永磁直线同步电机解耦自适应滑模混沌控制
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摘要
针对永磁直线同步电机系统的混沌问题,建立考虑动子的边缘效应的同步直线电机的数学模型,且通过时标变换法导出类Lorenz混沌方程。运用Wolf算法计算最大Lyapunov指数谱,并判定电机混沌运动域。基于反馈解耦控制的混沌降阶系统,提出一种解耦自适应滑模混沌控制策略,改进了系统在未知参数的情况下,对不确定的系统参数进行实时修正的能力,利用Lyapunov稳定判据证明了系统全局一致的收敛性。仿真结果表明,解耦自适应滑模控制策略可使电机系统迅速脱离混沌状态,抑制了抖振现象,鲁棒性强、控制精度高。
Aiming at the chaos problem of permanent magnet linear synchronous motor system, a mathematical model of synchronous linear motor considering the edge effect of mover was established and the Lorenz-like chaotic equation was derived by time-shift transformation. Wolf algorithm to calculate the maximum Lyapunov exponent spectrum, and determine the motor chaotic motion domain. Based on feedback decoupling control of chaotic reduction system, a decoupled adaptive sliding-mode chaos control strategy was proposed to improve the system's capability of real-time correction of uncertain system parameters under unknown parameters. By using Lyapunov stability criterion, it was proved that the global convergence of the system is consistent. The simulation results show that the decoupled adaptive sliding mode control strategy can make the motor system quickly out of chaos, suppress the chattering phenomenon, and it has strong robustness and high control accuracy.
Aiming at the chaos problem of permanent magnet linear synchronous motor system, a mathematical model of synchronous linear motor considering the edge effect of mover was established and the Lorenz-like chaotic equation was derived by time-shift transformation. Wolf algorithm to calculate the maximum Lyapunov exponent spectrum, and determine the motor chaotic motion domain. Based on feedback decoupling control of chaotic reduction system, a decoupled adaptive sliding-mode chaos control strategy was proposed to improve the system's capability of real-time correction of uncertain system parameters under unknown parameters. By using Lyapunov stability criterion, it was proved that the global convergence of the system is consistent. The simulation results show that the decoupled adaptive sliding mode control strategy can make the motor system quickly out of chaos, suppress the chattering phenomenon, and it has strong robustness and high control accuracy.
引文
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[22] A Wolf,et al.Determining Lyapunov Exponents From a Time Series[J].Physica D:Nonlinear Phenomena,1985,16(3):285-317.
[23] D D Reigosa,et al.Modeling and Adaptive Decoupling of High-Frequency Resistance and Temperature Effects in Carrier-Based Sensorless Control of PM Synchronous Machines[J].IEEE Transactions on Industry Applications,2010,46(1):139-149.
[24] V IUtkin.Sliding Modes in Control and Optimization[J].Communications & Control Engineering,1992,189(3):1372-9.
[2] Z Wang,K T Chau.Design,Analysis,and Experimentation of Chaotic Permanent Magnet DC Motor Drives for Electric Compaction[J].IEEE Transactions on Circuits & Systems II Express Briefs,2009,56(3):245-249.
[3] X H Mai,et al.Controlling Chaos in Complex Motor Networks by Environment[J].IEEE Transactions on Circuits & Systems II Express Briefs,2017,62(6):603-607.
[4] R Yang,et al.Robustness improvement of predictive current control for PMLSM integrating adaptive internal model with time delay compensation[C].International Conference on Electrical Machines and Systems.Sydney,Australia,August 2017:1-5.
[5] 张波,等.一类永磁同步电动机混沌模型与霍夫分叉[J].中国电机工程学报,2001,21(9):13-17.
[6] 党选举,等.永磁同步直线电机的小波神经网络控制[J].电机与控制学报,2013,17(1):43-50.
[7] 陈强,南余荣,邢科新.基于扩张状态观测器的永磁同步电机混沌系统自适应滑模控制[J].物理学报,2014,63(22):113-120.
[8] 李东,等.参数不确定永磁同步电机混沌的模糊脉冲控制[J].物理学报,2009,58(3):2939-2948.
[9] 韩彦东,等.基于遗传算法的永磁同步直线电机PID控制研究[J].电子测量技术,2016,39(5):115-119.
[10] S Y Chen,T S Liu.Intelligent tracking control of a PMLSM using self-evolving probabilistic fuzzy neural network[J].Iet Electric Power Applications,2017,11(6):1043-1054.
[11] A Loría.Robust Linear Control of (Chaotic) Permanent-Magnet Synchronous Motors With Uncertainties[J].IEEE Transactions on Circuits & Systems I Regular Papers,2009,56(9):2109-2122.
[12] H Chaoui,M Khayamy,A A Aljarboua.Adaptive Interval Type-2 Fuzzy Logic Control for PMSM Drives With a Modified Reference Frame[J].IEEE Transactions on Industrial Electronics,2017,64(5):3786-3797.
[13] 夏加宽,等.高精度数控机床用直线电机端部效应分析及神经网络补偿技术研究[J].中国电机工程学报,2003,23(8):100-104.
[14] 徐伟,汪旭东,袁世鹰.交通牵引大功率单边直线感应电机性能研究[J].电机与控制学报,2008,12(4):396-402.
[15] 刘莉莉,夏加宽,姜平.永磁直线同步电机端部效应及其补偿技术[J].沈阳工业大学学报,2005,27(3):261-265.
[16] 李庆雷,王先逵.永磁交流同步直线电机位置伺服控制系统设计[J].中国机械工程,2001,12(5):577-581.
[17] A Wolf,et al.Determining Lyapunov exponents from a time series[J].Physica D Nonlinear Phenomena,1985,16(3):285-317.
[18] E N Lorenz.Deterministic Nonperiodic Flow[M].The Theory of Chaotic Attractors.Springer New York,2004:25-36.
[19] E N Lorenz,R C Hilborn.The Essence of Chaos[J].Physics Today,1995,63(48):862-863.
[20] 陈集思.无刷双馈风力发电系统的无源性控制及其混沌研究[D].广东工业大学,2016.
[21] 张海龙,闵富红,王恩荣.关于Lyapunov指数计算方法的比较[J].南京师范大学学报(工程技术版),2012,12(1):5-9.
[22] A Wolf,et al.Determining Lyapunov Exponents From a Time Series[J].Physica D:Nonlinear Phenomena,1985,16(3):285-317.
[23] D D Reigosa,et al.Modeling and Adaptive Decoupling of High-Frequency Resistance and Temperature Effects in Carrier-Based Sensorless Control of PM Synchronous Machines[J].IEEE Transactions on Industry Applications,2010,46(1):139-149.
[24] V IUtkin.Sliding Modes in Control and Optimization[J].Communications & Control Engineering,1992,189(3):1372-9.