基于LMI的结构主动控制系统故障诊断与隔离设计
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摘要
基于H∞鲁棒控制原理,提出了结构主动控制系统故障检测器的设计方法,形成了结构主动控制系统的故障诊断与隔离技术(Fault Detection and Isolation,FDI)。首先根据H∞控制目标提出了FDI系统的模型,将故障信号的检测问题转化为一个鲁棒控制问题,应用线性矩阵不等式(Linear Matrix Inequality,LMI)算法解出H∞最优控制器,即故障检测器。通过一个三层框架结构的数值算例验证了设计的有效性。该研究工作为结构主动控制系统的健康检测提供了参考,为进一步进行容错控制的研究奠定了基础。
The fault detection and isolation(FDI) technique was introduced and the design method of FDI filter in active control system of structure was presented based on H∞ robust control theory.The FDI system model was constructed according to H∞ object which changes the fault detection problem to a robust control problem.The H∞ optimal controller named FDI filter is worked out applying the algorithm of linear matrix inequality(LMI).Simulation results of a three-story building demonstrate the effectiveness of FDI filter.The study provides a reference to the health monitoring of active control system of structure and gives the base of the fault tolerant control.
The fault detection and isolation(FDI) technique was introduced and the design method of FDI filter in active control system of structure was presented based on H∞ robust control theory.The FDI system model was constructed according to H∞ object which changes the fault detection problem to a robust control problem.The H∞ optimal controller named FDI filter is worked out applying the algorithm of linear matrix inequality(LMI).Simulation results of a three-story building demonstrate the effectiveness of FDI filter.The study provides a reference to the health monitoring of active control system of structure and gives the base of the fault tolerant control.
引文
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[13]Bai Y Q,Grigoriadis,Karolos M,et al.Active fault tolerantcontrol of a flexible beam[J].Proceedings of SPIE-TheInternational Society for Optical Engineering,v 6523,2007,Modeling,Signal Processing,and Control for Smart Structures,2007.
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[2]Wang S G,Yeh H Y,Roschke P N.Robust control for structuralsystems with parametric and unstructured uncertainties[J].Journal of Vibration and Control,2001,7(5):753-772.
[3]Stavroulakis G E,Marinova D G,Zacharenakis E C.Robustcontrol in structural dynamics,taking into account structuraluncertainties[C]//5th GRACM International Congress onComputational MechanicsLimassol,29 June-1 July,2005.
[4]唐功友,赵翀.线性系统的动态输出反馈最优扰动抑制[J].信息与控制,2008,37(1):119-123,128.
[5]高振斌,钱富才,刘丁.基于LMI的不确定随机系统输出反馈保性能控制[J].信息与控制,2008,37(4):385-390.
[6]宋刚,吴志刚,林家浩.考虑参数不确定性的结构抗震鲁棒H∞控制[J].地震工程与工程振动,2008,28(6):40-44.
[7]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.
[8]赵春晖,张朝柱,李刚.自适应信号处理[M].哈尔滨:哈尔滨工程大学出版社,2006.
[9]Kalman R E.A new approach to linear filtering and predictionproblems[J].Transactions of the ASME Journal of BasicEngineering,1960,82(Series D):35-45.
[10]Doyle J C,Glover K,Khargonekar P P,et al.State-spacesolutions to standard H2 and H∞control problems[C].IEEETransactions on Automatic Control,1989,34(8):831-847.
[11]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.
[12]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
[13]Bai Y Q,Grigoriadis,Karolos M,et al.Active fault tolerantcontrol of a flexible beam[J].Proceedings of SPIE-TheInternational Society for Optical Engineering,v 6523,2007,Modeling,Signal Processing,and Control for Smart Structures,2007.
[14]周克敏.鲁棒与最优控制[M].北京:国防工业出版社,2002.
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