一种严密的结构最优控制极值条件及算法实现
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摘要
针对结构振动控制的特点,导出了可用于时域响应最优控制的极值条件。该组表达式对于采用线性二次型最优控制的强迫振动系统而言,是概念上严密的极值条件。对比了几种现有最优控制算法的思路,介绍了对结构控制算法建模思路进行改进的技术要点。利用伴随方程与状态方程形式上的相似性,用数值方法实现了一种新的结构最优控制算法。选用由作者承担设计过的三个实际隔震工程作为算例,对比了输入三种不同地震波时各种算法在模型表达和减震效果上的几个重要特点。
An extreme value condition is derived for optimal control to time-domain response of structures subjected to earthquake excitation by taking the special properties of structural vibration control into account. For the purpose of calculating the control force of a forced vibration system using LQR method, the extreme value condition presented in the study is conceptually rigorous. Several current algorithms for optimal control to structural vibration were compared, and the main improvement over the current algorithms was highlighted. A new algorithm of optimal control to structural vibration has been realized by using state transition method which is based on the similarity between the companion equation and the state equation. Three isolated buildings designed by the author are employed as numerical examples, and several important features such as the model expression and control effect of different algorithms are investigated due to three different earthquake signals.
An extreme value condition is derived for optimal control to time-domain response of structures subjected to earthquake excitation by taking the special properties of structural vibration control into account. For the purpose of calculating the control force of a forced vibration system using LQR method, the extreme value condition presented in the study is conceptually rigorous. Several current algorithms for optimal control to structural vibration were compared, and the main improvement over the current algorithms was highlighted. A new algorithm of optimal control to structural vibration has been realized by using state transition method which is based on the similarity between the companion equation and the state equation. Three isolated buildings designed by the author are employed as numerical examples, and several important features such as the model expression and control effect of different algorithms are investigated due to three different earthquake signals.
引文
[1]周福霖.工程结构减震控制[M].北京:地震出版社,1997Zhou Fulin.Seismic control of engineering structures[M].Beijing:Seismology Press,1997.(in Chinese)
[2]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.Ou Jinping.Structural vibration control—active,semi-active and smart control[M].Beijing:Scientific Press,2003.(in Chinese)
[3]Suhardjo J,Spencer Jr B F,Sain M K.Feedback-feedforward control of structures under seismic excitation[J].Structural Safety,1990,8:69~89.
[4]Abdel-Rohman,M,Leipholz H H E.Automatic active control of structures[J].J Structural Engineering Div.,ASCE,1980,106:663~677.
[5]Yang J N,Akbarpour A,Ghaemmaghami P.New optimal control algorithms for structural control[J].J.Engineering Mechanics,ASCE,1987,113(9):1369~1386.
[6]Soong T T.Active structural control:theory and practice[M].New York:Wiley,1990.
[7]杜永峰,李慧.地震下结构振动最优控制算法模型的比较和改进[J].世界地震工程,2005,21(3):57~63.Du Yongfeng,Li Hui.Comparison and improvement of models of optimal control algorithms for dynamic response of structures under earthquakes[J].WorldEarthquake Engineering,2005,21(3):57~63.(in Chinese)
[8]杜永峰,李慧,赵国藩.地震作用下结构振动最优控制的一种一般算法[J].大连理工大学学报,2004,44(6):860~865.Du Yongfeng,Li Hui,Zhao Guofan.A generalized algorithm for optimal control of structures subjected to seismic excitation[J].J.Dalian University of Technology,2004,44(6):860~865.(in Chinese)
[9]何玉敖,吴建军.应用自递归神经网络(SRNN)预测结构响应[J].土木工程学报,1998,31(2):46~51.He Yu’ao,Wu Jianjun.Prediction of structural response using SRNN[J].J.Civil Engineering,1998,31(2):46~51.(in Chinese)
[10]Du Yongfeng,Li Hui,Spencer Billie F,Jr.Effect of non-proportional damping on seismic isolation[J].J.Structural Control,2002,9(3):205~236.
[11]杜永峰,李慧,吴永诚.结构地震振动最优控制的目标函数和稳定性[J].兰州理工大学学报,2005,31(3):109~113.Du Yongfeng,Li Hui,Wu Yongcheng.Objective function and stability of optimal control of algorithms for seismic control of structures.[J].J.Lanzhou University of Technology,2005,31(3):109~113.(in Chinese)
[12]杜永峰.被动与智能隔震结构地震响应分析及控制算法[D].大连:大连理工大学,2003.Du Yongfeng.Analysis of seismic response of passive and smart isolated structures and investigation to control algorithms[D].Dalian:Dalian University of Technology,2003.(in Chinese)
[2]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.Ou Jinping.Structural vibration control—active,semi-active and smart control[M].Beijing:Scientific Press,2003.(in Chinese)
[3]Suhardjo J,Spencer Jr B F,Sain M K.Feedback-feedforward control of structures under seismic excitation[J].Structural Safety,1990,8:69~89.
[4]Abdel-Rohman,M,Leipholz H H E.Automatic active control of structures[J].J Structural Engineering Div.,ASCE,1980,106:663~677.
[5]Yang J N,Akbarpour A,Ghaemmaghami P.New optimal control algorithms for structural control[J].J.Engineering Mechanics,ASCE,1987,113(9):1369~1386.
[6]Soong T T.Active structural control:theory and practice[M].New York:Wiley,1990.
[7]杜永峰,李慧.地震下结构振动最优控制算法模型的比较和改进[J].世界地震工程,2005,21(3):57~63.Du Yongfeng,Li Hui.Comparison and improvement of models of optimal control algorithms for dynamic response of structures under earthquakes[J].WorldEarthquake Engineering,2005,21(3):57~63.(in Chinese)
[8]杜永峰,李慧,赵国藩.地震作用下结构振动最优控制的一种一般算法[J].大连理工大学学报,2004,44(6):860~865.Du Yongfeng,Li Hui,Zhao Guofan.A generalized algorithm for optimal control of structures subjected to seismic excitation[J].J.Dalian University of Technology,2004,44(6):860~865.(in Chinese)
[9]何玉敖,吴建军.应用自递归神经网络(SRNN)预测结构响应[J].土木工程学报,1998,31(2):46~51.He Yu’ao,Wu Jianjun.Prediction of structural response using SRNN[J].J.Civil Engineering,1998,31(2):46~51.(in Chinese)
[10]Du Yongfeng,Li Hui,Spencer Billie F,Jr.Effect of non-proportional damping on seismic isolation[J].J.Structural Control,2002,9(3):205~236.
[11]杜永峰,李慧,吴永诚.结构地震振动最优控制的目标函数和稳定性[J].兰州理工大学学报,2005,31(3):109~113.Du Yongfeng,Li Hui,Wu Yongcheng.Objective function and stability of optimal control of algorithms for seismic control of structures.[J].J.Lanzhou University of Technology,2005,31(3):109~113.(in Chinese)
[12]杜永峰.被动与智能隔震结构地震响应分析及控制算法[D].大连:大连理工大学,2003.Du Yongfeng.Analysis of seismic response of passive and smart isolated structures and investigation to control algorithms[D].Dalian:Dalian University of Technology,2003.(in Chinese)
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