毗邻建筑LQG抗震控制的组合精细积分策略
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摘要
LQG调节器在许多工程领域得到了日益广泛的应用。但是当系统受到的外部随机干扰是非平稳时,相关的LQG控制技术还亟需进一步发展。以毗邻建筑非平稳地震响应避碰控制为例对这类问题的求解进行了新的尝试。假定地面运动由基岩处的非平稳随机激励经过单层土的滤波而产生。结合虚拟激励法,对于非平稳随机地震响应分析和微分Riccati方程求解分别采用不同的精细积分策略并予以组合运用。对两座20层毗邻建筑的地震响应LQG控制进行了仿真分析,取得较好的效果。
Although LQG regulators have been used frequently, the relevant control technique still requires further development, particularly with non-stationary random disturbances. In this paper, a new attempt is reported in which the LQG control is applied to adjacent tall buildings subjected to non-stationary seismic random excitations. The ground motion is induced by the random excitations from the bedrock through a single-layer soil that is regarded as filter. In combination with the pseudo excitation method (PEM), two precise integration schemes are applied to the analysis of structural non-stationary seismic random responses and the solution of the differential Riccati equations in the transient LQG control process, respectively. Satisfactory control effects are achieved in the numerical simulation with two adjacent 20-storey buildings.
Although LQG regulators have been used frequently, the relevant control technique still requires further development, particularly with non-stationary random disturbances. In this paper, a new attempt is reported in which the LQG control is applied to adjacent tall buildings subjected to non-stationary seismic random excitations. The ground motion is induced by the random excitations from the bedrock through a single-layer soil that is regarded as filter. In combination with the pseudo excitation method (PEM), two precise integration schemes are applied to the analysis of structural non-stationary seismic random responses and the solution of the differential Riccati equations in the transient LQG control process, respectively. Satisfactory control effects are achieved in the numerical simulation with two adjacent 20-storey buildings.
引文
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[13]钟万勰,蔡志勤.LQG量测反馈最优控制的精细积分[J].应用数学和力学,2000,21(12):1279～1284.Zhong Wanxie,Cai Zhiqin.Precise integration method for LQG optimal measurement feedback control problem[J].Applied Mathematics and Mechanics,2000,21(12):1279～1284.(in Chinese)
[2]Akhiev SS,Aldemir U,Bakioglu M.Multipoint instantaneous optimal control of structures[J].Computers and Structures,2002,80:909～917.
[3]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.
[4]Choi Seung-Bok,Han Sang-Soo.H∞control of electrorheological suspension system subjected to parameter uncertainties[J].Mechatronics,2003,13:639～657.
[5]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.Wu Zhigang.Theory and computation of linear robust control[M].Dalian:Dalian University of Technology Press,2003.(in Chinese)
[6]Yoshimura T,Nakaminami K,Kurimoto M,Hino J.Active suspension of passenger cars using linear and fuzzy-logic controls[J].Control Engineering Practice,1999,7:41～47.
[7]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)
[8]徐幼麟,张文首.毗邻建筑地震响应LQG控制问题的闭合解[J].地震工程与工程振动,2001,21(4):40～46.Xu Youlin,Zhang Wenshou.Closed form solution of LQG control problem for seismic response of adjacent buildings[J].Earthquake Engineering and Engineering Vibration,2001,21(4):40～46.(in Chinese)
[9]钟万勰.线性二次最优控制的精细积分法[J].自动化学报,2001,27(2):166～173.Zhong Wanxie.The precise integration of LQ control problems[J].Acta Automatica Sinica,2001,27(2):166～173.(in Chinese)
[10]钟万勰.卡尔曼-布西滤波的精细积分[J].大连理工大学学报,1999,39(2):191～200.Zhong Wanxie.Precise integration of Kalman-Bucy filtering problems[J].Journal of Dalian University of Technology,1999,39(2):191～200.(in Chinese)
[11]钟万勰.应用力学对偶体系[M].北京:科学出版社,2002.Zhong Wanxie.Duality System in Applied Mechanics[M].Beijing:Science Press,2002.(in Chinese)
[12]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.Lin Jiahao,Zhang Yahui.Pseudo Excitation Method for Random Vibration Analysis[M].Beijing:Science Press,2004.(in Chinese)
[13]钟万勰,蔡志勤.LQG量测反馈最优控制的精细积分[J].应用数学和力学,2000,21(12):1279～1284.Zhong Wanxie,Cai Zhiqin.Precise integration method for LQG optimal measurement feedback control problem[J].Applied Mathematics and Mechanics,2000,21(12):1279～1284.(in Chinese)
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