考虑控制器时滞的建筑结构减振H_∞控制方法
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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。在此基础上采用离散的H∞反馈控制理论完成了建筑结构减振控制器的设计,对于地震激励的不确定性有很好的鲁棒性。得到的控制器含有对滞后控制量的线性组合,反映了时滞因素的影响,对大时滞情况也有效。最后通过算例仿真与分析验证了这种控制器的有效性。
This paper presents the application of full-information H_∞control theory to the field of vibration attenuation of buildings with control time-delays under seismic excitation.By introducing the extended vectors in state space,the motion equation of original system with time-delays is transformed into standard discrete form that contains no delays.Then a robust controller is designed based on H_∞disturbance attenuation theory,considering of the uncertainty of seismic excitation.The deduced controller contains linear combinations 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.
This paper presents the application of full-information H_∞control theory to the field of vibration attenuation of buildings with control time-delays under seismic excitation.By introducing the extended vectors in state space,the motion equation of original system with time-delays is transformed into standard discrete form that contains no delays.Then a robust controller is designed based on H_∞disturbance attenuation theory,considering of the uncertainty of seismic excitation.The deduced controller contains linear combinations 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.
引文
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[7]Tan Shujun,Wu Zhigang,Zhong Wanxie.Optimal induced norm computation of discrete H∞controldystems with time-delays[A].International Conference on Complementarily,Duality,and Global Optimization in Science and Engineering[C],2005,Blacksburg,Virginia,USA.
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[10]孙增圻.计算机控制理论及应用[M].北京:清华大学出版社,1987.
[11]钟万勰,谭述君,吴志刚.时滞系统的最优控制[A].第24届中国控制会议论文集[C],广州:华南理工大学出版社,2005,394—398.
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[13]钟万勰.H∞状态反馈与瑞利商精细积分[J].计算力学学报,1999,16(1):1-8.
[14]Chung L L,Wang Y P,Tung C C.Instantaneous control of structures with time-delay consideration[J].Engineering Structures,1997,19(6):465—475.
[2]Yang J N,Akbarpour A,Ghaemmaghami P.Newoptimal control algorithms for structural control[J].Journal of Engineering Mechanics,ASCE,1987,113(6):1 369—1 386.
[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.
[4]Malek M,Jamashidi M.Time-delay Systems,Analysis,Optimization and Applications[M].North-Holland,1987.
[5]Chung L L,Lin C C,Lu K H.Time-delay control of structures[J].Journal Earthquake Engineering andStructural Dynamics,1995,(24):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.
[7]Tan Shujun,Wu Zhigang,Zhong Wanxie.Optimal induced norm computation of discrete H∞controldystems with time-delays[A].International Conference on Complementarily,Duality,and Global Optimization in Science and Engineering[C],2005,Blacksburg,Virginia,USA.
[8]Michael Green,David J N Limebeer.Linear Robust Control[M].Prentice-Hall,Inc.1995.
[9]Hu H Y,Wang Z H.Dynamics of Controlled Me-chanical Systems with Delayed Feedback[M].Berlin:Springer,2002.
[10]孙增圻.计算机控制理论及应用[M].北京:清华大学出版社,1987.
[11]钟万勰,谭述君,吴志刚.时滞系统的最优控制[A].第24届中国控制会议论文集[C],广州:华南理工大学出版社,2005,394—398.
[12]吴志刚.线性鲁棒控制的理论与计算[M].大连:大连理工大学出版社,2003.
[13]钟万勰.H∞状态反馈与瑞利商精细积分[J].计算力学学报,1999,16(1):1-8.
[14]Chung L L,Wang Y P,Tung C C.Instantaneous control of structures with time-delay consideration[J].Engineering Structures,1997,19(6):465—475.
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