复杂工况下分数阶永磁同步风力发电机混沌运动的H鲁棒控制

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振动与冲击 ›› 2022, Vol. 41 ›› Issue (24) : 117-124.

论文

杨莉1,2，黄天民2，丁菊霞2，魏伟3

作者信息 +

H∞ robust control of chaotic motion of a fractional order permanent magnet synchronous wind turbine under complex working conditions

YANG Li1,2，HUANG Tianmin2，DING Juxia2，WEI Wei3

Author information +

文章历史 +

摘要

为了抑制永磁同步风力发电机在复杂运行工况下的混沌振荡行为，研究了具有状态时滞和负载扰动下的分数阶混沌模型渐近稳定性控制方法。建立了受扰时滞分数阶永磁同步风力发电机T-S模糊混沌模型，采用模糊PDC控制技术，设计出具有模糊状态记忆的H鲁棒控制器，依据Lyapunov直接函数法，通过Cauchy 矩阵不等式，以LMI形式得到受扰时滞分数阶永磁同步风力发电机满足H性能指标的渐近稳定性条件。通过Oustaloup滤波器无限逼近分数阶微积分算子，搭建Simulink仿真模型。仿真结果表明，所提出的控制方法能有效地抑制状态时滞和负载扰动下永磁同步发电机的混沌运动现象，具有良好的控制性和较强的鲁棒性。
关键词：分数阶风力发电机；T-S模糊模型；混沌控制；复杂工况

Abstract

In order to suppress the chaotic oscillation of permanent magnet synchronous wind turbine under complex operating conditions, the asymptotic stability control method of fractional order chaotic model with state delay and load disturbance is studied. The T-S fuzzy chaotic model of fractional order permanent magnet synchronous wind turbine with state delay and external disturbance is established. Applying fuzzy PDC control technology, an H robust controller with fuzzy state memory is designed. According to Lyapunov direct function method and Cauchy matrix inequality, the asymptotic stability condition satisfying the H performance index is obtained in the form of LMIs. Though the infinite approximation of fractional calculus operator by Oustaloup filter. The simulation results show that the proposed control method can effectively suppress the chaotic motion of permanent magnet synchronous generator under state delay and load disturbance, and has good control and strong robustness.
Key words: fractional order wind turbine; T-S fuzzy model; chaos control; complex working condition

导出引用

杨莉1,2，黄天民2，丁菊霞2，魏伟3. 复杂工况下分数阶永磁同步风力发电机混沌运动的H鲁棒控制[J]. 振动与冲击, 2022, 41(24): 117-124

YANG Li1,2，HUANG Tianmin2，DING Juxia2，WEI Wei3. H∞ robust control of chaotic motion of a fractional order permanent magnet synchronous wind turbine under complex working conditions[J]. Journal of Vibration and Shock, 2022, 41(24): 117-124

参考文献

[1] Porté-Agel F，Bastankhah M，Shamsoddin S. Wind-turbine and wind-farm flows: a review [J]. Boundary-Layer Meteorology，2020，174:1-59.
[2] Ngamroo I. Review of DFIG wind turbine impact on power system dynamic performances [J]. IEEJ Transactions on Electronic Engineering，2017，12(3):301-311.
[3] Yan J，Feng Y，Dong J. Study on dynamic characteristic of wind turbine emulator based on PMSM [J]. Renewable Energy，2016，97:731-736.
[4] Ren Z R，Verma A S，Li Y，et al. Offshore wind turbine operations and maintenance: A state-of-the-art review [J]. Renewable and Sustainable Energy Reviews， 2021，144:110886-110901.
[5] Li Z，Park J B，Joo Y H，et al. Bifurcations and chaos in a permanent-magnet synchronous motor [J]. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications， 2002，49(3):383-387.
[6] Jing Z J，Yu C，Chen G R. Complex dynamics in a permanent-magnet synchronous motor model [J]. Chaos，Solitons & Fractals， 2004，22(4):831-848.
[7] 孙黎霞，鲁胜，温正赓等. 永磁同步电机混沌运动机理分析[J]. 电机与控制学报，2019, 23(3):97-104.
SUN Li-xia, LU Sheng, WEN Zheng-geng, et al. Analysis of chaotic motion mechanism of permanent magnet synchronous motors [J]. Electric Machine and Control, 2019, 23(3): 97-104.
[8] 杨国良，李惠光. 直驱式永磁同步风力发电机中混沌运动的滑模变结构控制[J]. 物理学报，2009, 58(11):7552-7557.
YANG Guo-liang, LI Hui-guang. Sliding mode variable-structure control of chaos in direct-driven permanent magnet synchronous generators for wind turbines [J]. Acta Physica Sinica, 2009, 58(11): 7552-7557.
[9] 王磊，李颖晖，逯国亮等. 直驱式永磁同步风力发电机混沌运动跟踪控制器设计[J]. 电力自动化设备，2011, 31(6):45-49.
WANG Lei, Li Ying-hui, LU Guo-liang, et al. Tranking controller of D-PMSG chaos motion [J]. Electric Power Automation Equipment, 2011, 31(6): 45-49.
[10] Deng W，Li C P. Chaos synchronization of the fractional Lü system [J]. Physica A: Statistical Mechanics and its Applications, 2005, 353: 61-72.
[11] Xue W，Li Y L，Cang S J，et al. Chaos behavior and circuit implementation of a fractional-order permanent magnet synchronous motor model [J]. Journal of the Franklin Institute, 2015, 352: 2887-2898.
[12] Yang L，Shen Z J，Sheng W T，et al. H robust control for chaotic motion of the fractional-order D-PMSG via the PDC approach [J]. Mathematical Problems in Engineering, 2021, Article ID:8279107, 1-16.
[13] Gu Y，Liu J C，Li X L. State space model identification of multirate processes with time-delay using the expectation maximization [J]. Journal of the Franklin Institute Engineering and Applied Mathematics, 2019, 356(3): 1623-1639.
[14] 钟国翔，韦笃取，张波. 永磁同步电机系统、网络混沌振荡同步中断分析与控制 [J]. 振动与冲击，2020, 39(7):8-13,20.
ZHONG Guo-xiang, WEI Du-qu, ZHANG Bo. Analysis and control for chaotic oscillation synchronization interruption of permanent magnet synchronous motor systems and networks [J]. Journal of Vibration and Shock, 2020, 39(7): 8-13,20.
[15] 王晓东，陈予怒. 一类电力系统的分岔与奇异性分析 [J]. 振动与冲击，2014, 33(4):1-6.
WANG Xiao-dong, CHEN Yu-shu. Bifurcation and singularity analysis for a class of power systems [J]. Journal of Vibration and Shock, 2014, 33(4): 1-6.
[16] Hu D M，Hua O Y，Du Z H. A study on stall-delay for horizontal axis wind turbine [J]. Renewable Energy, 2006, 31(6): 821-836.
[17] 李健昌，韦笃取，罗晓曙，等. 混沌电机自适应时滞同步控制研究 [J]. 振动与冲击，2014, 33(16):105-108.
LI Jian-chang, WEI Du-qu, LUO Xiao-shu, et al. Adaptive lag-synchronization of chaotic permanent magnet synchronous motors [J]. Journal of Vibration and Shock, 2014, 33(16): 105-108.
[18] Podlubny I. Fractional differential equations [M]. Academic Press, San Diego, 1999.
[19] Ji Y D，Du M X，Guo Y P. Stabilization of non-linear fractional-order uncertain systems [J]. Asian Journal of Control， 2018，20(3):1-9.
[20] Yang L，Huang T M，Deng L，et al. Analysis on chaotic mechanism of direct-drive permanent magnet synchronous generators based on Lyapunov stability theory [J]. European Journal of Electrical Engineering， 2019，21(6):531-537.
[21] Hu J B，Lu G P，Zhang S B，et al. Lyapunov stability theorem about fractional system without and with delay [J]. Communications in Nonlinear Science and Numerical Simulation， 2015，20(3):905-913.
[22] Zhang S，Yu Y，Yu J. LMI conditions for global stability of fractional-order neural networks [J]. IEEE Transactions Neural Network Learning Systems， 2017，28(10):2423-2433.
[23] Boyd S，EL Ghaoui L，Feron E，et al. Linear matrix inequalities in system and control theory [J]. Philadelphia: SIAM Studies in Applied Mathematics, 1994.
[24] Aguila-Camacho N，Duarte-Mermoud M A，Gallegos J A. Lyapunov functions for fractional order systems [J]. Communications in Nonlinear Science and Numerical Simulation, 2014, 14(9):2951-2957.
[25] Petersen I R. A stabilization algorithm for a class of uncertain linear systems [J]. Systems & Control Letters, 1987, 8(4):351-357.
[26] Huong D C，Thuan M V. Mixed H and passive control for fractional-order nonlinear systems via LMI approach [J]. Acta Applicandae Mathematica, 2020, 170:37-52.