Optimal Control of Chaos in Permanent Magnet Synchronous Motor Based on LMI Algorithm
-
摘要: 永磁同步电机是水下航行器的重要组成部分, 其复杂的非线性行为会形成混沌运动, 导致电机的控制性能下降, 严重影响点击工作效率。文中对永磁同步电机运行系统的Hopf分岔及其混沌行为进行分析与控制, 首先将系统的物理模型进行无量纲化, 得到简化后的类混沌数学模型, 分析得出系统的Hopf分岔点是由外部输入参数ud和系统的不确定参数σ决定, 系统在达到临界分岔点后, 随着分岔参数γ的变化, 会产生连续的Hopf分岔现象并最终进入混沌状态。在此基础上, 构造了一种基于线性矩阵不等式(LMI)算法的自适应混沌控制器来控制系统的混沌运动。仿真验证可知, 在加入控制后, 系统原来的紊乱混沌状态能够有效地回到稳定平衡点。Abstract: Permanent magnet synchronous motors(PMSMs) are an important part of undersea vehicles. Its complex nonlinear behavior will form a chaotic motion, reducing the control performance of the motor and seriously affecting its working efficiency. In this study, Hopf bifurcation and chaotic behavior analysis and control of its operating system are studied. First, the physical model of the PMSM is dimensionalized, and a simplified chaos-like mathematical model is obtained. After the external input is determined, the Hopf bifurcation of the system is analyzed. It is found that the Hopf bifurcation point of the system is determined by the external input parameter ud and uncertain parameter σ of the system. When the system reaches the critical bifurcation point, with a change in the bifurcation parameter γ, the system produces a continuous Hopf bifurcation phenomenon and finally enters the chaotic state, and each state of the system will show the phenomenon of irregular motion. Aiming at the parameter uncertainty of the PMSM operating system, an adaptive chaos controller based on the linear matrix inequality(LMI) algorithm is proposed to control the chaotic behavior of the system. The simulation results show that the original chaotic state of the system can effectively return to a stable equilibrium point after the addition of the control.
-
[1] 郭志荣, 高峰, 王其林. 基于RBF网络和MRAS的鱼雷永磁同步电机无速度传感器控制方法[J]. 水下无人系统学报, 2017, 25(6): 448-452.Guo Zhi-rong, Gao Feng, Wang Qi-lin. Speed-Sensorless Control Method of Torpedo PMSM Based on RBF and MRAS[J]. Journal of Unmanned Undersea Systems, 2017, 25(6): 448-452. [2] 闫明, 于博洋, 张磊, 等. 永磁推进电机双层隔离系统冲击响应谱分析[J]. 机械设计与制造, 2017(2): 239-242.Yan Ming, Yu Bo-yang, Zhang Lei, et al. Shock Response Spectrum Analysis of Double Isolation System for Per-manent Magnet Propulsion Motor[J]. Machinery Design & Manufacture, 2017(2): 239-242. [3] 韩建群. 同量分数阶永磁同步电机的混沌运动相电流信号频谱特点仿真研究[J]. 国外电子测量技术, 2020, 39(4): 1-5.Han Jian-qun. Simulation Research on the Spectrum Characteristics of Chaotic Phase Current Signal of the Same Quantity Fractional Order PMSM[J]. Foreign Electronic Measurement Technology, 2020, 39(4): 1-5. [4] Cheukem A, Tsafack A, Kingni ST, et al. Permanent Magnet Synchronous Motor: Chaos Control Using Single Controller, Synchronization and Circuit Implementation[J]. SN Applied Sciences, 2020, 2(3): 4226-4230. [5] Yousri D, Allam D, Eteiba M B. Chaotic Heterogeneous Comprehensive Learning Particle Swarm Optimizer Variants for Permanent Magnet Synchronous Motor Models Parameters Estimation[J]. Iranian Journal of Science and Technology, Transactions of Electrical Engineering, 2020, 44(1): 1299-1318. [6] Huang J, Li C, Huang T, et al. Finite-time Lag Synchronization of Delayed neural networks[J]. Neurocomputing, 2014, 139: 145-149. [7] 张能, 蒋云峰, 程成. 参数约束下永磁同步电机混沌动力学特性仿真[J]. 计算机仿真, 2019, 36(10): 223-226, 348.Zhang Neng, Jiang Yun-feng, Cheng Cheng. Simulation of Chaotic Dynamics of Permanent Magnet Synchronous Motor under Parameter Constraints[J]. Computer Simulation, 2019, 36(10): 223-226, 348. [8] Zheng,W J, Zhang G S. Control and Synchronization of a New Class of Finance Chaotic Systems[C]//第31届中国控制与决策会议论文集. 南昌: 《控制与决策》编辑部, 2019: 201-206. [9] 衣涛, 王承民, 谢民, 等. 电力系统的多重(维)鞍结分岔点及其特征分析[J]. 电工技术学报, 2015, 30(20): 145-150.Yi Tao, Wang Cheng-min, Xie Min, et al. Power System Multiple Saddle-Node Bifurcation Point and Its Characteristic Analysis[J]. Transactions of China Electrotechnical Society, 2015, 30(20): 145-150. [10] Xie D, Yang J, Cai H, et al. Blended Chaos Control of Permanent Magnet Linear Synchronous Motor[J]. IEEE Access, 2018, 7: 61670-61678. [11] Skubov D, Lukin A, Popov I. Bifurcation Curves for Synchronous Electrical Machine[J]. Nonlinear Dynamics, 2016, 83(4): 2323-2329. [12] 刘加勋, 王佐勋, 雷腾飞, 等. 永磁同步电机有限时间混沌同步控制[J]. 微特电机, 2019, 47(8): 45-47, 53.Liu Jia-xun, Wang Zuo-xun, Lei Teng-fei, et al. Finite-Time Chaotic Synchronization Control of Permanent Magnet Synchronous Motor[J]. Small & Special Electrical Machines, 2019, 47(8): 45-47, 53. [13] 王东东, 陆益民, 张波. IFOC感应电动机分岔混沌的单双时滞反馈控制[J]. 电机与控制学报, 2014, 18(10): 55-67.Wang Dong-dong, Lu Yi-min, Zhang Bo. Bifurcation and the Single and Double Time-delayed Feedback Control of Chaos in IFOC Induction Motors[J]. Electric Machines and Control, 2014, 18(10): 55-67. [14] Zhou S. Chaos Control of Permanent Magnet Synchronous Motor via Second Order Sliding Mode[C]//2016 IEEE Chinese Guidance, Navigation and Control Conference(CG NCC). Nanjing: IEEE, 2016: 1026-1028. [15] Tan Y J, Pan W, Han Y, et al. Research on Force Assignment of Radar Jamming System Based on Chaos Genetic Algorithm[C]//第31届中国控制与决策会议论文集(1).南昌:《控制与决策》编辑部, 2019: 1194-1198. [16] 谢东燊, 杨俊华, 熊锋俊, 等. 永磁直线同步电机解耦自适应滑模混沌控制[J]. 计算机仿真, 2019, 36(5): 263- 268.Xie Dong-shen, Yang Jun-hua, Xiong Feng-jun, et al. Decoupling Adaptive Sliding Mode Chaos Control of Permanent Magnet Linear Synchronous Motor[J]. Computer Simulation, 2019, 36(5): 263-268. [17] Wei D Q, Zhang B. Controlling Chaos in Permanent Magnet Synchronous Motor Based on Finite-time Stability Theory[J]. Chinese Physics B, 2009, 18(4): 1399. [18] 董新勇, 肖伸平, 张晓虎, 等. 基于矩阵不等式的永磁同步电机鲁棒H∞控制[J]. 电工技术, 2019(7): 4-6, 9.Dong Xin-yong, Xiao Shen-ping, Zhang Xiao-hu, et al. Research on Robust H∞ Control of Permanent Magnet Synchronous Motor Based on LMI[J]. Electric Engineering, 2019(7): 4-6, 9. [19] Messadi M, Mellit A. Control of Chaos in An Induction Motor System with LMI Predictive Control and Experimental Circuit Validation[J]. The Interdisciplinary Journal of Nonlinear Science, 2017, 97: 51-58. [20] 王凯东, 李宏浩. 基于LMI的永磁同步伺服电机的混合H2/H∞鲁棒预测控制器[J]. 微电机, 2019, 52(7): 40-44.Wang Kai-dong, Li Hong-hao. Direct Torque Control of Permanent Magnet Motor Based on Second Order Sliding Mode Algorithm[J]. Micromotors, 2019, 52(7): 40-44.
点击查看大图
计量
- 文章访问数: 144
- HTML全文浏览量: 20
- PDF下载量: 83
- 被引次数: 0