteristics of the chaotic attractor of permanent magnet synchronous motors. Finally,the physical implementation of permanent magnet synchronous motor was constructed using electronic circuit to verify the correctness of the theoretical analysis.
Changes in parameters of permanent magnet synchronous motors may influence its stability,such as the instability of motors speed and the irregular oscillation of current. To solve this problem,a novel method was proposed to analyze chaotic motion mechanism of permanent magnet synchronous motors which is based on trajectory stability-preserving dimension-reduction. Firstly,Lyapunov stability theory and bifurcation diagram was adopted to study the dynamic characteristics of permanent magnet synchronous motors under different parameters,which analyzes the stability of the system in a macroscopic perspective. Then,the lane coordinate projection method was proposed to explore the micro mechanism of chaotic motion of permanent magnet synchronous motors and the varying rule of equilibrium point was analyzed during the chaotic motion,which reveals the characteristics of the chaotic attractor of permanent magnet synchronous motors. Finally,the physical implementation of permanent magnet synchronous motor was constructed using electronic circuit to verify the correctness of the theoretical analysis.
引文
[1]WEI Duqu,ZHANG Bo,LUO Xiaoshu,et al.Effects of couplings on the collective dynamics of permanent-magnet synchronous motors[J].IEEE Transactions on Circuits and Systems II:Express Briefs,2013,60(10):692.
[2]刘刚,肖烨然,孙庆文.基于改进反电势积分的永磁同步电机位置检测[J].电机与控制学报,2016,20(2):36.LIU Gang,XIAO Yeran,SUN Qingwen.Position detection of PMSM based on the improved back-EMF integration method[J].Electric Machines and Control,2016,20(2):36.
[3]张兴华,沈捷,梅磊,等.永磁同步电机混沌运动的逆系统控制[J].电机与控制学报,2010,14(10):73.ZHANG Xinghua,SHEN Jie,MEI Lei,et al.Inverse system control of chaos in permanent magnet synchronous motors[J].Electric Machines and Control,2010,14(10):73.
[4]张波,李忠,毛宗源,等.一类永磁同步电动机混沌模型与霍夫分叉[J].中国电机工程学报,2001,21(9):13.ZHANG Bo,LI Zhong,MAO Zongyuan,et al.The chaotic model and Hopf bifurcation of a type of permanent magnet synchronous motor[J].Proceedings of the CSEE,2001,21(9):13.
[5]LI Zhong,JIN B P,JOO Y H,et al.Bifurcations and chaos in a permanent-magnet synchronous motor[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2002,49(3):383.
[6]薛禹胜,曹树谦,陈予恕.坐标平面投影法及其在Lorenz混沌系统中的应用[J].非线性动力学学报,2002(3):99.XUE Yusheng,CAO Shuqian,CHEN Yushu.Coordinate plane projection method(CPP)and its applications in Lorenz chaotic system[J].Journal of Nonlinear Dynamics in Science and Technology,2002(3):99.
[7]薛禹胜,WU Q H,周海强,等.Lorenz吸引子的微观结构[J].非线性动力学学报,2003(1):1.XUE Yusheng,WU Q H,ZHOU Haiqiang,et al.Application of stability-preserving trajectory-reduction methodology to reveal the fine structure of Lorenz system[J].Journal of Nonlinear Dynamics in Science and Technology,2003(1):1.
[8]葛晓慧.混沌理论在电机及其系统中的应用[D].杭州:浙江大学,2007.
[9]ZHAN Tungsheng,CHEN Jianliung,CHEN Shijaw,et al.Design of a chaos synchronisation-based maximum power tracking controller for a wind-energy-conversion system[J].Iet Renewable Power Generation,2014,8(6):590.
[10]TIAN Xingjun,LI Yunhua,LI Xiaqiang.Hybrid algorithm for traction transformer differential protection based on intrinsic mode function energy entropy and correlation dimension[J].Iet Generation Transmission and Distribution,2014,8(7):1274.
[11]CHEN Jianliung,HUANG Conghui,DU Yichun,et al.Combining fractional-order edge detection and chaos synchronisation classifier for fingerprint identification[J].Iet Image Processing,2014,8(6):354.
[12]HU Xiaonan,YANG Xuelin,HU Weisheng.Chaos-based selected mapping scheme for physical layer security in OFDM-PON[J].Electronics Letters,2015,51(18):1429.
[13]LI Dong,WANG Shilong,ZHANG Xiaohong,et al.Impulsive control of permanent magnet synchronous motors with parameters uncertainties[J].Chinese Physics B,2008,17(5):1678.
[14]张新国,孙洪涛,赵金兰,等.蔡氏电路的功能全同电路与拓扑等效电路及其设计方法[J].物理学报,2014,63(20):95.ZHANG Xinguo,SUN Hongtao,ZHAO Jinlan,et al.Equivalent circuit in function and topology to Chua's circuit and the design methods of these circuits[J].Acta Physica Sinica,2014,63(20):95.
[15]黄沄.一类多翼蝴蝶混沌吸引子及其电路实现[J].物理学报,2014,63(8):52.HUANG Yun.A family of multi-gyring chaotic attractors and its circuit implementation[J].Acta Physica Sinica,2014,63(8):52.
[16]李云峰,孙黎霞.永磁同步电机系统混沌现象分析和电路实现[J].微电机,2015(8):61.LI Yunfeng,SUN Lixia.Analysis of chaos and circuit implementation of permanent magnet synchronous motor system[J].Micromotors,2015(8):61.
[17]薛薇,郭彦岭,陈增强.永磁同步电机的混沌分析及其电路实现[J].物理学报,2009,58(12):8146.XUE Wei,GUO Yanling,CHEN Zengqiang.Analysis of chaos and circuit implementation of a permanent magnet synchronous motor[J].Acta Physica Sinica,2009,58(12):8146.
[18]孔庆媛,安跃军,孙昌志,等.精确线性化的永磁同步电机变结构混沌反控制[J].自动化技术与应用,2008,27(1):8.KONG Qingyuan,AN Yuejun,SUN Changzhi,et al.Variable structure chaos anti-control of an exact linearized PMSM[J].Techniques of Automation and Applications,2008,27(1):8.
[19]刘凌,苏燕辰,刘崇新.新三维混沌系统及其电路仿真实验[J].物理学报,2007,56(4):1966.LIU Ling,SU Yanchen,LIU Chongxin.A new chaotic system and its circuit simulation[J].Acta Physica Sinica,2007,56(4):1966.
[20]陈强,任雪梅.基于多核最小二乘支持向量机的永磁同步电机混沌建模及其实时在线预测[J].物理学报,2010,59(4):2310.CHEN Qiang,REN Xuemei.Chaos modeling and real-time online prediction of permanent magnet synchronous motor based on multiple kernel least squares support vector machine[J].Acta Physica Sinica,2010,59(4):2310.
[21]张波,李忠,毛宗源.永磁同步电动机的混沌特性及其反混沌控制[J].控制理论与应用,2002,19(4):545.ZHANG Bo,LI Zhong,MAO Zongyuan.Anti-control of its chaos and chaos characteristics in the permanent magnet synchronous motors[J].Control Theory and Application,2002,19(4):545.
[22]WIGGINS S,MAZEL D S.Introduction to applied nonlinear dynamical systems and chaos[J].Computers in Physics,2003,4(4):843.
[23]HASSARD B D,KAZARINOFF N D,WAN Y H.Theory and applications of Hopf bifurcation[M].New York:Cambridge University Press,1981:961-969.
[24]孙慧静.非线性动力系统分岔、混沌理论及其应用[D].北京:北京交通大学,2006.
[2]刘刚,肖烨然,孙庆文.基于改进反电势积分的永磁同步电机位置检测[J].电机与控制学报,2016,20(2):36.LIU Gang,XIAO Yeran,SUN Qingwen.Position detection of PMSM based on the improved back-EMF integration method[J].Electric Machines and Control,2016,20(2):36.
[3]张兴华,沈捷,梅磊,等.永磁同步电机混沌运动的逆系统控制[J].电机与控制学报,2010,14(10):73.ZHANG Xinghua,SHEN Jie,MEI Lei,et al.Inverse system control of chaos in permanent magnet synchronous motors[J].Electric Machines and Control,2010,14(10):73.
[4]张波,李忠,毛宗源,等.一类永磁同步电动机混沌模型与霍夫分叉[J].中国电机工程学报,2001,21(9):13.ZHANG Bo,LI Zhong,MAO Zongyuan,et al.The chaotic model and Hopf bifurcation of a type of permanent magnet synchronous motor[J].Proceedings of the CSEE,2001,21(9):13.
[5]LI Zhong,JIN B P,JOO Y H,et al.Bifurcations and chaos in a permanent-magnet synchronous motor[J].IEEE Transactions on Circuits and Systems I:Fundamental Theory and Applications,2002,49(3):383.
[6]薛禹胜,曹树谦,陈予恕.坐标平面投影法及其在Lorenz混沌系统中的应用[J].非线性动力学学报,2002(3):99.XUE Yusheng,CAO Shuqian,CHEN Yushu.Coordinate plane projection method(CPP)and its applications in Lorenz chaotic system[J].Journal of Nonlinear Dynamics in Science and Technology,2002(3):99.
[7]薛禹胜,WU Q H,周海强,等.Lorenz吸引子的微观结构[J].非线性动力学学报,2003(1):1.XUE Yusheng,WU Q H,ZHOU Haiqiang,et al.Application of stability-preserving trajectory-reduction methodology to reveal the fine structure of Lorenz system[J].Journal of Nonlinear Dynamics in Science and Technology,2003(1):1.
[8]葛晓慧.混沌理论在电机及其系统中的应用[D].杭州:浙江大学,2007.
[9]ZHAN Tungsheng,CHEN Jianliung,CHEN Shijaw,et al.Design of a chaos synchronisation-based maximum power tracking controller for a wind-energy-conversion system[J].Iet Renewable Power Generation,2014,8(6):590.
[10]TIAN Xingjun,LI Yunhua,LI Xiaqiang.Hybrid algorithm for traction transformer differential protection based on intrinsic mode function energy entropy and correlation dimension[J].Iet Generation Transmission and Distribution,2014,8(7):1274.
[11]CHEN Jianliung,HUANG Conghui,DU Yichun,et al.Combining fractional-order edge detection and chaos synchronisation classifier for fingerprint identification[J].Iet Image Processing,2014,8(6):354.
[12]HU Xiaonan,YANG Xuelin,HU Weisheng.Chaos-based selected mapping scheme for physical layer security in OFDM-PON[J].Electronics Letters,2015,51(18):1429.
[13]LI Dong,WANG Shilong,ZHANG Xiaohong,et al.Impulsive control of permanent magnet synchronous motors with parameters uncertainties[J].Chinese Physics B,2008,17(5):1678.
[14]张新国,孙洪涛,赵金兰,等.蔡氏电路的功能全同电路与拓扑等效电路及其设计方法[J].物理学报,2014,63(20):95.ZHANG Xinguo,SUN Hongtao,ZHAO Jinlan,et al.Equivalent circuit in function and topology to Chua's circuit and the design methods of these circuits[J].Acta Physica Sinica,2014,63(20):95.
[15]黄沄.一类多翼蝴蝶混沌吸引子及其电路实现[J].物理学报,2014,63(8):52.HUANG Yun.A family of multi-gyring chaotic attractors and its circuit implementation[J].Acta Physica Sinica,2014,63(8):52.
[16]李云峰,孙黎霞.永磁同步电机系统混沌现象分析和电路实现[J].微电机,2015(8):61.LI Yunfeng,SUN Lixia.Analysis of chaos and circuit implementation of permanent magnet synchronous motor system[J].Micromotors,2015(8):61.
[17]薛薇,郭彦岭,陈增强.永磁同步电机的混沌分析及其电路实现[J].物理学报,2009,58(12):8146.XUE Wei,GUO Yanling,CHEN Zengqiang.Analysis of chaos and circuit implementation of a permanent magnet synchronous motor[J].Acta Physica Sinica,2009,58(12):8146.
[18]孔庆媛,安跃军,孙昌志,等.精确线性化的永磁同步电机变结构混沌反控制[J].自动化技术与应用,2008,27(1):8.KONG Qingyuan,AN Yuejun,SUN Changzhi,et al.Variable structure chaos anti-control of an exact linearized PMSM[J].Techniques of Automation and Applications,2008,27(1):8.
[19]刘凌,苏燕辰,刘崇新.新三维混沌系统及其电路仿真实验[J].物理学报,2007,56(4):1966.LIU Ling,SU Yanchen,LIU Chongxin.A new chaotic system and its circuit simulation[J].Acta Physica Sinica,2007,56(4):1966.
[20]陈强,任雪梅.基于多核最小二乘支持向量机的永磁同步电机混沌建模及其实时在线预测[J].物理学报,2010,59(4):2310.CHEN Qiang,REN Xuemei.Chaos modeling and real-time online prediction of permanent magnet synchronous motor based on multiple kernel least squares support vector machine[J].Acta Physica Sinica,2010,59(4):2310.
[21]张波,李忠,毛宗源.永磁同步电动机的混沌特性及其反混沌控制[J].控制理论与应用,2002,19(4):545.ZHANG Bo,LI Zhong,MAO Zongyuan.Anti-control of its chaos and chaos characteristics in the permanent magnet synchronous motors[J].Control Theory and Application,2002,19(4):545.
[22]WIGGINS S,MAZEL D S.Introduction to applied nonlinear dynamical systems and chaos[J].Computers in Physics,2003,4(4):843.
[23]HASSARD B D,KAZARINOFF N D,WAN Y H.Theory and applications of Hopf bifurcation[M].New York:Cambridge University Press,1981:961-969.
[24]孙慧静.非线性动力系统分岔、混沌理论及其应用[D].北京:北京交通大学,2006.