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## Robust control for permanent magnet synchronous motors based on Hamiltonian function

Wu Zhong-Qiang, Wu Chang-Han, Zhao Li-Ru, Jia Wen-Jing
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• #### 摘要

哈密顿系统理论是研究非线性系统的一种重要工具, 近年来在电机调速、控制等方面得到广泛应用. 本文针对永磁同步电机运行中存在的混沌现象, 提出一种基于哈密顿函数的永磁同步电机混沌系统鲁棒控制器设计方法. 将永磁同步电机动态模型变换为类Lorenz混沌方程, 在特定参数下, 通过Lyapunov指数和Lyapunov维数的计算可知系统是混沌的. 令电机转速跟踪给定值得误差方程. 由于误差方程并不具有标准哈密顿函数形式, 将其转化为具有扰动不确定项的哈密顿系统, 并与负载扰动一起作为系统的总扰动量, 设计了一种鲁棒控制器. 控制器由两部分组成, 一部分基于互联与阻尼配置法, 实现任意转速的有效跟踪, 另一部分实现扰动补偿. 仿真表明, 控制器使电机迅速脱离混沌状态, 并能实现转速趋近跟踪, 验证了控制器的可行性与有效性. 该方法扩展了哈密顿函数的适用范围, 具有一定的优越性.

#### Abstract

Hamiltonian system theory is an important reflearch tool for nonlinear systems, and has been widely used in motor speed regulation and control during reflent years. Aiming at the chaotic phenomenon in permanent magnet synchronous motors, a design method of robust controller based on the Hamiltonian function is preflented for the chaotic systems. The dynamic model of permanent magnet synchronous motor is transformed into a model similar to the Lorenz chaotic equation, and the model is chaotic at certain parameters according to the Lyapunov exponent and the Lyapunov dimension calculated. Let the rotator speed of the motor track a set of values, an error equation is obtained accordingly. Because the error equation does not satisfy the standard form of Hamilton exactly, it can be transformed into the Hamiltonian system containing uncertain disturbance terms. While the uncertain disturbance terms as well as the load term are regarded as a total disturbance term to the system, a kind of robust controller is designed. The controller consists of two parts. One part is based on the method of interconnection and damping assignment, and can make the rotator speed track any value well; The other part is used as a disturbance compensator. Simulation result shows that the controller drives the permanent magnet synchronous motor out of the chaotic state rapidly and the rotator speed tracks the set of values well. It is proven that the controller is feasible and effective. The method mentioned in this paper extends the range of application of Hamiltonian function and has a certain advantage.

#### 作者及机构信息

###### 1. 燕山大学电气工程学院工业计算机控制工程河北省重点实验室, 秦皇岛 066004
• 基金项目: 国家自然科学基金委员会与宝钢集团有限公司联合资助项目(批准号: U1260203)和河北省自然科学基金(批准号: F2012203088)资助的课题.

#### Authors and contacts

###### 1. Key Lab of Industrial Computer Control Engineering of Hebei Province, College of Electric Engineering, Yanshan University, Qinhuangdao 066004, China
• Funds: Project supported by the National Natural Science Foundation of China and Baosteel Group Co. Ltd (Grant No.U1260203), and the Natural Science Foundation of Hebei Province, China (Grant No. F2012203088).

#### 参考文献

 [1] Krishnan R, Bharadwaj A S 1991 IEEE Trans. Power Electron. 6 695 [2] Li C L, Yu S M 2011 Acta Phys. Sin. 60 120505 (in Chinese) [李春来, 禹思敏 2011 物理学报 60 120505] [3] Tang C S, Dai Y H 2013 Acta Phys. Sin. 62 180504 (in Chinese) [唐传胜, 戴跃洪 2013 物理学报 62 180504] [4] Tang C S, Dai Y H, Zhen W X 2014 Control Theory Appl. 31 404 (in Chinese) [唐传胜, 戴跃洪, 甄文喜 2014 控制理论与应用 31 404] [5] Zhang X H, Ding S G 2009 Control Theory Appl. 26 661 (in Chinese) [张兴华, 丁守刚 2009 控制理论与应用 26 661] [6] Yao Q G 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE) Shanghai, China, June 10-12, 2011 p104 [7] Yu J P, Yu H S, Chen B, Gao J W, Qin Y 2012 Nonlinear Dynam. 70 1879 [8] Zeng Y, Zhang L X, Yu F R, Qian J 2009 Proceedings of the CSEE. 29 54 (in Chinese) [曾云, 张立翔, 于凤荣, 钱晶 2009 中国电机工程学报 29 54] [9] Wu C, Qi R, Gao F 2014 Control and Decision. 29 895 (in Chinese) [吴春, 齐蓉, 高峰 2014 控制与决策 29 895] [10] Wu Z Q, Zhuang S Y, Han Y G 2013 Chinese Journal of Scientific Instrument. 34 344 (in Chinese) [吴忠强, 庄述燕, 韩延光 2013 仪器仪表学报 34 344] [11] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese) [任丽娜, 刘福才, 焦晓红, 李俊义 2012 物理学报 61 060506] [12] Guo Y, Xi Z, Cheng D 2007 IET Control Theory Appl. 1 281 [13] Zhang B, Li Z, Mao Z Y 2002 Control Theory Appl. 19 545 (in Chinese) [张波, 李忠, 毛宗源 2002 控制理论与应用 19 545] [14] Ortega R, Van der Schaft A J, Mareels I, Maschke B 2001 IEEE Control. Syst. Mag. 21 18

#### 施引文献

•  [1] Krishnan R, Bharadwaj A S 1991 IEEE Trans. Power Electron. 6 695 [2] Li C L, Yu S M 2011 Acta Phys. Sin. 60 120505 (in Chinese) [李春来, 禹思敏 2011 物理学报 60 120505] [3] Tang C S, Dai Y H 2013 Acta Phys. Sin. 62 180504 (in Chinese) [唐传胜, 戴跃洪 2013 物理学报 62 180504] [4] Tang C S, Dai Y H, Zhen W X 2014 Control Theory Appl. 31 404 (in Chinese) [唐传胜, 戴跃洪, 甄文喜 2014 控制理论与应用 31 404] [5] Zhang X H, Ding S G 2009 Control Theory Appl. 26 661 (in Chinese) [张兴华, 丁守刚 2009 控制理论与应用 26 661] [6] Yao Q G 2011 IEEE International Conference on Computer Science and Automation Engineering (CSAE) Shanghai, China, June 10-12, 2011 p104 [7] Yu J P, Yu H S, Chen B, Gao J W, Qin Y 2012 Nonlinear Dynam. 70 1879 [8] Zeng Y, Zhang L X, Yu F R, Qian J 2009 Proceedings of the CSEE. 29 54 (in Chinese) [曾云, 张立翔, 于凤荣, 钱晶 2009 中国电机工程学报 29 54] [9] Wu C, Qi R, Gao F 2014 Control and Decision. 29 895 (in Chinese) [吴春, 齐蓉, 高峰 2014 控制与决策 29 895] [10] Wu Z Q, Zhuang S Y, Han Y G 2013 Chinese Journal of Scientific Instrument. 34 344 (in Chinese) [吴忠强, 庄述燕, 韩延光 2013 仪器仪表学报 34 344] [11] Ren L N, Liu F C, Jiao X H, Li J Y 2012 Acta Phys. Sin. 61 060506 (in Chinese) [任丽娜, 刘福才, 焦晓红, 李俊义 2012 物理学报 61 060506] [12] Guo Y, Xi Z, Cheng D 2007 IET Control Theory Appl. 1 281 [13] Zhang B, Li Z, Mao Z Y 2002 Control Theory Appl. 19 545 (in Chinese) [张波, 李忠, 毛宗源 2002 控制理论与应用 19 545] [14] Ortega R, Van der Schaft A J, Mareels I, Maschke B 2001 IEEE Control. Syst. Mag. 21 18
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##### 出版历程
• 收稿日期:  2014-07-26
• 修回日期:  2014-12-13
• 刊出日期:  2015-05-05

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