地震作用下结构振动保性能鲁棒H_2/H_∞控制
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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 multi-objective 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.
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 multi-objective 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.
引文
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[15]孙万泉,李庆斌.基于LMI的高层建筑结构分散H2/H∞鲁棒控制[J].地震工程与工程振动,2007,27(6):218-222.
[16]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.
[2]Yang J N,Long F X,and Wong D.Optimal control of nonlinearstructures[J].Journal of Applied Mechanics,ASME,1988,55(4):931-938.
[3]王刚,欧进萍.结构振动的模糊建模与模糊控制规则提取[J].建筑结构学报,1998,19(5):28-36.
[4]何玉敖,何亚东.基于Lyapunov稳定性原理和遗传算法的结构半主动控制[J].土木工程学报,2000,33(6):88-93.
[5]欧进萍.结构振动控制—主动、半主动和智能控制[M].北京:科学出版社,2003.
[6]陈静,瞿伟廉.基于泛布尔代数的MR阻尼器半主动控制方法[J].武汉理工大学学报,2002,24(7):62-64.
[7]周云,徐龙河,李忠献.磁流体阻尼器半主动控制结构的地震反应分析[J].土木工程学报,2001,34(5):10-14.
[8]张提波,唐家祥.主动基础隔震结构随机最优控制系统和电流变体阻尼器设计[J].工程抗震,1999(1):30-32.
[9]蒙文流,韦树英.结构振动半主动控制策略的研究进展[J].四川建筑科学研究,2009,35(5):155-158.
[10]王威,王社良,苏三庆.土木结构应用SMA进行振动控制存在的难点问题[J].四川建筑科学研究,2009,35(3):141-144.
[11]李志军,邓子辰.建筑结构滑模控制的模糊趋近律方法[J].四川建筑科学研究,2008,34(5):131-134.
[12]杜永峰,刘彦辉,李慧.智能隔震结构控制算法Simulink仿真分析[J].系统仿真学报,2007,19(18):4270-4278.
[13]韩兵康,张静怡.土木工程结构鲁棒控制的发展[J].地震工程与工程振动,2004,24(6):131-135.
[14]张远勤,林桐,穆静,等.基于LMI的建筑结构地震动H2/H∞混合控制[J].福州大学学报:自然科学版,2004,32(1):60-64.
[15]孙万泉,李庆斌.基于LMI的高层建筑结构分散H2/H∞鲁棒控制[J].地震工程与工程振动,2007,27(6):218-222.
[16]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.
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