基于相位偏移自适应LMS算法的电磁轴承柔性转子系统多频激励补偿控制

doi:10.3901/JME.2021.17.110

摘要/Abstract

摘要： 针对电磁轴承柔性转子系统在实际工作中受到多频激励的问题，提出了一种基于相位偏移自适应最小均方（Least mean square，LMS）算法的陷波滤波器，从而实现对多频激励的补偿控制。首先建立了电磁轴承柔性转子系统的动力学模型，给出了反馈补偿控制系统的闭环传递函数；然后推导了基于相位偏移自适应LMS算法的陷波器的脉冲传递函数，分析了相位偏移角对陷波器频率特性和闭环系统稳定性的影响，通过分析不同转速段控制系统的根轨迹，得到了全转速范围内使闭环控制系统保持稳定的相位偏移角；最后分别在不平衡激励和多频激励条件下对电磁轴承柔性转子系统振动控制性能进行了仿真分析，结果说明了所提出的基于相位偏移自适应LMS算法的陷波器能有效地抑制柔性转子的多频振动。

关键词: 多频振动, 柔性转子, 最小二乘法, 移相, 振动控制, 电磁轴承

Abstract: For multi-frequency vibration in active magnetic bearing (AMB)-flexible rotor system, a modified notch filter based on adaptive least mean square (LMS) algorithm with a phase shift is proposed to achieve multi-frequency compensation. First, the dynamic model of the AMB-flexible rotor system is built, and the closed-loop system transfer function for the feedback compensation control is obtained; then, the pulse transfer function for the notch filter based on the phase shift adaptive LMS algorithm is obtained, which is used to analyze the influence of different values of the phase shift angle on the frequency characteristics of phase shift adaptive LMS notch filter and the stability of the closed-loop system. By analyzing the system root locus in different rotational speed regions, the value of phase shift angle is obtained, which is able to keep the closed loop system stable in the full rotational speed region. Finally, the numerical simulations under unbalance excitation and multi-frequency excitation are carried out respectively to show the possibility of the notch filter based on phase shift adaptive LMS algorithm to suppress the multi-frequency vibration of the AMB-flexible rotor system.

Key words: multi-frequency vibration, flexible rotor, least mean square algorithm, phase shift, vibration control, active magnetic bearing

中图分类号:

TG156

王晓波, 祝长生. 基于相位偏移自适应LMS算法的电磁轴承柔性转子系统多频激励补偿控制[J]. 机械工程学报, 2021, 57(17): 110-119.

WANG Xiaobo, ZHU Changsheng. Multi-frequency Compensation for Active Magnetic Bearing-Flexible Rotor System Based on Adaptive Least Mean Square Algorithm with a Phase Shift[J]. Journal of Mechanical Engineering, 2021, 57(17): 110-119.

参考文献

[1] SCHWEITZER G,MASLEN E H. Magnetic bearings:Theory,design,and application to rotating machinery[M]. Berlin-Springer,2009.
[2] TANG J,LIU B,FANG J,ET AL. Suppression of vibration caused by residual unbalance of rotor for magnetically suspended flywheel[J]. Journal of Vibration and Control,2013,19(13):1962-1979.
[3] KANG C,TSAO T C. Control of magnetic bearings for rotor unbalance with plug-in time-varying resonators[J]. Journal of Dynamic Systems,Measurement and Control, 2016,138(1):0110011-1100111.
[4] ZENGER K,ALTOWATI A,TAMMI K,et al. Feedforward multiple harmonic control for periodic disturbance rejection[C]. 11th International Conference on Control,Automation,Robotics and Vision,2010,2010:305-310.
[5] LIU C,LIU G. Autobalancing control for MSCMG based on sliding-mode observer and adaptive compensation[J]. IEEE Transactions on Industrial Electronics,2016,63(7):4346-4356.
[6] 毛川,祝长生. 主动电磁轴承-刚性转子系统实时变步长迭代不平衡补偿[J]. 中国电机工程学报,2018, 38(13):3960-3968,4037. MAO Chuan,ZHU Changsheng. A real-time variable step size iterative unbalance compensation for active magnetic bearing-rigid rotor systems[J]. Proceedings of the Chinese Society of Electrical Engineering,2018, 38(13):3960-3968,4037.
[7] MAO C,ZHU C S. Unbalance compensation for active magnetic bearing rotor system using a variable step size real-time iterative seeking algorithm[J]. IEEE Transactions on Industrial Electronics,2018,65(5):4177-4186.
[8] KUSEYRI I S. Robust control and unbalance compensation of rotor/active magnetic bearing systems[J]. Journal of Vibration and Control,2012,18(6):817-832.
[9] CUI P,LI S,ZHAO G,et al. Suppression of harmonic current in active-passive magnetically suspended CMG using improved repetitive controller[J]. IEEE/ASME Transactions on Mechatronics,2016,21(4):2132-2141.
[10] HE Y,SHI L,SHI Z,et al. Unbalance compensation of a full scale test rig designed for HTR-10GT:A frequency-domain approach based on iterative learning control[J]. Science and Technology of Nuclear Installations, 2017,2017(PT.1):6.1-6.15.
[11] 王忠博,毛川,祝长生. 电磁轴承高速电机转子多频振动的电流补偿控制[J]. 中国电机工程学报,2018,38(1):275-284,365. WANG Zhongbo,MAO Chuan,ZHU Changsheng. Current compensation control of multiple frequency vibrations of the rotor in active magnetic bearing high speed motors[J]. Proceedings of the Chinese Society of Electrical Engineering,2018,38(1):275-284,365.
[12] 王忠博,祝长生,陈亮亮. 基于不平衡系数辨识的电磁轴承-刚性飞轮转子系统不平衡补偿控制[J]. 中国电机工程学报,2018,38(12):3699-3708,30. WANG Zhongbo,ZHU Changsheng,CHEN Liangliang. Unbalance compensation control of active magnetic bearing-rigid flywheel rotor system based on unbalance coefficients identification[J]. Proceedings of the Chinese Society of Electrical Engineering,2018,38(12):3699-3708,30.
[13] XU X,FANG J,LIU G,et al. Model development and harmonic current reduction in active magnetic bearing systems with rotor imbalance and sensor runout[J]. Journal of Vibration and Control,2015,21(13):2520-2535.
[14] SUZUKI Y,MICHIMURA S,TAMURA A. Unbalance response attenuation of a flexible rotor suspended by magnetic bearings with open loop control[J]. JSME International Journal,Series C:Dynamics, Control,Robotics,Design and Manufacturing,1994,37(2):285-291.
[15] CUI P,LI S,WANG Q,et al. Harmonic current suppression of an AMB rotor system at variable rotation speed based on multiple phase-shift notch filters[J]. IEEE Transactions on Industrial Electronics,2016,63(11):6962-6969.
[16] CUI P,WANG Q,LI S,et al. Combined FIR and fractional-order repetitive control for harmonic current suppression of magnetically suspended rotor system[J]. IEEE Transactions on Industrial Electronics,2017,64(6):4828-4835.
[17] PENG C,SUN J,SONG X,et al. Frequency-varying current harmonics for active magnetic bearing via multiple resonant controllers[J]. IEEE Transactions on Industrial Electronics,2017,64(1):517-526.
[18] PENG C,SUN J,MIAO C,et al. A novel cross-feedback notch filter for synchronous vibration suppression of an MSFW with significant gyroscopic effects[J]. IEEE Transactions on Industrial Electronics,2017,64(9):7181-7190.
[19] PENG C,ZHU M,WANG K,et al. A two-stage synchronous vibration control for magnetically suspended rotor system in the full speed range[J]. IEEE Transactions on Industrial Electronics,2020,67(1):480-489.
[20] KANG M S,YOON W H. Acceleration feedforward control in active magnetic bearing system subject to base motion by filtered-X LMS algorithm[J]. IEEE Transactions on Control Systems Technology,2006,14(1):134-140.
[21] SHI J,ZMOOD R,QIN L J. The direct method for adaptive feed-forward vibration control of magnetic bearing systems[C]. Proceedings of the 7th International Conference on Control,Automation,Robotics and Vision,December 2-5,2002,2002:675-680.
[22] 高辉,徐龙祥. 基于LMS算法的磁悬浮轴承系统振动补偿[J]. 振动工程学报,2009,22(6):583-588. GAO Hui,XU Longxiang. Real-time vibration compensation for active magnetic bearing systems based on LMS algorithm[J]. Journal of Vibration Engineering,2009,22(6):583-588.
[23] 宋腾,韩邦成,郑世强. 基于最小位移的磁悬浮转子变极性LMS反馈不平衡补偿[J]. 振动与冲击,2015,34(7):24-32. SONG Teng,HAN Bangcheng,ZHENG Shiqiang. Variable polarity LMS feedback based on displacement nulling to compensate unbalance of magnetic bearing[J]. Journal of Vibration and Shock,2015,34(7):24-32.
[24] 周天豪,陈磊,祝长生. 基于自适应变步长最小均方算法的磁悬浮高速电机不平衡补偿[J]. 电工技术学报,2020,35(9):1900-1911. ZHOU Tianhao,CHEN Lei,ZHU Changsheng. Unbalance compensation for magnetically levitated high-speed motors based on adaptive variable step size least mean square algorithm[J]. Transactions of China Electrotechnical Society,2020,35(9):1900-1911.
[25] TANG E,FANG J,HAN B. Active vibration control of the flexible rotor in high energy density magnetically suspended motor with mode separation method[J]. Journal of Engineering for Gas Turbines and Power,2015,137(8):082503.