基于LMI的结构振动多目标鲁棒H_2/H_∞控制
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摘要
研究了考虑建筑结构动力特性具有不确定性的多目标鲁棒H2/H∞控制问题。在设计控制器的过程中,将模型参数(包括质量、刚度和阻尼)的不确定性引入到状态方程的摄动矩阵之中,使得闭环系统对所有允许的不确定性同时满足H∞干扰抑制和最优H2性能。基于线性矩阵不等式优化技术,推导得到了线性矩阵不等式组来求解相应的多目标优化问题,应用MATLAB的线性矩阵不等式工具箱设计了输出反馈控制器。最后对一3层结构进行了振动控制仿真分析,结果表明了所提方法的有效性和优越性。
This paper deals with the robust H2/H∞ control problem for structure with dynamic characteristic uncertainties.In the process of designing the controller,uncertain parameters(including mass,stiffness and damping) of structures are introduced into perturbation matrix,meanwhile,both the H∞ disturbance suppression and the optimal H2 performances of the closed-loop control system are satisfied simultaneously for all allowable uncertainties.To solve the proposed multi-objective optimization problem,linear matrix inequalities(LMIs) are deduced based on the LMI optimization technology,and LMI toolbox of MATLAB is employed to obtain the output feedback controller.Results of vibration control analysis for a 3-story simplified structure show that the proposed method is efficient and superior.
This paper deals with the robust H2/H∞ control problem for structure with dynamic characteristic uncertainties.In the process of designing the controller,uncertain parameters(including mass,stiffness and damping) of structures are introduced into perturbation matrix,meanwhile,both the H∞ disturbance suppression and the optimal H2 performances of the closed-loop control system are satisfied simultaneously for all allowable uncertainties.To solve the proposed multi-objective optimization problem,linear matrix inequalities(LMIs) are deduced based on the LMI optimization technology,and LMI toolbox of MATLAB is employed to obtain the output feedback controller.Results of vibration control analysis for a 3-story simplified structure show that the proposed method is efficient and superior.
引文
[1]韩兵康,张静怡.土木工程结构鲁棒控制的发展[J].地震工程与工程振动,2004,24(6):131—135.
[2]李文章,吴凌尧,郭雷.基于LMI的结构振动鲁棒H∞控制[J].振动工程学报,2008,21(2):157—161.
[3]吴凌尧,李文章,郭雷,等.一类非线性不确定结构系统的鲁棒饱和主动控制[J].振动工程学报,2008,21(6):542—546.
[4]周星德,竺启泽,徐艳红.基于LMI的基准建筑物鲁棒控制研究[J].振动工程学报,2008,21(1):7—12.
[5]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.
[6]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.
[7]孙万泉,李庆斌.基于LMI的高层建筑结构分散H2/H∞鲁棒控制[J].地震工程与工程振动,2007,27(6):218—222.
[8]孙宜标,金石,王成元.基于线性矩阵不等式的环形永磁力矩电机H2/H∞静态输出反馈控制[J].中国电机工程学报,2007,27(15):8—14.
[9]Farsangi M M,Song Y H,Tan M.Multi-objective de-sign of damping controllers of FACTS devices viamixed H2/H∞with regional pole placement[J].Elec-trical Power and Energy Systems,2003,25:339—346.
[10]王曦,陈华荣.不确定性系统鲁棒H∞/H2混合控制在航空发动机中的应用[J].航空动力学报,2002,17(2):250—254.
[11]宋刚,林家浩,吴志刚.考虑参数不确定性的主动悬架鲁棒H2/H∞混合控制[J].动力学与控制学报,2008,6(2):156—164.
[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]Kothare M,Balakrishnan V,Morsri M.Robust con-strained model predictive control using linear matrixinequalities[J].Automatica,1996,32(10):1 361—1 379.
[14]Xie L H.Output feedback H∞control of systems withparameters uncertainty[J].International Journal ofControl,1996,63(4):741—750.
[2]李文章,吴凌尧,郭雷.基于LMI的结构振动鲁棒H∞控制[J].振动工程学报,2008,21(2):157—161.
[3]吴凌尧,李文章,郭雷,等.一类非线性不确定结构系统的鲁棒饱和主动控制[J].振动工程学报,2008,21(6):542—546.
[4]周星德,竺启泽,徐艳红.基于LMI的基准建筑物鲁棒控制研究[J].振动工程学报,2008,21(1):7—12.
[5]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.
[6]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.
[7]孙万泉,李庆斌.基于LMI的高层建筑结构分散H2/H∞鲁棒控制[J].地震工程与工程振动,2007,27(6):218—222.
[8]孙宜标,金石,王成元.基于线性矩阵不等式的环形永磁力矩电机H2/H∞静态输出反馈控制[J].中国电机工程学报,2007,27(15):8—14.
[9]Farsangi M M,Song Y H,Tan M.Multi-objective de-sign of damping controllers of FACTS devices viamixed H2/H∞with regional pole placement[J].Elec-trical Power and Energy Systems,2003,25:339—346.
[10]王曦,陈华荣.不确定性系统鲁棒H∞/H2混合控制在航空发动机中的应用[J].航空动力学报,2002,17(2):250—254.
[11]宋刚,林家浩,吴志刚.考虑参数不确定性的主动悬架鲁棒H2/H∞混合控制[J].动力学与控制学报,2008,6(2):156—164.
[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]Kothare M,Balakrishnan V,Morsri M.Robust con-strained model predictive control using linear matrixinequalities[J].Automatica,1996,32(10):1 361—1 379.
[14]Xie L H.Output feedback H∞control of systems withparameters uncertainty[J].International Journal ofControl,1996,63(4):741—750.
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