建筑结构基于LMI的鲁棒非脆弱H_∞控制

ROBUST AND NON-FRAGILE H_∞ CONTROL FOR BUILDINGS VIA LMI APPROACH

考虑一维地震动作用和结构参数不确定性影响,提出一种基于线性矩阵不等式(Linear Matrix Inequalities,LMI)的鲁棒非脆弱H∞控制方法。引入工程中常用的二次型最优指标,并应用线性矩阵不等式减小求解的复杂度,使得控制器的性能指标容易衡量,设计相对简单,便于工程应用。以一个三层剪切型结构模型为例进行数值分析,并与传统H∞控制方法进行对比,仿真结果初步表明:1)所提方法具有很好的控制效果和鲁棒性;2)合理地计算结构参数值,可使控制系统在具有最优反应品质的前提下,获得相对更好的鲁棒性和非脆弱性。

The behavior of building structures is naturally uncertain because of the numerous uncertainties of seismic disturbances and structural parameters.In this paper,we present a new robust and non-fragile H∞ control approach that can provide a convenient design procedure for active controllers to facilitate practical implementations of control systems through 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 and non-fragile H∞ controller for buildings can be designed to guarantee the robust stability and performance of the closed-loop system in the presence of parameter uncertainties.In view of the uncertainty of seismic disturbance and the model errors of the building structure,a three-storey shear building model containing active brace systems is analyzed.The simulation results obtained from the proposed control method are compared with those obtained from traditional H∞ control method,which shows preliminarily that the performance of robust and non-fragile H∞ controllers is remarkable and robust.Considering reasonable parameter values,the controller can acquire considerably better performance of robust and non-fragile than traditional H∞ controller under the optimal response quantities.Therefore,the robust and non-fragile H∞control method is quite promising for practical implementations of active control systems on seismically excited linear structures.