地震作用下结构振动保性能鲁棒H_2/H_∞控制  

Guaranteed-cost robust H_2/H_∞ control of structures under earthquake

作　　者：赵世平[1] 刘彦辉[2,3] 谭平[2] 

机构地区：[1]海南大学土木建筑工程学院,海南海口570228 [2]广州大学广东省地震工程与应用技术重点实验室,广东广州510405 [3]北京工业大学建筑工程学院,北京100124

出　　处：《四川建筑科学研究》2011年第6期153-156,178,共5页Sichuan Building Science

基　　金：国家自然科学基金重大研究计划"重大工程的动力灾变"重点支持项目"重大工程地震损伤破坏的理论与方法"(90815027);国家教育部博士点专项基金(20061028001)

摘　　要：针对建筑结构振动控制模型的不确定性,研究了被控建筑结构模型参数不确定性时的保性能鲁棒混合H2/H∞控制问题。将结构模型参数不确定性引入到被控结构状态方程的摄动矩阵之中,基于线性矩阵不等式设计了多目标保性能鲁棒混合H2/H∞鲁棒控制器。该控制器在规定的模型参数变化范围内,使得闭环控制系统同时满足H∞干扰抑制和最优H2性能。最后,以一个缩尺的多层剪切型建筑结构模型为例,给出了保性能鲁棒混合H2/H∞控制问题的设计过程,验证所提控制方法的有效性。数值分析结果表明,所提出的保性能鲁棒混合H2/H∞控制方法的控制效果明显,能有效地减小结构的地震峰值响应,且控制系统对结构参数不确定性有很强的鲁棒性。Aimed to the controlled structures with uncertain model parameters, the guaranteed-cost robust mixed H2/H∞ control problem of structures with uncertain model parameters is study in this paper. In the process of designing H2/H∞ controller,the uncertain model parameters of structures are included in perturbation matrix of state equation, and the muhi-objeetive guaranteed-cost robust mixed H2/H∞ controller is employed to design according to the linear matrix inequality. This H2/H∞ controller can satisfy H∞ disturbance suppression and the optimal H2 performance of the closed-loop control system simultaneously within the range of perturbation of modal parameters. Finally, a three-storey shear-type frame structure is used to verify the effectiveness of the guaranteed-cost robust mixed H2/H∞ controller, suggesting that the guaranteed-cost robust mixed H2/H∞ controller have the favorable control efficiency for the reduced scale frame structure under earthquake and the seismic responses of structure are decreased in different degree. In addition, the guaranteed-cost robust mixed H2/H∞ controller has favorable robustness for the controlled structures with uncertain model parameters.

关 键 词：地震响应 振动控制 保性能鲁棒混合H2/H∞ 不确定性结构 线性矩阵不等式 

分 类 号：TU311.3[建筑科学—结构工程] TP273.1[自动化与计算机技术—检测技术与自动化装置]