考虑频域不确定性的结构H_∞鲁棒控制
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摘要
针对高阶结构系统不便直接进行控制器设计的问题,建立基于结构降阶模型和频域不确定性的H∞鲁棒控制设计方法,给出系统满足鲁棒稳定性和鲁棒性能所需的条件,并利用频域不确定性影响灵敏度和干扰抑制灵敏度的混合灵敏度方法设计出H∞控制器。为说明该方法的有效性,对三自由度结构振动系统进行H∞控制数值模拟,并与常用的LQR最优控制方法进行比较,结果表明由于考虑了降阶模型的频域不确定性,对高频截断模态没发生控制溢出现象,因而具有对模型误差的鲁棒性,而LQR方法有较为明显的控制溢出现象。
This paper presents a H∞ robust control method for the reduced order structural system with frequency domain uncertainties.Necessary and sufficient conditions are presented,which guarantee stability and disturbance attenuation for all admissible uncertainties.A mixed sensitivity method based on sensitivity of frequency domain uncertainties and sensitivity of disturbance attenuation is employed to design H∞ controller.Finally,numerical examples illustrate the above advantages.A 3DOF structural system is adopted to verify the proposed method being effective.Numerical simulation results show that the method is better than conventional LQR at controlling the high order modal spillover.
This paper presents a H∞ robust control method for the reduced order structural system with frequency domain uncertainties.Necessary and sufficient conditions are presented,which guarantee stability and disturbance attenuation for all admissible uncertainties.A mixed sensitivity method based on sensitivity of frequency domain uncertainties and sensitivity of disturbance attenuation is employed to design H∞ controller.Finally,numerical examples illustrate the above advantages.A 3DOF structural system is adopted to verify the proposed method being effective.Numerical simulation results show that the method is better than conventional LQR at controlling the high order modal spillover.
引文
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[2]Schmitendorf W E,Jabbari F and Yang J N.Roust Con-trol Techniques for Buildings Under Earthquake Excitation[J].Earthquake Engineering and Structural Dynamics,1994,23:539-552.
[3]Schmitendorf W E,Kose I E,Jabbari F and Yang J N.H∞Control of Seismic-excited Buildings Using DirectOutput Feedback[C].Proc.1stWorld Conf.on Struct.Control,1994,TA1,11-20.
[4]Schmitandorf W E,Monti S,Jabbari F and Yang J N.Active Control of Seismic-excited Buildings with ModelUncertainty[C].Proc.Fifth U.S.Nat.Conf.on Earth-quake Engrg.,1994,951-959.
[5]Kose I E,Schmitendorf W E,Jabbari F and Yang J N.H∞Active Seismic Response Control Using Static OutputFeedback[J].Journal of Eng.Mech.ASCE.1996.122(7):651-659.
[6]Chase J G and Smith HA.RobustH∞Control Consider-ing Actuator Saturation Part 1:Theory[J].J.Eng.Mech.ASCE,1996,122(10):976-983.
[7]Wang S G,Roschke P N,Yeh H Y.Robust Control forStructural System with Unstructured Uncertainties[J].Journal of Engineering Mechanics,2004,130(3):337-346.
[8]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 W J,OuJ P.Robust Control Approach of Structural VibrationBased on State Feedback[J].World Earthquake Engi-neering,2002,18(3):37-41(in Chinese)).
[9]张微敬,闫维明,钱稼茹.基于二次稳定算法的结构主动控制仿真分析[J].系统仿真学报.2006,18(3):685-697.(Zhang W J,Yan W M,Qian J R.SimulationStudy of Active Control Based on Quadratic StabilizationAlgorithm[J].Journal of System Simulation,2006,18(3):685-697(in Chinese)).
[10]梅生伟,申铁龙,刘康志.现代鲁棒控制理论及应用[M].北京:清华大学出版社,2003.(Mei S W,Shen TL,Liu K Z.Modern Robust Control Theory and Applica-tion.Beijing:Tsinghua University Press,2003(in Chi-nese)).
[11]韩京清,何关玉,许可康.线性系统理论代数基础[M].沈阳:辽宁科技出版社,1987(Han J Q,He G Y,Xu K K.Algebra Principia of Linear System Theory.Shenyang:Liaoning Press of Science and Technology,1987(in Chinese)).
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