基于一维时间序列的无刷直流电动机混沌引子重构

Reconstruction of strange attractor of BLDCM based on one-dimension time series

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.