PMSM混沌系统无初始状态约束的固定时间有界控制

doi:10.16088/j.issn.1001-6600.2023101701

摘要/Abstract

摘要： 永磁同步电机(PMSM)是一种多变量、耦合性强的非线性系统,在实际运行过程中会出现混沌振荡。为了抑制PMSM系统的混沌,本文设计一种无初始状态约束的固定时间有界控制器。首先根据PMSM系统各个子系统的虚拟误差设计虚拟控制器,通过反步法推导得出控制器具有较高的抗干扰性能和鲁棒性,并证明时变反馈参数能够保证系统在到达有限时间收敛的同时达到渐近稳定,且稳定时间只与规定的边界有关。最后数值仿真通过调整控制系数k使系统能够在不同的初始状态下快速达到稳定,验证了所设计的控制器无论系统的初始状态如何,都能够使系统在2.8 s内达到稳定状态且输出收敛于给定的边界。

关键词: PMSM, 混沌振荡, 混沌控制, 稳定状态

Abstract: Permanent magnet synchronous motor (PMSM) is a multivariable and highly coupled nonlinear system,which is subject to chaotic oscillations during practical operation. In order to suppress the chaos of the PMSM system,a fixed-time bounded controller without initial state constraints is designed,which can make the system reach a stable state within 2.8 s. Firstly,the virtual controller is designed according to the virtual errors of each subsystem of the PMSM system,and the controller is derived by backstepping to have high anti-interference performance and robustness. Secondly, it is proved that the time-varying feedback parameter ensures that the system achieves asymptotic stabilization while arriving at the finite-time convergence,and the stabilization time is only related to the prescribed boundary. Finally,numerical simulations are carried out by adjusting the control coefficients k so that the system can reach stability quickly under different initial states,and it is verified that the designed controller is able to make the system reach asymptotic stability and the output converge to the given boundary regardless of the initial state of the system.

Key words: PMSM, chaotic oscillation, chaotic control, stable state

中图分类号: TP273;TM341

张锦忠, 韦笃取. PMSM混沌系统无初始状态约束的固定时间有界控制[J]. 广西师范大学学报（自然科学版）, 2024, 42(5): 72-78.

ZHANG Jinzhong, WEI Duqu. Fixed Time Bounded Control of PMSM Chaotic Systems without Initial State Constraints[J]. Journal of Guangxi Normal University(Natural Science Edition), 2024, 42(5): 72-78.

参考文献

[1] 陈诚,李世华,田玉平. 永磁同步电机调速系统的自抗扰控制[J]. 电气传动,2005,35(9): 13-16. DOI: 10.3969/j.issn.1001-2095.2005.09.003.
[2] 俞沛宙,杨刚,杨继辉,等. 基于自适应反推的永磁同步电动机转速控制策略[J]. 电气工程学报,2020,15(3): 38-43. DOI: 10.11985/2020.03.005.
[3] 梅春草,许丽娟. 环形电机耦合网络混沌行为的抑制控制[J]. 吉林大学学报(理学版),2022,60(4): 970-976. DOI: 10.13413/j.cnki.jdxblxb.2021309.
[4] 张敬,汤涛,方文华,等. 基于直流电机系统的广义同步混沌化[J]. 动力学与控制学报,2020,18(2): 91-97. DOI: 10.6052/1672-6553-2020-017.
[5] 曹书磊,谢进,丁维高. 永磁同步电机-2R机构多非线性耦合系统动力学分析及混沌控制[J]. 机械传动,2019,43(10): 113-117. DOI: 10.16578/j.issn.1004.2539.2019.10.021.
[6] 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. DOI: 10.15938/j.emc.2019.03.013.
[7] ZIRKOHI M M. Command filtering-based adaptive control for chaotic permanent magnet synchronous motors considering practical considerations[J]. ISA Transactions, 2021, 114: 120-135. DOI: 10.1016/j.isatra.2020.12.036.
[8] LU S K, WANG X C. Observer-based command filtered adaptive neural network tracking control for fractional-order chaotic PMSM[J]. IEEE Access, 2019, 7: 88777-88788. DOI: 10.1109/ACCESS.2019.2926526.
[9] XUE W, ZHANG M, LIU S L, et al. Mechanical analysis and ultimate boundary estimation of the chaotic permanent magnet synchronous motor[J]. Journal of the Franklin Institute, 2019, 356(10): 5378-5394. DOI: 10.1016/j.jfranklin.2019.05.007.
[10] JUNEJO A K, XU W, MU C X, et al. Adaptive speed control of PMSM drive system based a new Sliding-Mode reaching law[J]. IEEE Transactions on Power Electronics, 2020, 35(11): 12110-12121. DOI: 10.1109/TPEL.2020.2986893.
[11] DERAKHSHANNIA M, MOOSAPOUR S S. Disturbance observer-based sliding mode control for consensus tracking of chaotic nonlinear multi-agent systems[J]. Mathematics and Computers in Simulation, 2022, 194: 610-628. DOI: 10.1016/j.matcom.2021.12.017.
[12] 戴磊,魏海峰,李洋洋,等. 基于分岔理论的永磁同步电机有限时间混沌控制[J]. 控制工程,2022,29(1): 27-32. DOI: 10.14107/j.cnki.kzgc.20200206.
[13] WU J, MA R R. Robust finite-time and fixed-time chaos synchronization of PMSMs in noise environment[J]. ISA Transactions, 2022, 119: 65-73. DOI: 10.1016/j.isatra.2021.02.034.
[14] 王聪,张宏立,马萍. 基于有限时间函数投影的电力系统混沌控制[J]. 振动与冲击,2021,40(14): 125-131. DOI: 10.13465/j.cnki.jvs.2021.14.017.
[15] YIN X, SHE J H, LIU Z T, et al. Chaos suppression in speed control for permanent-magnet-synchronous-motor drive system[J]. Journal of the Franklin Institute, 2020, 357(18): 13283-13303. DOI: 10.1016/j.jfranklin.2020.05.007.
[16] 何宏骏,崔岩,孙观. 一个新非线性系统的动力学分析与混沌控制[J]. 吉林大学学报(理学版),2019,57(5): 1224-1230. DOI: 10.13413/j.cnki.jdxblxb.2018147.
[17] DU H B, WEN G H, CHENG Y Y, et al. Design and implementation of bounded finite-time control algorithm for speed regulation of permanent magnet synchronous motor[J]. IEEE Transactions on Industrial Electronics, 2021, 68(3): 2417-2426. DOI: 10.1109/TIE.2020.2973904.
[18] WANG Y Q. Bounded UDE-based robust control for MIMO systems with application to vector control of a PMSM drive[EB/OL].(2023-05-03)[2023-10-15]. https://www.techrxiv.org/doi/full/10.36227/techrxiv.22723444.v1. DOI: 10.36227/techrxiv.22723444.v1.
[19] YUE H X, WANG H Q, WANG Y Y. Adaptive fuzzy fixed-time tracking control for permanent magnet synchronous motor[J]. International Journal of Robust and Nonlinear Control, 2022, 32(5): 3078-3095. DOI: 10.1002/rnc.5922.
[20] FALLAHA C J, SAAD M, KANAAN H Y, et al. Sliding-Mode robot control with exponential reaching law[J]. IEEE Transactions on Industrial Electronics, 2011, 58(2): 600-610. DOI: 10.1109/TIE.2010.2045995.
[21] 杨秀,韦笃取. 基于单状态变量的永磁同步电机混沌跟踪控制[J]. 广西师范大学学报(自然科学版),2023,41(2): 58-66. DOI: 10.16088/j.issn.1001-6600.2022032303.
[22] MOZAYAN S M, SAAD M, VAHEDI H, et al. Sliding mode control of PMSG wind turbine based on enhanced exponential reaching law[J]. IEEE Transactions on Industrial Electronics, 2016, 63(10): 6148-6159. DOI: 10.1109/TIE.2016.2570718.
[23] 胡锦铭,韦笃取. 不同阶次分数阶永磁同步电机的混合投影同步[J]. 广西师范大学学报(自然科学版),2021,39(4): 1-8. DOI: 10.16088/j.issn.1001-6600.2020070603.
[24] WANG Y Q, FENG Y T, ZHANG X G, et al. A new reaching law forantidisturbance sliding-mode control of PMSM speed regulation system[J]. IEEE Transactions on Power Electronics, 2020, 35(4): 4117-4126. DOI: 10.1109/TPEL.2019.2933613.
[25] WANG S B, TAO L, CHEN Q, et al. USDE-based sliding mode control for servo mechanisms with unknown system dynamics[J]. IEEE-ASME Transactions on Mechatronics, 2020, 25(2): 1056-1066. DOI: 10.1109/TMECH.2020.2971541.
[26] TAO L, CHEN Q, NAN Y R, et al. Double hyperbolic reaching law with chattering-free and fast convergence[J]. IEEE Access, 2018, 6: 27717-27725. DOI: 10.1109/ACCESS.2018.2838127.
[27] BHAT S P, BERNSTEIN D S. Finite-time stability of continuous autonomous systems[J]. SIAM Journal on Control and Optimization, 2000, 38(3): 751-766. DOI: 10.1137/S0363012997321358.
[28] PAP E, ŠTRBOJA M. Generalization of the Jensen inequality for pseudo-integral[J]. Information Sciences, 2010, 180(4): 543-548. DOI: 10.1016/j.ins.2009.10.014.
[29] GAO H, WANG Z Y, MA J, et al. Fixed-time bounded control of nonlinear systems without initial-state constraint[J]. International Journal of Control,2024,97(7):1594-1600. DOI: 10.1080/00207179.2023.2218946.
[30] ASLAM CHAUDHRY M, ZUBAIR S M. Generalized incomplete gamma functions with applications[J]. Journal of Computational and Applied Mathematics, 1994, 55(1): 99-124. DOI: 10.1016/0377-0427(94)90187-2.
[31] WEI D Q, LUO X S, WANG B H, et al. Robust adaptive dynamic surface control of chaos in permanent magnet synchronous motor[J]. Physics Letters A, 2007, 363(1/2): 71-77. DOI: 10.1016/j.physleta.2006.10.074.

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