建筑结构的鲁棒H_∞最优控制
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摘要
针对传统线性二次型最优控制(Linear quadratic optimal control,LQR)等主动控制方法存在鲁棒性较差的不足,考虑结构参数和外部激励的不确定性,提出一种控制算法简单、便于工程应用的鲁棒H∞最优控制方法。将工程中常用的二次型最优指标结合于鲁棒H∞控制系统的分析中,使得控制器的性能指标容易衡量;通过引入线性矩阵不等式(Linear Matrix Inequalities,LMI)减小求解的复杂度。以一个多层剪切型建筑结构模型为例进行了仿真,并与LQR方法进行对比,仿真结果初步表明该方法具有较好的控制效果和鲁棒性。
The building structure is uncertain because of the numerous uncertainties of seismic disturbances and structural parameters.Existing active control methods for reducing seismic responses of building structures,such as those of linear quadratic optimal control(LQR) etc,suffer from,in our opinion,the shortcoming that it is almost very difficult to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.In this paper,we present a new robust H ∞ optimal control approach that can provide a convenient design procedure for active controllers to facilitate the practical implementations of control systems by the use of a quadratic performance index and the use of an efficient solution procedure based on linear matrix inequalities(LMI).Such a new robust H ∞ optimal controller for buildings can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.An MDOF shear building model containing active brace systems is analyzed.In the simulation,the active control forces of the active brace systems are designed by the robust H ∞ optimal control algorithm and the structural system uncertainties are assumed in the model errors and seismic disturbance.The simulation results obtained from the proposed control method are compared with those obtained from LQR method,which shows preliminarily that the performance of robust H ∞ optimal controller is remarkable and robust.
The building structure is uncertain because of the numerous uncertainties of seismic disturbances and structural parameters.Existing active control methods for reducing seismic responses of building structures,such as those of linear quadratic optimal control(LQR) etc,suffer from,in our opinion,the shortcoming that it is almost very difficult to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.In this paper,we present a new robust H ∞ optimal control approach that can provide a convenient design procedure for active controllers to facilitate the practical implementations of control systems by the use of a quadratic performance index and the use of an efficient solution procedure based on linear matrix inequalities(LMI).Such a new robust H ∞ optimal controller for buildings can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.An MDOF shear building model containing active brace systems is analyzed.In the simulation,the active control forces of the active brace systems are designed by the robust H ∞ optimal control algorithm and the structural system uncertainties are assumed in the model errors and seismic disturbance.The simulation results obtained from the proposed control method are compared with those obtained from LQR method,which shows preliminarily that the performance of robust H ∞ optimal controller is remarkable and robust.
引文
[1]欧进萍.结构振动控制-主动、半主动和智能控制[M].北京:科学出版社,2003.OU Jinping.Vibration control of structures[M].Beijing:Science Press,2003.(in Chinese)
[2]Fisco N O,Adeli H.Smart structures:PartⅠ-Active and semi-active control[J].Scientia Iranica,2011,18(3):275-284.
[3]Housner C W,Berg man L A,Caughey Y K.Structural control:past,present,and future[J].ASCE Journal of Engineering Mechanics,1997,123(9):897-971.
[4]Calise A J,Sweriduk G D.Active attenuation of building structural response using robust control[J].Journal of Engineering Mechanics,1998,124(5):520-528.
[5]Wang S G,Roschke P N,,Yeh H Y.Robust control for structural systems with unstructured uncertainties[J].ASCE Journal of Engineering Me-chanics,2004,130(3):337-346.
[6]贾英民.鲁棒H∞控制[M].北京:科学出版社,2007.JIA Yingmin.Robust H∞control[M].Beijing:Science Press,2007.(in Chinese)
[7]薛安克.鲁棒最优控制理论与应用[M].北京:科学出版社,2008.XUE Anke.Theory and application of robust optimal control[M].Beijing:Science Press,2008.(in Chinese)
[8]Yang J N,Wu J C.Experimental verifications of H∞and sliding-mode control for seismically excited buildings[J].ASCE Journal of StructuralEngineering,1996,122(1):69-75.
[9]张远勤,林桐.基于线性矩阵不等式(LMI)的建筑结构抗震H∞控制[J].地震工程与工程振动,2003,23(5):169-173.ZHAGN Yuanqin,LIN Tong.H∞control for seismic-excited buildings based on linear matrix in equalities(LMI)[J].Journal of Earthquake En-gineering and Engineering Vibration,2003,23(5):169-173.(in Chinese)
[10]Du H P,Lam J,Sze K Y.Non-fragile H∞vibration control for uncertain structural systems[J].Journal of Sound and Vibration,2004,273:1031-1045.
[11]李文章,吴凌尧,郭雷.基于LMI的结构振动鲁棒H∞控制[J].振动工程学报,2008,21(2):157-161.LI Wenzhang,WU Lingyao,GUO Lei.Robust H∞control of structural vibration based on LMI[J].Journal of Vibration Engineering,2008,21(2):157-161.(in Chinese)
[12]徐洋,姜洪洲,叶正茂,等.H∞控制在AMD Benchmark结构主动控制中的应用研究[J].振动与冲击,2005,24(5):14-22.XU Yang,JIANG Hongzhou,YE Zhengmao,et al.Research on the application of H∞control in the AMD active structure control benchmark prob-lem[J].Journal of Vibration and Shock,2005,24(5):14-22.(in Chinese)
[13]Wu J C,Chih H H,Chen C H.A robust method for seismic protection of civil frame building[J].Journal of Sound and Vibration,2006,294:314-328.
[14]Boyd S P,Ghaoui L E,Feron E,et al.Linear matrix inequality in systems and control theory[M].Philadelphia:SIAM,1994.
[2]Fisco N O,Adeli H.Smart structures:PartⅠ-Active and semi-active control[J].Scientia Iranica,2011,18(3):275-284.
[3]Housner C W,Berg man L A,Caughey Y K.Structural control:past,present,and future[J].ASCE Journal of Engineering Mechanics,1997,123(9):897-971.
[4]Calise A J,Sweriduk G D.Active attenuation of building structural response using robust control[J].Journal of Engineering Mechanics,1998,124(5):520-528.
[5]Wang S G,Roschke P N,,Yeh H Y.Robust control for structural systems with unstructured uncertainties[J].ASCE Journal of Engineering Me-chanics,2004,130(3):337-346.
[6]贾英民.鲁棒H∞控制[M].北京:科学出版社,2007.JIA Yingmin.Robust H∞control[M].Beijing:Science Press,2007.(in Chinese)
[7]薛安克.鲁棒最优控制理论与应用[M].北京:科学出版社,2008.XUE Anke.Theory and application of robust optimal control[M].Beijing:Science Press,2008.(in Chinese)
[8]Yang J N,Wu J C.Experimental verifications of H∞and sliding-mode control for seismically excited buildings[J].ASCE Journal of StructuralEngineering,1996,122(1):69-75.
[9]张远勤,林桐.基于线性矩阵不等式(LMI)的建筑结构抗震H∞控制[J].地震工程与工程振动,2003,23(5):169-173.ZHAGN Yuanqin,LIN Tong.H∞control for seismic-excited buildings based on linear matrix in equalities(LMI)[J].Journal of Earthquake En-gineering and Engineering Vibration,2003,23(5):169-173.(in Chinese)
[10]Du H P,Lam J,Sze K Y.Non-fragile H∞vibration control for uncertain structural systems[J].Journal of Sound and Vibration,2004,273:1031-1045.
[11]李文章,吴凌尧,郭雷.基于LMI的结构振动鲁棒H∞控制[J].振动工程学报,2008,21(2):157-161.LI Wenzhang,WU Lingyao,GUO Lei.Robust H∞control of structural vibration based on LMI[J].Journal of Vibration Engineering,2008,21(2):157-161.(in Chinese)
[12]徐洋,姜洪洲,叶正茂,等.H∞控制在AMD Benchmark结构主动控制中的应用研究[J].振动与冲击,2005,24(5):14-22.XU Yang,JIANG Hongzhou,YE Zhengmao,et al.Research on the application of H∞control in the AMD active structure control benchmark prob-lem[J].Journal of Vibration and Shock,2005,24(5):14-22.(in Chinese)
[13]Wu J C,Chih H H,Chen C H.A robust method for seismic protection of civil frame building[J].Journal of Sound and Vibration,2006,294:314-328.
[14]Boyd S P,Ghaoui L E,Feron E,et al.Linear matrix inequality in systems and control theory[M].Philadelphia:SIAM,1994.
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