不确定性AMD系统的鲁棒控制器设计研究
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摘要
任何控制系统的数学模型只是真实动力学系统的一种近似,在系统模型中总是存在一些不确定性,系统模型的不确定性会影响结构的减振效果。以主动质量阻尼器控制系统为例,考虑系统的质量、刚度和阻尼存在不确定性时,提出H无穷鲁棒控制器的设计方法。为便于控制器的设计,采用基于线性不等式的求解算法。利用一个安装主动质量阻尼器的两层结构模型的振动台实验来验证所提出的H无穷鲁棒控制器的有效性。在结构的底层安装一对形状记忆合金丝,通过电流加热形状记忆合金丝来调整结构的刚度,以引入结构的刚度不确定性。在结构的各层放置质量块,以引入质量的不确定性。试验结果验证了所提出的H无穷鲁棒控制器能有效处理结构参数中的不确定性。
A mathematical model of any real system is always just an approximation of the true,physical reality of the system dynamics.There are always uncertainties in the system modeling.This paper outlines a general approach to the design of an H-infinity control of an Active Mass Damper(AMD) for the vibration reduction of a building with mass and stiffness uncertainties.Linear fractional transformation(LFT) is utilized in this paper for uncertainty modeling.To facilitate the computation of the H-infinity controller,an efficient solution procedure based on Linear Matrix Inequalities(LMIs) is employed.The controller uses the acceleration signal for feedback.A two-story building test-bed with an AMD is used to test the designed H-infinity controller.Earthquake ground motion is introduced by a shaking table.A pair of diagonal shape memory alloy(SMA) wire braces is installed in the first floor to introduce stiffness uncertainty to the structure by controlling the temperature of the SMA wire brace.Masses are added to the structure to introduce mass uncertainty.Experiments were conducted and the results validate the effectiveness of the proposed H-infinity controller in dealing with stiffness and mass uncertainties.
A mathematical model of any real system is always just an approximation of the true,physical reality of the system dynamics.There are always uncertainties in the system modeling.This paper outlines a general approach to the design of an H-infinity control of an Active Mass Damper(AMD) for the vibration reduction of a building with mass and stiffness uncertainties.Linear fractional transformation(LFT) is utilized in this paper for uncertainty modeling.To facilitate the computation of the H-infinity controller,an efficient solution procedure based on Linear Matrix Inequalities(LMIs) is employed.The controller uses the acceleration signal for feedback.A two-story building test-bed with an AMD is used to test the designed H-infinity controller.Earthquake ground motion is introduced by a shaking table.A pair of diagonal shape memory alloy(SMA) wire braces is installed in the first floor to introduce stiffness uncertainty to the structure by controlling the temperature of the SMA wire brace.Masses are added to the structure to introduce mass uncertainty.Experiments were conducted and the results validate the effectiveness of the proposed H-infinity controller in dealing with stiffness and mass uncertainties.
引文
[1]李宏男,霍林生.结构多维减震控制[M].北京:科学出版社,2008.
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[6]Gahinet P,Apkarian P.A Linear Matrix Inequality Approach to H∞Control[J].International Journal of Robust and Nonlin-ear Control,2007,4(4):421-448.
[2]Kobori T,Koshiak N,Yamada K,et al.Seismic Response Controlled Structure with Active Mass Driver System-part 1[J].Earthquake Engineering and Structural Dynamics,1991,20(2):133-149.
[3]Doyle J C,Glover K,Khargonekar P P,et al.State-space Solutions to Standard H2and H∞Control Problems[J].IEEETransactions on Automatic Control,1989,34(8):831-847.
[4]Skelton R E,Iwasaki T,Grigoriadis K M.A Unified Algebraic Approach to Linear Control Design[M].London:Taylor&Francis,1998.
[5]Iwasaki T,Skelton RE.All Controllers for the General H∞Control Problem:LMI Existence Conditions and State Space For-mulas[J].Automatica,1994,30(8):1307-1317.
[6]Gahinet P,Apkarian P.A Linear Matrix Inequality Approach to H∞Control[J].International Journal of Robust and Nonlin-ear Control,2007,4(4):421-448.
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