地震作用下建筑结构基于平衡降阶的时滞离散H_∞控制
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摘要
在状态空间下直接对结构振动的时滞微分方程进行离散,并引入适当的增广向量将之转化为不显含时滞项的标准离散形式,然后将该离散系统平衡降阶,大大降低了离散系统的维数。在此基础上采用离散的H∞全信息反馈控制理论完成了建筑结构减振控制器的设计,得到的控制器含有对当前和滞后控制量的线性组合,反映了时滞因素的影响,对大时滞情况亦有效。最后通过算例仿真与分析验证了该控制器的有效性,它在不牺牲控制效果的前提下,大大降低了控制器的维数。
The application of full-information H ∞ control theory to vibration attenuation of buildings with control time-delays under seismic excitation was presented. By introducing the extended vectors in state space, the motion equation of original system with time-delays was transformed into the standard discrete form that contains no delays. Then by using balanced-reduction method for this discrete system, the dimension can be significantly reduced. Thusly, a robust controller was designed based on H ∞ disturbance attenuation theory, concerning the uncertainty of seismic excitation. The vibration-reduction controller contains linear combination of some former steps of control, which reflects the character of controlled systems with time-delays. It is also suitable for the case of large time-delays. Simulation results for a three-story building demonstrate the effectiveness of the control method presented. Furthermore, the parameter effects on the performance of the controller are also discussed. Moreover, the dimension of the controller can be reduced without discounting the control efficiency.
The application of full-information H ∞ control theory to vibration attenuation of buildings with control time-delays under seismic excitation was presented. By introducing the extended vectors in state space, the motion equation of original system with time-delays was transformed into the standard discrete form that contains no delays. Then by using balanced-reduction method for this discrete system, the dimension can be significantly reduced. Thusly, a robust controller was designed based on H ∞ disturbance attenuation theory, concerning the uncertainty of seismic excitation. The vibration-reduction controller contains linear combination of some former steps of control, which reflects the character of controlled systems with time-delays. It is also suitable for the case of large time-delays. Simulation results for a three-story building demonstrate the effectiveness of the control method presented. Furthermore, the parameter effects on the performance of the controller are also discussed. Moreover, the dimension of the controller can be reduced without discounting the control efficiency.
引文
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[2]Yang J N,Akbarpour A,Ghaemmaghami P.New optimal control algorithms for structural control[J].Journal of Engineering Mechanics,ASCE,1987,113(6):1369―1386.
[3]张微敬,欧进萍.基于状态反馈的结构鲁棒控制[J].世界地震工程,2002,18(3):37―41.Zhang Weijing,Ou Jinping.Robust control approach of structural vibration based on state feedback[J].World Information on Earthquake Engineering,2002,18(3):37―41.(in Chinese)
[4]Malek M,Jamashidi M.Time-delay systems,analysis,optimization and applications[M].New York:North-Holland,1987.
[5]Chung L L,Lin C C,Lu K H.Time-delay control of structures[J].Journal Earthquake Engineering and Structural Dynamics,1995,24(5):687―701.
[6]潘颖,王超,蔡国平.地震作用下主动减震结构的时滞离散最优控制[J].工程力学,2004,21(2):88―94.Pan Ying,Wang Chao,Cai Guoping.Discrete-time optimal control method for seismic-excited building structures with time delay[J].Engineering Mechanics,2004,21(2):88―94.(in Chinese)
[7]Pernebo L,Silverman L M.Model reduction via balanced state space representations[J].IEEE Transactions on Automatic Control,1982,27(2):382―387.
[8]张文首,林家浩,于骁.海洋平台地震响应的LQG控制[J].动力学与控制学报,2003,1(1):47―52.Zhang Wenshou,Lin Jiahao,Yu Xiao.Seismic response of offshore platform with linear quadratic gaussian controllers[J].Journal of Dynamics and Control,2003,1(1):47―52.(in Chinese)
[9]Green M,Limebeer D J N.Linear robust control[M].New Jersey:Prentice-Hall,1995.
[10]Hu H Y,Wang Z H.Dynamics of controlled mechanical systems with delayed feedback[M].Berlin:Springer,2002.
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[13]Zhou K M,Doyle J C,Glover K.Robust and optimal control[M].New Jersey:Prentice Hall,1996.
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