考虑参数不确定性的结构抗震鲁棒H_∞控制
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摘要
基于线性矩阵不等式方法,本文给出了一种新的考虑参数不确定性的鲁棒H∞控制器设计方法,并用于建筑结构的抗震控制。假定结构不确定参数是范数有界的,通过有界实引理,把考虑参数不确定性的鲁棒H∞控制器设计化为具有线性矩阵不等式约束的凸优化问题,进而可以应用内点法等凸优化技术进行求解。以6层建筑结构在Kobe地震动输入和突加Kanai-Tajimi过滤白噪声随机地震激励下的抗震控制为例,进行了数值仿真。数值结果表明,鲁棒H∞控制器具有很强的鲁棒性,无论结构刚度和阻尼是否存在变异,均能实现很好的控制效果。
Based on linear matrix inequalities(LMIs),a new method for the design of robust H∞ controllers for linear systems with parameter uncertainties is proposed.The parameter uncertainties considered are assumed to be norm-bounded.By introducing bounded real lemma,the robust H∞ controller design is transformed into a convex optimal problem with the constraints of linear matrix inequalities to which the existing convex optimization techniques such as the interior-point algorithm can be applied.To illustrate the effectiveness of the proposed robust H∞ controller,a six-storey building subjected to the 1995 Kobe earthquake record or to a suddenly applied Kanai-Tajimi filtered white noise random excitation is investigated respectively,which shows that whether the stiffness or damping variation exists or not,the proposed robust H∞ controller behaves very satisfactorily.
Based on linear matrix inequalities(LMIs),a new method for the design of robust H∞ controllers for linear systems with parameter uncertainties is proposed.The parameter uncertainties considered are assumed to be norm-bounded.By introducing bounded real lemma,the robust H∞ controller design is transformed into a convex optimal problem with the constraints of linear matrix inequalities to which the existing convex optimization techniques such as the interior-point algorithm can be applied.To illustrate the effectiveness of the proposed robust H∞ controller,a six-storey building subjected to the 1995 Kobe earthquake record or to a suddenly applied Kanai-Tajimi filtered white noise random excitation is investigated respectively,which shows that whether the stiffness or damping variation exists or not,the proposed robust H∞ controller behaves very satisfactorily.
引文
[1]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.
[2]Wang S G.Linear quadratic Gaussian-alpha control with relative stability and gain parameter for the structural benchmark problems[J].Journalof Engineering Mechanics(ASCE),2004,130(4):511-517.
[3]张微敬,欧进萍.基于状态反馈的结构鲁棒控制[J].世界地震工程,2002,18(3):37-41.
[4]张远勤,林桐.基于线性矩阵不等式(LMI)的建筑结构抗震H∞控制[J].地震工程与工程振动,2003,23(5):169-173.
[5]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.
[6]张微敬,欧进萍.基于参数灵敏度最小的鲁棒主动控制方法[J].地震工程与工程振动,2002,22(3):106-110.
[7]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.
[8]钟万勰,吴志刚,谭述君.状态空间控制理论与计算[M].北京:科学出版社,2007.
[9]盛严,王超,潘颖.带有补偿器的高层建筑结构滑模控制[J].应用力学学报,2003,20(3):38-42.
[10]何玉敖,李江.基于模糊逻辑与神经网络的高层结构半主动控制[J].建筑结构学报,2003,24(2):33-37.
[11]Yu Li.Optimal guaranteed cost control of linear uncertain system:an LMI approach[J].控制理论与应用,2000,17(3):423-428.
[12]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.
[13]Arfiadi Y,Hadi MNS.Continuous bounded controllers for active control of structures[J].Computers and Structures,2006,84(12):798-807.
[14]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.
[2]Wang S G.Linear quadratic Gaussian-alpha control with relative stability and gain parameter for the structural benchmark problems[J].Journalof Engineering Mechanics(ASCE),2004,130(4):511-517.
[3]张微敬,欧进萍.基于状态反馈的结构鲁棒控制[J].世界地震工程,2002,18(3):37-41.
[4]张远勤,林桐.基于线性矩阵不等式(LMI)的建筑结构抗震H∞控制[J].地震工程与工程振动,2003,23(5):169-173.
[5]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.
[6]张微敬,欧进萍.基于参数灵敏度最小的鲁棒主动控制方法[J].地震工程与工程振动,2002,22(3):106-110.
[7]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.
[8]钟万勰,吴志刚,谭述君.状态空间控制理论与计算[M].北京:科学出版社,2007.
[9]盛严,王超,潘颖.带有补偿器的高层建筑结构滑模控制[J].应用力学学报,2003,20(3):38-42.
[10]何玉敖,李江.基于模糊逻辑与神经网络的高层结构半主动控制[J].建筑结构学报,2003,24(2):33-37.
[11]Yu Li.Optimal guaranteed cost control of linear uncertain system:an LMI approach[J].控制理论与应用,2000,17(3):423-428.
[12]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.
[13]Arfiadi Y,Hadi MNS.Continuous bounded controllers for active control of structures[J].Computers and Structures,2006,84(12):798-807.
[14]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.
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