参数不确定建筑结构输出反馈保性能抗震控制
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摘要
对存在模型参数不确定的建筑结构,研究其在给定二次型性能指标下的输出反馈保性能抗震控制问题.基于线性矩阵不等式处理方法,推导了输出反馈保性能控制器存在的充分条件,并给出了该类控制器设计的具体步骤.以6层建筑结构抗震控制为例,分别对确定性和Kanai-Tajimi过滤白噪声随机性地震加速度激励下控制前后结构的振动响应,进行了数值仿真.结果表明,无论结构模型参数是否存在变异,保性能控制器均有很好的控制效果.
A dynamic output feedback guaranteed cost control approach is presented for structures with model parameter uncertainties under seismic excitations. With quadratic cost function given,sufficient conditions for the existence of such an output feedback guaranteed cost controller are derived in the framework of linear matrix inequality optimization,while the steps for controller designing are suggested. To verify the effectiveness of the proposed guaranteed cost control strategy,a six-storey building subjected to a deterministic earthquake acceleration record or to a Kanai-Tajimi filtered white noise random excitation is investigated respectively,which shows that whether the model parameter uncertainties exist or not,the guaranteed cost controller can provide satisfactory results.
A dynamic output feedback guaranteed cost control approach is presented for structures with model parameter uncertainties under seismic excitations. With quadratic cost function given,sufficient conditions for the existence of such an output feedback guaranteed cost controller are derived in the framework of linear matrix inequality optimization,while the steps for controller designing are suggested. To verify the effectiveness of the proposed guaranteed cost control strategy,a six-storey building subjected to a deterministic earthquake acceleration record or to a Kanai-Tajimi filtered white noise random excitation is investigated respectively,which shows that whether the model parameter uncertainties exist or not,the guaranteed cost controller can provide satisfactory results.
引文
[1]AKHIEV S S,ALDEMIR U,BAKIOGLU M.Multipoint instantaneous opti mal control of structures[J].Computers and Structures,2002,80(11):909-917
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[6]WANG S G.Linear quadratic Gaussian-alpha control with relative stability and gain parameter for the structural benchmark problems[J].Journal of Engineering Mechanics,ASCE,2004,130(4):511-517
[7]CHOI S B,HAN S S.H∞control of electrorheological suspension system subjected to parameter uncertainties[J].Mechatronics,2003,13(7):639-657
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[9]LIEN C H,YU K W.LMI opti mization approach on robustness andH∞control analysis for observer-based control of uncertain systems[J].Chaos,Solitons and Fractals,2008,36(3):617-627
[10]WU H N,FEI Y C.MixedH2/H∞robust output feedback control for uncertain linear systems[J].Control Theory&Applications,2000,17(3):367-373
[11]YU L.Opti mal guaranteed cost control of linear uncertain system:an LMI approach[J].Control Theory&Applications,2000,17(3):423-428
[12]XUE A K,SUN Y X.On the robustness of quadratic guaranteed cost control for parameter uncertain systems[J].Control Theory&Applications,2000,17(6):941-944
[13]熊军林,张庆灵.不确定广义系统的最优保性能控制[J].自动化学报,2004,30(4):588-591
[14]QIN C T,DUAN G R.Opti mal robust guaranteed cost control of uncertain linear continuous ti me systems via dynamical output feedback[C]//Proceedings of the6th World Congress on Intelligent Control and Automation.Dalian:IEEE,2006:2441-2445
[15]俞立.鲁棒控制———线性矩阵不等式处理方法[M].北京:清华大学出版社,2002
[16]ARFIADI Y,HADI M N S.Continuous bounded controllers for active control of structures[J].Computers and Structures,2006,84(12):798-807
[17]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004
[2]BAKIOGLU M,ALDEMIR U.A new numerical algorithm for sub-opti mal control of earthquake excited linear structures[J].International Journal for Numerical Methods in Engineering,2001,50(12):2601-2616
[3]XU Y L,ZHANG W S.Closed-form solution for seismic response of adjacent buildings with linear quadratic Gaussian controllers[J].Earthquake Engineering and Structural Dynamics,2002,31(2):235-259
[4]WU J C,YANG J N.LQG control of lateral-torsional motion of Nanjing TV transmission tower[J].Earthquake Engineering and StructuralDynamics,2000,29(8):1111-1130
[5]张微敬,欧进萍.基于参数灵敏度最小的鲁棒主动控制方法[J].地震工程与工程振动,2002,22(3):106-110
[6]WANG S G.Linear quadratic Gaussian-alpha control with relative stability and gain parameter for the structural benchmark problems[J].Journal of Engineering Mechanics,ASCE,2004,130(4):511-517
[7]CHOI S B,HAN S S.H∞control of electrorheological suspension system subjected to parameter uncertainties[J].Mechatronics,2003,13(7):639-657
[8]LAI C T,FANG C H,KAUS W,et al.RobustH2control of norm-bounded uncertain continuous-ti me system—an LMI approach[C]//2004IEEE International Symposium on Computer Aided Control Systems Design.Taipei:IEEE,2004:243-248
[9]LIEN C H,YU K W.LMI opti mization approach on robustness andH∞control analysis for observer-based control of uncertain systems[J].Chaos,Solitons and Fractals,2008,36(3):617-627
[10]WU H N,FEI Y C.MixedH2/H∞robust output feedback control for uncertain linear systems[J].Control Theory&Applications,2000,17(3):367-373
[11]YU L.Opti mal guaranteed cost control of linear uncertain system:an LMI approach[J].Control Theory&Applications,2000,17(3):423-428
[12]XUE A K,SUN Y X.On the robustness of quadratic guaranteed cost control for parameter uncertain systems[J].Control Theory&Applications,2000,17(6):941-944
[13]熊军林,张庆灵.不确定广义系统的最优保性能控制[J].自动化学报,2004,30(4):588-591
[14]QIN C T,DUAN G R.Opti mal robust guaranteed cost control of uncertain linear continuous ti me systems via dynamical output feedback[C]//Proceedings of the6th World Congress on Intelligent Control and Automation.Dalian:IEEE,2006:2441-2445
[15]俞立.鲁棒控制———线性矩阵不等式处理方法[M].北京:清华大学出版社,2002
[16]ARFIADI Y,HADI M N S.Continuous bounded controllers for active control of structures[J].Computers and Structures,2006,84(12):798-807
[17]林家浩,张亚辉.随机振动的虚拟激励法[M].北京:科学出版社,2004
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