本文首先介紹了永磁同步電機與混沌Lorenz系統(tǒng)在數(shù)學(xué)模型上的相似之處。永磁同步電機本身是不會呈現(xiàn)混沌特性的，但是隨著電機外部力矩的變化及q軸電壓的變化，就有可能產(chǎn)生混沌現(xiàn)象。傳統(tǒng)的PI控制器在抑制混沌上作用又不是很明顯。由此引入了非線性反饋控制，該控制器能夠使非線性的電機系統(tǒng)轉(zhuǎn)化為普通的一階系統(tǒng)，從而可以通過線性系統(tǒng)的零極點配置達到期望的響應(yīng)特性?？紤]到實際系統(tǒng)的某些變量可能無法測量，在非線性反饋的基礎(chǔ)之上，引入了基于混沌降階同步的狀態(tài)觀測器，用估計值代替某些不可測量的變量，進而構(gòu)成非線性反饋，實現(xiàn)了電機系統(tǒng)的控制。同時通過Lyapunov直接法證明了觀測器的穩(wěn)定性。仿真結(jié)果也證明了該控制器的有效性。
參考文獻
[1] 王立欣, 王宇野, 王豐欣. 基于DSP的電動車用永磁同步電機的控制方法[J]. 電機與控制學(xué)報, 2005,9(1): 51-54.
[2] JAHNS T M, KLINMAN G B, NEUMANN T W. Interior permanent magnet synchronous motors for adjustable-speed drives[J]. IEEE Transactions on Industrial Applications, 1986,22(4):738-747.
[3] HEMATI N, KWATNY H. Bifurcation of equilibria and chaos in permanent-magnet machines[C]. Proceedings of the 32nd conference on Decision and control, December 1993:425-429.
[4] 楊志紅, 姚瓊薈. 無刷直流電動機系統(tǒng)非線性研究[J].動力學(xué)與控制學(xué)報, 2006,4(1):59-62.
[5] HEMATI N. Strange attractors in brushless DC motors. IEEE Transactions on Circuits and Systems-I:Fundamental Theory and Application. 1994,41(1):40-45.
[6] LI Shuang, XU Wei, LI Rui Hong. Synchronization of two  different chaotic systems with unknown parameters[J].Phys.  Lett. A, 2007,361(1):98-102.
[7] LI Xiao Run, ZHAO Liao Ying, ZHAO Guang Zhou. Sliding mode controlfor synchronization of chaotic systems with structure or parameters mismatching[J]. Zhejiang Univ SCI, 2005(6):571-576.
[8] HUANG L L,WANG M, FENG R. Parameters identification and adaptive synchronization of chaotic systems with unknown parameters[J]. Phys. Lett. A, 2005,342:299-304.
[9] PECORA L M, CARROLL T M.Synchronization of chaotic systems[J]. Phys Rev Lett, 1990,64(8):821-830.
[10] HEMATI N, LEU M C. A complete model characterization of brushless DC motors[J]. IEEE Transactions on Industry Applications. 1992,28(1):172-180.
[11] GE Zheng Ming, CHANG Ching Ming, CHEN Yen Sheng. Anti-control of chaos of single time scale brushless dc motors and chaos synchronization of different order systems[J]. Chaos, Solitons and Fractals, 2006,27:1298-1315.
[12] JING Zhu Jun, CHANG Yu, CHEN Guan Rong. Complex dynamics in a permanent-magnet synchronous motor model[J]. Chaos, Solitons and Fractals, 2004,22:831-848.
[13] GE Z M, CHENG J W. Chaos synchronization and parameter identification of three time scales brushless DC motor system[J]. Chaos, Solitons and Fractals, 2005, 24:597-616.
[14] ZAHER A A. A nonlinear controller design for permanent magnet motors using a synchronization-based technique inspired from the Lorenz system[J]. CHAOS, 2008,18:(1).