基于LMI方法的建筑结构AMD容错控制
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摘要
对于建筑结构主动控制系统,传感器或执行器在实际工程中可能会出现故障而失效,这将严重影响结构的减震效果。针对AMD建筑结构系统传感器出现故障的情况,基于AMD建筑结构模型,提出建筑结构主动控制系统的故障诊断与隔离技术(fault detection and isolation,FDI),设计基于容错控制技术(fault tolerant control,FTC)的主动容错控制器。将FDI和FTC的设计过程转化为H∞控制问题,利用变量替换法推导线性矩阵不等式(linear matrixinequality,LMI)凸约束,通过LMI算法解算出结果。最后通过带有AMD装置的三层框架结构数值算例,考虑位移传感器出现故障而失效,应用故障检测隔离技术,设计容错控制器,并且验证故障检测隔离技术和容错控制的有效性。
In the civil structures with AMD control system,the sensors or actuators may work bad or even lose their performance,which can worsen the vibration suppression.Considering the sensors with faults in AMD control system of the civil structural model,this paper presents fault detection and isolation(FDI) and fault tolerant control(FTC).The FDI filter and FTC controller are designed based on H∞ control schemes and computed by solving linear matrix inequality(LMI) problem with convex constrains.Through an example of three-story structure numerical with AMD control system,FDI filter and FTC controller are designed considering the fault of displacement sensors.The results validate the efficiency of FDI and FTC.
In the civil structures with AMD control system,the sensors or actuators may work bad or even lose their performance,which can worsen the vibration suppression.Considering the sensors with faults in AMD control system of the civil structural model,this paper presents fault detection and isolation(FDI) and fault tolerant control(FTC).The FDI filter and FTC controller are designed based on H∞ control schemes and computed by solving linear matrix inequality(LMI) problem with convex constrains.Through an example of three-story structure numerical with AMD control system,FDI filter and FTC controller are designed considering the fault of displacement sensors.The results validate the efficiency of FDI and FTC.
引文
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[29]Wang Y,Lynch J P,Law K H.Decentralized H∞controller design for large-scale civil structures[J].Earthquake Engineering&Structural Dynamics,2009,38(3):377-401
[30]林岳松,薛安克,钱积新.基于LMI方法的鲁棒H∞滤波器设计[J].电路与系统学报,2004,9(5):81-85(Lin Yuesong,Xue Anke,Qian Jixin.Design of robust H∞filter based on LMI approach[J].Journal of Circuitsand Systems,2004,9(5):81-85(in Chinese))
[31]张明,施鼎汉.代数Riccati不等式与H∞滤波器[J].厦门大学学报:自然科学版,1997,36(6):825-828(Zhang Ming,Shi Dinghan.Algebraic Riccati inequalityand H∞filter[J].Journal of Xiamen University:NaturalScience Edition,1997,36(6):825-828(in Chinese))
[32]Zhou K,Doyle J C,Glover K.Robust and optimal control[M].Prentice Hall:Englewood Cliffs,1996
[2]Soong T T,Dargush G F.Passive energy dissipation systemsin structural engineering[M].London:Wiley,1997
[3]Soong T T.Active structure control theory and practice[M].New York:Longman Scientific&Technical,1990
[4]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
[5]李宏男.结构振动与控制[M].中国建筑工业出版社,2005
[6]李宏男.结构多维减震控制[M].北京:科学出版社,2008
[7]周福霖.工程结构减震控制[M].北京:地震出版社,1997
[8]Yang J N,Wu J C,Agrawal A K.Sliding mode control fornonlinear and hysteretic structures[J].Journal ofEngineering Mechanics,1995,121(12):1330-1339
[9]Yang J N,Wu J C,Agrawal A K.Sliding mode control forseismically excited linear structures[J].Journal ofEngineering Mechanics,1995,121(12):1386-1390
[10]Soong T T,Reinhorn A M,Yang J N.A StandardizedModel for Structural Control Experiments and SomeExperimental Results[M].Amsterdam:Structural ControlMartinus Nijhoff,1987:669-693
[11]Tanaka K,Ikede T,Wang H O.Robust stabilization of aclass of uncertain nonlinear systems via fuzzy control:quadratic stabilizability,H∞control theory,and linearmatrix inequalities[C]//IEEE Transactions on FuzzySystems,1996:1-13
[12]Lee K R,Kim J H,Jeung E T,et al.Output feedbackrobust H∞control of uncertain fuzzy dynamic systems withtime-varying delay[C]//IEEE Transactions on FuzzySystems,2000:657-664
[13]Jabbari F,Schmitendorf W E,Yang J N.H∞control forseismic-excited buildings with acceleration feedback[J].Journal of Engineering Mechanics,1995,121(9):994-1002
[14]Wang S G,Yeh H Y,Roschke P N.Robust control forstructural systems with parametric and unstructureduncertainties[J].Journal of Vibration and Control,2001,7(5):753-772
[15]Schmitendorf W E,Jabbari F,Yang J N.Robust controltechniques for buildings under earthquake excitation[J].Earthquake Engineering&Structural Dynamics,1994,23(5):539-552
[16]Dyke S J,Spencer B F,Sain M K,et al.Modeling andcontrol of magnetorheological dampers for seismic responsereduction[J].Smart Materials and Structures,1999,5(5):565-575
[17]Lynch J P,Law K H.Decentralized control techniques forlarge-scale civil structural systems[C]//Proceedings ofthe 20th International Modal Analysis Conference.LosAngeles,2002
[18]Liao J J,Wang A P,Ho C M,et al.A robust control of adynamic beam structure with time delay effect[J].Journalof Sound and Vibration,2002,252(5):835-847
[19]Kelly J M,Leitmann G,Soldatos A G.Robust control ofbase-isolated structures under earthquake excitation[J].Journal of Optimization Theory and Applications,1987,53(2):159-180
[20]Peeters,B.System identification and damage detection incivil engineering[D].Belgium:KULEUVEN,2000
[21]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(Zhang Weijing,Ou Jinping.A robust active control basedon minimum sensitivity[J].Earthquake Engineering andEngineering Vibration,2002,22(3):106-110(inChinese))
[22]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(Zhang Yuanqin,Lin Tong.H∞control forseismic-excited buildings based on linear matrix inequalities(LMI)[J].Earthquake Engineering and EngineeringVibration,2003,23(5):169-173(in Chinese))
[23]Stavroulakis G E,Marinova D G,Zacharenakis E C.Robust control in structural dynamics taking into accountstructural uncertainties[C]//Proceedings of the 5thGRACM International Conference on ComputationalMechanics.Limmasol,Cyprus,2005
[24]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(TangGongyou,Zhao Chong.Optimal disturbance rejection viadynamic output feedback for linear systems[J].Information and Control,2008,37(1):119-123,128(inChinese))
[25]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(Gao Zhenbin,Qian Fucai,Liu Ding.Output feedbackguaranteed cost control of uncertain stochastic systemsbased on LMI[J].Information and Control,2008,37(4):385-390(in Chinese))
[26]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):226-232(Song Gang,Wu Zhigang,Lin Jiahao.Robust H∞control for earthquake-excited structures withparameter uncertainties[J].Journal of EarthquakeEngineering and Engineering Vibration,2008,28(6):226-232(in Chinese))
[27]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
[28]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(Zhang Weijing,OuJinping.Robust control approach of structural vibrationbased on state feedback[J].World EarthquakeEngineering,2002,18(3):37-41(in Chinese))
[29]Wang Y,Lynch J P,Law K H.Decentralized H∞controller design for large-scale civil structures[J].Earthquake Engineering&Structural Dynamics,2009,38(3):377-401
[30]林岳松,薛安克,钱积新.基于LMI方法的鲁棒H∞滤波器设计[J].电路与系统学报,2004,9(5):81-85(Lin Yuesong,Xue Anke,Qian Jixin.Design of robust H∞filter based on LMI approach[J].Journal of Circuitsand Systems,2004,9(5):81-85(in Chinese))
[31]张明,施鼎汉.代数Riccati不等式与H∞滤波器[J].厦门大学学报:自然科学版,1997,36(6):825-828(Zhang Ming,Shi Dinghan.Algebraic Riccati inequalityand H∞filter[J].Journal of Xiamen University:NaturalScience Edition,1997,36(6):825-828(in Chinese))
[32]Zhou K,Doyle J C,Glover K.Robust and optimal control[M].Prentice Hall:Englewood Cliffs,1996
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