主动隔振系统的最优控制时滞
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摘要
针对主动隔振系统带有时滞的鲁棒渐进稳定问题,研究了时滞的存在对最优控制算法控制效果的影响,运用MATLAB中LMI工具,采用变步长试凑的方法,解出了最优控制系统反馈控制鲁棒渐进稳定的最大允许时滞上界。最后,通过数值仿真,验证了理论的正确性。仿真结果表明:随着控制时滞的增大,主动隔振效果逐渐变差,一旦反馈控制力时滞超过最大允许时滞上界,系统便将发散。同时,增大反馈控制力和减小加权矩阵控制目标的相应权值,可以提高最大允许时滞上界。
The asymptotic stability of robust with time lag generally exists in the active vibration isolation system.The influence of time lag on the optimal control algorithm was studied.By use of LMI tools in MATLAB,a variable step method was introduced to get the maximum allowable upper bound of the robust time lag in the optimal control system.The numerical simulation verified the theory.The results show that with time lag increasing,the effect of controlling will become worse;once the time lag exceeds the maximum allowable delay boundary,the system will diverge.At the same time,the upper bound can be improved by increasing feedback control and decreasing the corresponding weight of the target-controlling weighting matrix.The work done is beneficial for relevant experimental designs.
The asymptotic stability of robust with time lag generally exists in the active vibration isolation system.The influence of time lag on the optimal control algorithm was studied.By use of LMI tools in MATLAB,a variable step method was introduced to get the maximum allowable upper bound of the robust time lag in the optimal control system.The numerical simulation verified the theory.The results show that with time lag increasing,the effect of controlling will become worse;once the time lag exceeds the maximum allowable delay boundary,the system will diverge.At the same time,the upper bound can be improved by increasing feedback control and decreasing the corresponding weight of the target-controlling weighting matrix.The work done is beneficial for relevant experimental designs.
引文
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[3]孙清,张智谦,周进雄,等.时滞对结构振动半主动控制效果的影响[J].应用力学学报,2002,19(3):77-80.SUN Qing,ZHANG Zhi-qian,ZHOU Jin-xiong,et al.Effects of time delay on semi-active control of structural vi-bration[J].Chinese Journal of Applied Mechanics,2002,19(3):77-80.(in Chinese)
[4]徐建功,王肇民,何玉敖.基于预测控制的结构振动半主动控制研究[J].世界地震工程,2003,19(2):126-131.XU Jian-gong,WANG Zhao-min,HE Yu-ao.Study of semi-active control of structure based on predictive control[J].World Information on Earthquake Engineering,2003,19(2):126-131.(in Chinese)
[5]潘继,蔡国平.柔性悬臂梁时滞主动控制的实验验证[J].宇航学报,2008,29(2):596-600.PAN Ji,CAI Guo-ping.Experiment study of a flexible cantilever beam with time delay in control[J].Journal ofAstronautics,2008,29(2):596-600.(in Chinese)
[6]毛为民,曹跃云,朱石坚.船舶动力机械混合隔振系统的优化设计[J].海军工程大学学报,2004,16(6):78-82.MAO Wei-min,CAO Yue-yun,ZHU Shi-jian.Optimal design of hybrid vibration isolation system of marine powermachinery[J].Journal of Naval University of Engineering,2004,16(6):78-82.(in Chinese)
[7]楼京俊,朱石坚,谢向荣,等.基于LabVIEW的振动主动控制试验研究[J].武汉理工大学学报:交通科学与工程版,2009,33(4):643-646.LOU Jing-jun,ZHU Shi-jian,XIE Xiang-rong,et al.Experimental study of active vibration control based on Lab-VIEW system[J].Journal of Wuhan University of Technology:Transportation Science&Engineering,2009,33(4):643-646.(in Chinese)
[8]黄操军,刘坤,许秀英,等.不确定时滞系统的时滞依赖稳定性条件研究[J].黑龙江八一农垦大学学报,2009,21(5):56-60.HUANG Cao-jun,LIU Kun,XU Xiu-ying,et al.Research on delay-dependent stability criteria for time-delaysystems with uncertainties[J].Journal of Heilongjiang Bayi Agricultural University,2009,21(5):56-60.(inChinese)
[9]GU K.An integer inequality in the stability problem of time-delay systems[J].Proc.39th IEEE Conf.:Decisionand Control,2000,12(5).2805-2810.
[10]SKELTON R E,IWASAKI T,GRIGORIADIS K.A unified algebraic approach to linear control design[J].Trans.Taylor and Francis,1998,13(2):156-168.
[11]SAADNI M S,MEHDI D.Stability and stabilizability of a class of state retarded uncertain polytopic systems[J].IEEE International Conference on Systems,Man and Cybernetics,2004,10(3):4244-4248.
[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.
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