在线阅读 --自然科学版 2020年5期《基于Adomian分解法分数阶永磁同步风力发电机系统求解及动力学分析》
基于Adomian分解法分数阶永磁同步风力发电机系统求解及动力学分析--[在线阅读]
雷腾飞1,2,3, 付海燕1, 王艳玲1, 黄明键3, 刘瑞宏1
1. 齐鲁理工学院 机电工程学院, 山东 济南 250200;
2. 齐鲁理工学院 忆阻计算应用协同创新中心, 山东 济南 250200;
3. 山东省中德智慧工厂 应用工程研究中心, 山东 济南 250200
起止页码: 395--402页
DOI: 10.13763/j.cnki.jhebnu.nse.2020.05.005
摘要
针对分数阶永磁同步风力发电机系统,运用Adomian分解法对系统非线性项进行分解,并通过Matalb绘制系统的吸引子与庞加莱截面图,同时采用分岔图、SE复杂度、C0复杂度与参数变化下的吸引子相图等数值仿真分析研究了系统,进一步揭示了分数阶混沌系统的可实现动力学特性.相关研究结果为风力发电机的控制奠定了良好的理论基础.

Solution and Dynamic Analysis on Fractional-order Permanent Magnet Synchronous Wind Generator System with Adomian Decomposition
LEI Tengfei1,2,3, FU Haiyan1, WANG Yanling1, HUANG Mingjian3, LIU Ruihong1
1. School of Mechanical and Electrical Engineering, Qilu Institute of Technology, Shandong Jinan 250200, China;
2. Collaborative Innovation Center of Memristive Computing Application(CICMCA), Qilu Institute of Technology, Shandong Jinan 250200, China;
3. Shandong Research and Engineering Center, China-Germany Intelligent Engineering Application, Shandong Jinan 250200, China
Abstract:
Fractional-order permanent magnet synchronous wind Generator system is studied, the nonlinear term of the system is decomposed by Adomian decomposition method,and the attractor and Poincare diagram of the system are drawn by Matalb.The system is analyzed by numerical simulation,such as bifurcation diagram,SE complexity,C0 complexity and attractor phase diagram under parameter changes.The realizable dynamic characteristics of fractional-order chaotic system are further revealed,and the relevant research results lay a good foundation for wind turbine control.

收稿日期: 2020-01-22
基金项目: 山东省高校科技计划项目(J18KA381);山东省重大科技创新工程(2019JZZY010111);山东省自然科学基金(ZR2017PA008);山东省重点研发计划(2019GGX104092)

参考文献:
[1]雷腾飞,陈恒,王震,等.分数阶永磁同步风力发电机中混沌运动的自适应同步控制[J].曲阜师范大学学报(自然科学版),2014,40(3):63-68.doi:10.3969/j.issn.1001-5337.2014.03.063 LEI Tengfei,CHEN Heng,WANG Zhen,et al.Adaptive Synchronization Control of Chaos in Fractional Order Permanent Magnet Synchronous Generators for Wind Power[J].Journal of Qufu Normal University(Natural Science),2014,40(3):63-68.
[2]杨国良,李惠光.直驱式永磁同步发电机中混沌运动的滑模变结构控制[J].物理学报,2009,58(11):166-171.doi:CNKI.SUN.WLXB.0.2009-11-027 YANG Guoliang,LI Huiguang.Sliding Mode Variable-structure Control of Chaos in Direct-driven Permanent Magnet Synchronous Generators for Wind Turbines[J].Acta Phys Sin,2009,58(11):166-171.
[3]郑刚,邹见效,徐红兵,等.直驱型永磁同步发电机中混沌运动的反步自适应控制[J].物理学报,2009,58(11):119-126.doi:CNKI.SUN.WLXB.0.2011-06-019 ZHENG Gang,ZOU Jianxiao,XU Hongbing,et al.Adaptive Backstepping Control of Chaotic Property in Direct-driveven Permanent Magnet Sychronous Generators for Wind Power[J].Acta Phys Sin,2009,58(11):119-126.
[4]吴忠强,谭拂晓.永磁同步电动机混沌系统的无源化控制[J].中国电机工程学报,2006,26(18):159-163.doi:CNKI.SUN.ZGDC.0.2006-18-028 WU Zhongqiang,TAN Fuxiao.Passivity Control of Permanent-magnet Synchronous Motors Chaotic System[J].Proceedings of the Chinese Society for Electrical Engineering,2006,26(18):159-163.
[5]LU J G.Nonlinear Observer Design to Synchronize Fractional-order Chaotic System via a Scalar Transmitted Signal[J].Physica A,2006,359:107-118.doi:10.1016/j.physa.2005.04.040
[6]崔力,欧青立,徐兰霞.分数阶Lorenz超混沌系统及其电路仿真[J].电子测量技术,2010,33(5):13-16.doi:CNKI.SUN.DZCL.0.2010-05-008 CUI Li,OU Qingli,XU Lanxia.Fractional of Hyperchaotic Lorenz System and Circuit Simulation[J].Electronic Measurement Technology,2010,33(5):13-16.
[7]刘明明,夏铁成,王金波.带有三角函数的二维分数阶离散系统的混沌现象[J].上海大学学报(自然科学版),2019,25(2):56-60.doi:CNKI.SUN.SDXZ.0.2019-02-007 LIU Mingming,XIA Tiecheng,WANG Jinbo.Two-dimensional Fractional Discrete Chaos Combined with Trigonometric Functions[J]Journal of Shanghai University(Natural Science),2019,25(2):56-60.
[8]刘崇新.一个超混沌系统及其分数阶电路仿真实验[J].物理学报,2007,56(12):6865-6873.doi:10.3321/j.issn.1000-3290.2007.12.014 LIU Chongxin.A Hyperchaotic System and Its Fractional Order Circuit Simulation[J].Acta Phys Sin,2007,56(12):6865-6873.
[9]贾红艳,陈增强,薛薇.分数阶Lorenz系统的分析及电路实现[J].物理学报,2013,62(14):140503-1-7.doi:CNKI.SUN.WLXB.0.2013-14-009 JIA Hongyan,CHEN Zengqiang,XUE Wei.Analysis and Circuit Implementation for the Fractional-order Lorenz System[J].Acta Phys Sin,2013,62(14):140503-1-7.
[10]陈恒,雷腾飞,王震,等.分数阶Chen混沌系统的动力学分析与电路实现[J].河北师范大学学报(自然科学版),2015,39(3):208-215.doi:10.13763/j.cnki.jhebnu.nse.2015.03.005 CHEN Heng,LEI Tengfei,WANG Zhen,et al.Dynamic Analysis and Circuit Implementation of Fractional-orde Chen Chaotic System[J].Journal of Hebei Normal University (Natural Science),2015,39(3):208-215.
[11]闵富红,余杨,葛曹君.超混沌分数阶LV系统电路实验与追踪控制[J].物理学报,2009,58(3):1456-1461.doi:CNKI.SUN.WLXB.0.2009-03-012 MIN Fuhong,YU Yang,GE Caojun.Circuit Implementation and Tracking Control of the Fractional-order Hyper-chaotic LV System[J].Acta Phys Sin,2009,58(3):1456-1461.
[12]HE Shaobo,SUN Kehui,MEI Xiaoyong.Numerical Analysis of a Fractional-order Chaotic System Based on Conformable Fractional-order Derivative[J].European Physical Journal Plus,2017,132(1):36-1-11.doi:10.1140/epjp/i2017-11306-3
[13]BEHINFARAZ R,BADAMCHIZADEH M,GHIASI A R.An Adaptive Method to Parameter Identification and Synchronization of Fractional-order Chaotic Systems with Parameter Uncertainty[J].Appl Math Model,2016,40:4468-4479.doi:10.1016/j.apm.2015.11.033
[14]SHI X R,WANG Z L.Adaptive Added-order Anti-synchronization of Chaotic Systems with Fully Unknown Parameters[J].Appl Math Comput,2009,215:1711-1717.doi:10.1016/j.amc.2009.07.023
[15]YU J Y,LEI J W,WANG L I.Backstepping Synchronization of Chaotic System Based on Equivalent Transfer Function Method[J].Optik,2017,130:900-913.
[16]WANG Z,LEI T F,XI X J,et al.Fractional Control and Generalized Synchronization for a Nonlinear Electromechanical Chaotic System and Its Circuit Simulation with Multisim[J].Turk J Elec Eng & Comp Sci,2016,24:1502-1515.
[17]张伟.基于新型滑模方法的分数阶金融超混沌系统的同步控制[J].内蒙古农业大学学报(自然科学版),2019,40(2):89-93. ZHANG Wei.Synchronization Control of Fractional Financial Hyperchaotic System Based on New Sliding Mode Method[J].Journal of Inner Mongolia Agricultural University (Natural Science),2019,40(2):89-93.
[18]王东晓.分数阶超混沌Bao系统的比例积分滑模同步[J].内蒙古农业大学学报(自然科学版),2018,39(3):83-89. WNAG Dongxiao.Proportional Integral Sliding Mode Synchronization for Fractional Order Hyperchaotic Bao Systems[J].Journal of Inner Mongolia Agricultural University (Natural Science),2018,39(3):83-89.
[19]王东晓.分数阶超混沌Rabinovich系统在指定时刻的同步控制[J].内蒙古农业大学学报(自然科学版),2018,39(6):93-100. WANG Dongxiao.Synchronization Control of Fractional-order Hyperchaotic Rabinovich System at Specified Time[J].Journal of Inner Mongolia Agricultural University (Natural Science),2018,39(6):93-100.