基于一维时间序列的无刷直流电动机混沌引子重构
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摘要
基于相空间重构原理,针对无刷直流电动机的混沌模型,运用一维时间序列在高维情形下对低维混沌吸引子进行重构,重构后的方程具有和原动力方程相同的动力学特性,可以用于判断系统目前的动力学状态,并通过基于混沌优化算法的改进Wolf方法对重构前后方程的Lyapunov指数进行比较,证明此种重构方法的正确性和实用性.结果表明:采用的重构方法是有效的,与前人的方法相比,不用计算其关联维数和最佳时间延迟,具有简单、快速的特点,为进一步研究混沌预测和混沌控制提供了基础条件.
Based on the theory of phase space reconstruction,a low-dimension stranger attractor was reconstructed in high-dimension for brushless direct current motor(BLDCM)by one dimension time series.The features of reconstructed function are similar to the original function,which can be used to judge the dynamic status of system.The similarity was proved by comparing Lyapunov exponents using the improved Wolf method based on chaotic optimal scheme.The analysis results show that the present reconstructed method is effective,simple and quick,compared with the previous schemes which need to calculate the best reconstruction parameters.The conclusions can be used for chaotic forecasting and chaotic control.
Based on the theory of phase space reconstruction,a low-dimension stranger attractor was reconstructed in high-dimension for brushless direct current motor(BLDCM)by one dimension time series.The features of reconstructed function are similar to the original function,which can be used to judge the dynamic status of system.The similarity was proved by comparing Lyapunov exponents using the improved Wolf method based on chaotic optimal scheme.The analysis results show that the present reconstructed method is effective,simple and quick,compared with the previous schemes which need to calculate the best reconstruction parameters.The conclusions can be used for chaotic forecasting and chaotic control.
引文
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[8]蔡聪波.混沌系统最大Lyapunov指数的计算及其在电脑数据分析中的应用[D].厦门:厦门大学,2001.(CAI Cong-bo.The application and calculation of thelargest Lyapunov exponents of the chaotic system inEEG analysis[D].Xiamen:Xiamen University,2001.)
[9]李国辉,周世平,徐得名.时间序列最大Lyapunov指数的计算[J].应用科学学报,2003,21(2):127-131.(LI Guo-hui,ZHOU Shi-ping,XU De-ming.Comput-ing the largest Lyapunov exponent from time series[J].Journal of Applied Science,2003,21(2):127-131.
[10]郑兆必,张军,汪秉宏.最大Lyapunov指数计算的几种方法[J].地震,1994,8(4):86-92.(ZHENG Zhao-bi,ZHANG Jun,WANG Bing-hong.Several calculation methods of maximum Lyapunov ex-ponent[J].Earthquake,1994,8(4):86-92.)
[11]梁志珊,王丽敏,付大鹏,等.基于Lyapunov指数的电力系统短期负荷预测[J].中国电机工程学报,1998,18(5):368-371.(LIANG Zhi-shan,WANG Li-min,FU Da-peng,et al.Electric power system short-term load forecastingusing Lyapunov exponents technique[J].Proceedingsof the CSEE,1998,18(5):368-371.
[2]周佰成,翟延慧.Takens理论和小波分析在非线性预测中的应用[J].吉林大学学报:自然科学版,2001,7(3):21-28.(ZHOU Bai-cheng,ZHAI Yan-hui.The application ofTakens theory and wavelets to nonlinear prediction[J].Journal of Jilin University:Science and Technolo-gy,2001,7(3):21-28.)
[3]张波,李忠.基于时间序列状态空间重构的PMSM混沌现象检测[J].仪器仪表学报,2002,20(3):12-13.(ZHANG Bo,LI Zhong.Detection of chaotic phenom-ena in PMSM based on reconstructing state-space oftime sequence[J].Chinese Journal of Scientific Instru-ment,2002,20(3):12-13.)
[4]侯越先,何丕廉,付大鹏,等.适用于高必要嵌入维的混沌时间序列预测算法[J].天津大学学报,1999,32(5):594-598.(HOU Yue-xian,HE Pi-lian,FU Da-peng,et al.Re-constructing high dimension phase space:an improvedapproach to chaotic time series forecasting[J].Journalof Tianjin University,1999,32(5):594-598.)
[5]安跃军.深海机器人推进电机混沌现象研究[D].沈阳:沈阳工业大学,2005.(AN Yue-jun.Chaos phenomena research of thrustermotor in deepwater robot[D].Shenyang:ShenyangUniversity of Technology,2005.)
[6]张波,李忠,毛宗源,等.利用Lyapunov指数和容量维分析永磁同步电机仿真中的混沌现象[J].控制理论与应用,2001,18(4):589-592.(ZHANG Bo,LI Zhong,MAO Zong-yuan,et al.Ana-lyzing chaotic phenomenon in permanent magnet syn-chronous motors with Lyapunov exponent and capacitydimension[J].Control Theory and Applications,2001,18(4):589-592.)
[7]韦笃取,罗晓曙,方锦清,等.基于微分几何方法的永磁同步电动机的混沌运动的控制[J].物理学报,2006,55(1):54-59.(WEI Du-qu,LUO Xiao-shu,FANG Jin-qing,et al.Controlling chaos in permanent magnet synchronousmotor based on the differential geometry method[J].Acta Physica Sinica,2006,55(1):54-59.)
[8]蔡聪波.混沌系统最大Lyapunov指数的计算及其在电脑数据分析中的应用[D].厦门:厦门大学,2001.(CAI Cong-bo.The application and calculation of thelargest Lyapunov exponents of the chaotic system inEEG analysis[D].Xiamen:Xiamen University,2001.)
[9]李国辉,周世平,徐得名.时间序列最大Lyapunov指数的计算[J].应用科学学报,2003,21(2):127-131.(LI Guo-hui,ZHOU Shi-ping,XU De-ming.Comput-ing the largest Lyapunov exponent from time series[J].Journal of Applied Science,2003,21(2):127-131.
[10]郑兆必,张军,汪秉宏.最大Lyapunov指数计算的几种方法[J].地震,1994,8(4):86-92.(ZHENG Zhao-bi,ZHANG Jun,WANG Bing-hong.Several calculation methods of maximum Lyapunov ex-ponent[J].Earthquake,1994,8(4):86-92.)
[11]梁志珊,王丽敏,付大鹏,等.基于Lyapunov指数的电力系统短期负荷预测[J].中国电机工程学报,1998,18(5):368-371.(LIANG Zhi-shan,WANG Li-min,FU Da-peng,et al.Electric power system short-term load forecastingusing Lyapunov exponents technique[J].Proceedingsof the CSEE,1998,18(5):368-371.
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