随机激励条件下转子系统的主动振动控制
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摘要
针对随机激励下线性转子系统的振动主动控制,给出了随机激励下受控柔性转子系统的状态空间模型,基于线性二次型高斯控制理论,提出了转子系统在白噪声和有色噪声激励下振动的最优控制策略。以一个柔性转子轴承系统为例,用数值方法研究了El.Centro地震激励作用下随机最优策略对转子-轴承系统的振动主动控制,并讨论了性能指标中不同权函数对控制效果的影响。结果表明:文中所提出的随机最优控制策略能有效地抑制转子系统的振动,控制效果随着与转子系统位移和速度相关的权矩阵的增大而变好,随着与控制相关的权矩阵的增大而变差。这对于旋转机械系统随机最优控制中权矩阵的选择具有一定的参考价值。
In order to study the active vibration control of a linear rotor system subjected to random excitation,a state space model of a controlled flexible rotor system subjected to random excitation was presented.Based on the Linear-Quadratic Gaussian(LQG)control theory,optimal vibration control strategies of the rotor system under the white noise and the coloured noise excitation were obtained.A numerical example was presented for a rotor-bearing system subjected to nonstationary El.Centro earthquake excitation.The influence of the performance index's weighting function on the control effectiveness was discussed.It is shown that the stochastic optimal control strategies presented can effectively attenuate the vibration of the rotor system.The control effectiveness becomes better with the increase of the weighting matrix corresponding to the displacement and velocity of the rotor system and becomes weaker with the increase of the weighting matrix corresponding to the control.This will provid some references for choosing weighting matrix in stochastic optimal control for rotating machinery.
In order to study the active vibration control of a linear rotor system subjected to random excitation,a state space model of a controlled flexible rotor system subjected to random excitation was presented.Based on the Linear-Quadratic Gaussian(LQG)control theory,optimal vibration control strategies of the rotor system under the white noise and the coloured noise excitation were obtained.A numerical example was presented for a rotor-bearing system subjected to nonstationary El.Centro earthquake excitation.The influence of the performance index's weighting function on the control effectiveness was discussed.It is shown that the stochastic optimal control strategies presented can effectively attenuate the vibration of the rotor system.The control effectiveness becomes better with the increase of the weighting matrix corresponding to the displacement and velocity of the rotor system and becomes weaker with the increase of the weighting matrix corresponding to the control.This will provid some references for choosing weighting matrix in stochastic optimal control for rotating machinery.
引文
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[15]Sawada Y,Ohsumi A.Active vibration control for flexible cantilever beam subject to seismic disturbance[C].IEEE International Conference on Systems Engineering,Kobe,1992.
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[17]Suarez L E,Singh M P,Rohanimanesh M S.Seismic response of rotating machines[J].Earthquake Engineering and Structural Dynamics,1992,21(1):21-36.
[2]Abduljabbar Z,Eimadany M M,Al-Bahkali E.On the vibration and control of a flexible rotor mounted on fluid film bearings[J].Computers&Structures,1997,65(6):849-856.
[3]Johnson M E,Nascimento L P,Kasarda M,et al.The Effect of Actuator and Sensor Placement on the Active Control of Rotor Unbalance[J].Journal of Vibration and Acoustics,2003,125(3):365-373.
[4]Lin Yih-Hwang,Yu Hsiang-Chieh.Active modal control of a flexible rotor[J].Mechanical Systems and Signal Processing,2004,18(5):1117-1131.
[5]孙海波,姚新港.基于反共振不平衡转子-轴承系统的振动控制[J].中国机械工程,2002,13(3):193-195.Sun Haibo,Yao Xingang.Controlling elastic vibration of rotor-bearing system with unbalance based on anti-resonance[J].China Mechanical Engineering,2002,13(3):193-195(in Chinese).
[6]骆志明,冯庚斌,顾家柳.转子动力系统的非线性H∞控制[J].振动工程学报,1998,11(2):224-228.Luo Zhiming,Feng Gengbin,Gu Jialiu.Nonlinear H∞control of rotor dynamic system[J].Journal of Vibration Engineering,1998,11(2):224-228(in Chinese).
[7]瞿红春,马元奎,陆颂元,等.汽轮发电机组转子动静碰摩故障检测的小波分析方法研究[J].中国电机工程学报,1999,19(3):1-5.Qu Hongchun,Ma Yuankui,Lu Songyuan,et al.Application of wavelets to turbogenerator unit for impact fault detection[J].Proceedings of the CSEE,1999,19(3):1-5(in Chinese).
[8]闫桂荣,王晓云,董龙雷,等.基于不确定性推理原理的机组振动信息融合技术[J].中国电机工程学报,2000,20(9):64-66.Yan Guirong,Wang Xiaoyun,Dong Longlei,et al.Vibration information-fusion technology of dynamo set based on uncertainty reasoning[J].Proceedings of the CSEE,2000,20(9):64-66(in Chinese).
[9]王宏华.基于两步换相控制策略的SR电机直接数字控制系统设计[J].中国电机工程学报,2001,21(7):18-21.Wang Honghua.Direct digital control of switched reluctance motor based on the new commutation strategy[J].Proceedings of the CSEE,2001,21(7):18-21(in Chinese).
[10]沈佩华,顾晃,任浩仁.关于引进型300MW汽轮发电机组振动异常问题的研究[J].中国电机工程学报,2004,24(9):267-271.Shen Peihua,Gu Huang,Ren Hao ren.A research of the vibration malfuction problem for imported type300MW turbogenerator sets[J].Proceedings of the CSEE,2004,24(9):267-271(in Chinese).
[11]Chung L L,Wu L Y,Jin T G.Acceleration feedback control of seismic structures[J].Engineering Structures,1998,20(1):62-74.
[12]Aldemir U,Bakioglu M.Active structural control based on the prediction and degree of stability[J].Journal of Sound and Vibration,2001,247(4):561-576.
[13]Yamada K,Kobori T.Fundamental dynamics and control strategies for aseismic structural control[J].International Journal of Solids and Structures,2001,38(34):6079-6121.
[14]Javad Marzbanrad,Goodarz Ahmadi,Ratneshwar Jha.Optimal preview active control of structures during earthquakes[J].Engineering Structures,2004,26(10):1463-1471.
[15]Sawada Y,Ohsumi A.Active vibration control for flexible cantilever beam subject to seismic disturbance[C].IEEE International Conference on Systems Engineering,Kobe,1992.
[16]Petersen Ian R,Pota Himanshu R.Minimax LQG optimal control of a flexible beam[J].Control Engineering Practice,2003,11(11):1273-1287.
[17]Suarez L E,Singh M P,Rohanimanesh M S.Seismic response of rotating machines[J].Earthquake Engineering and Structural Dynamics,1992,21(1):21-36.
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