偏心结构基于LMI的鲁棒H_∞控制  

Robust H_∞ Control for Eccentric Buildings via LMI Approach

作　　者：李志军[1] 刘园园[1] 王社良[2] 顾致平[1] 

机构地区：[1]西安工业大学建筑工程学院,西安710032 [2]西安建筑科技大学土木工程学院,西安710055

出　　处：《振动．测试与诊断》2014年第5期857-863,975,共7页Journal of Vibration,Measurement & Diagnosis

基　　金：国家自然科学基金资助项目(51178388);陕西省工业攻关项目(2013K07-07);陕西省教育厅专项科研计划资助项目(2013JK0612);西部地区人才培养特别项目(201208615016);西安工业大学校长基金重点项目(XAGDXJJ0919);西安工业大学青年英才项目

摘　　要：针对传统线性二次型最优控制(linear quadratic optimal control,简称LQR)等主动控制方法存在鲁棒性较差的不足,提出一种新的基于线性矩阵不等式的鲁棒H∞控制方法。通过将工程中常用的二次型最优性能指标结合于鲁棒H∞控制系统的分析中,应用线性矩阵不等式减小求解的复杂度,使得控制器的设计较为简单,便于工程应用。考虑到实际中地震动的不确定性和结构的非对称性,以多层偏心结构作为研究对象,在结构顶层沿两个主轴方向正交设置两个主动质量阻尼器(active mass damper,简称AMD)控制装置来控制结构在水平双向地震动作用下的扭转耦联振动,其中AMD系统的主动控制力由鲁棒H∞控制算法获得。仿真结果表明,该方法具有较好的控制效果和鲁棒性。Existing active control methods for reducing the seismological response of building structures,such as those of linear quadratic optimal control(LQR),have shortcomings in guaranteeing the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.A robust H∞control approach is thus proposed,which provides a convenient design procedure for active controllers to facilitate practical implementations of control systems,by using aquadratic performance index and an efficient solution procedure based on linear matrix inequalities(LMI).In view of the uncertainty of seismic disturbance and the non-symmetrical shape of the building structure,a multiple degrees of freedom(MDOF)eccentric building with two active mass damper(AMD)systems in the orthogonal direction of the top story subjected to bi-directional ground motions is analyzed.In the simulation,the active control forces of the AMD systems are designed by the robust H∞control algorithm,and the structural system uncertainties are assumed in the model errors and seismic disturbance.The simulation results demonstrate that the performance of robust H∞controllers is remarkable and robust,and the efficiency of the control approach is also confirmed.Therefore,the robust H∞control method is quite promising for practical implementations of active control systems on seismically excited structures.

关 键 词：鲁棒控制 性能指标 阻尼器 线性矩阵不等式 偏心结构 双向地震动 

分 类 号：TU311.4[建筑科学—结构工程] O328[理学—一般力学与力学基础]