﻿ 永磁同步电机的最优控制和自适应控制 Optimal Control and Adaptive Control for Permanent Magnet Synchronous Motor

Journal of Electrical Engineering
Vol.05 No.03(2017), Article ID:21774,9 pages
10.12677/JEE.2017.53027

Optimal Control and Adaptive Control for Permanent Magnet Synchronous Motor

Renming Wang, Hao Liu, Guibin Zhang, Lingyun Wang

College of Electrical Engineering and New Energy, Three Gorges University, Yichang Hubei

Received: Aug. 1st, 2017; accepted: Aug. 15th, 2017; published: Aug. 22nd, 2017

ABSTRACT

In this paper, the chaotic behavior of a permanent magnet synchronous motor (PMSM) with non- uniformity-air-gap is analyzed. Based on Pontryagin minimum principle, an optimal controller is developed to stabilize the chaotic system. Otherwise, an adaptive controller is designed by such PMSM system with multi unknown parameters according to Lyapunov stability theory and an adaptive regulating law of unknown parameters estimation is given to estimate the parameters values. Finally, numerical simulation based on MATLAB show that the effectiveness of our method.

Keywords:Permanent Magnet Synchronous Motor, Chaos System, Optimal Control, Adaptive Control

1. 引言

2. 永磁同步电机的数学模型及分析

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Figure 1. PMSM bifurcation diagram

Figure 2. State phase diagram when the PHM is in a chaotic state

3. 非均匀气隙PMSM的最优控制

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4. 非均匀气隙PMSM的自适应控制

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5. 数值仿真

Figure 3. Optimal control state variable graph

Figure 4. Control amount chart of optimal control

Figure 5. Optimal control state variable graph

Figure 6. Optimal control parameter error plot

6. 结论

Optimal Control and Adaptive Control for Permanent Magnet Synchronous Motor[J]. 电气工程, 2017, 05(03): 217-225. http://dx.doi.org/10.12677/JEE.2017.53027

1. 1. 郑泽东, 李永东. 永磁同步电机伺服控制系统的研究现状及发展[J]. 伺服控制, 2008(12): 20-22.

2. 2. 薛薇, 郭彦岭, 陈增强. 永磁同步电机的混沌分析及其电路实现[J]. 物理学报, 2009, 58(12): 8146-8151.

3. 3. Hu, J., Qiu, Y. and Lu, H. (2016) Adaptive Robust Nonlinear Feedback Control of Chaos in PMSM System with Modeling Uncertainty. Applied Mathematical Modelling, 40, 8265-8275.

4. 4. 张涛, 蒋静坪, 张国宏. 交流永磁同步电机伺服系统的线性化控制[J]. 中国电机工程学报, 2001, 21(6): 40-43.

5. 5. 刘小河, 王鹤华. 基于SVPWM永磁同步电机反馈线性化控制[J]. 现代电子技术, 2013(12): 159-162.

6. 6. 杜方. 交流永磁同步电机变结构控制器设计与研究[D]: [硕士学位论文]. 武汉: 华中科技大学, 2013.

7. 7. Formentini, A., Trentin, A., Marchesoni, M., et al. (2015) Speed Finite Control Set Model Predictive Control of a PMSM Fed by Matrix Converter. IEEE Transactions on Industrial Electronics, 62, 6786-6796.

8. 8. George, R. and Mathew, A.S. (2015) Speed Control of PMSM using Backstepping Method. International Journal of Engineering & Technical Research, 4.

9. 9. Lemmens, J., Vanassche, P. and Driesen, J. (2014) PMSM Drive Current and Voltage Limiting as a Constraint Optimal Control Problem. IEEE Journal of Emerging & Selected Topics in Power Electronics, 3, 1.

10. 10. 张兴华, 丁守刚. 非均匀气隙永磁同步电机的自适应混沌同步[J]. 控制理论与应用, 2009, 26(6): 661-664.

11. 11. 周群利. 永磁同步电动机混沌系统的控制研究[J]. 佳木斯大学学报(自然科学版), 2015(4): 545-547.

12. 12. 薛薇, 郭彦岭, 陈增强. 永磁同步电机的混沌分析及其电路实现[J]. 物理学报, 2009, 58(12): 8146-8151.