含时滞振动主动控制系统地震响应的数值分析
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摘要
采用精细积分方法计算了时滞受控系统在地震作用下的动力响应,得到在不同反馈增益下随时滞量变化的系统地震响应峰值分布。分析了在小时滞范围内随时滞量变化和反馈增益在不同的取值下对系统响应的影响,结果表明时滞对系统控制效果的影响程度随反馈增益的增大而增大,当时滞较大时,采用较小的控制增益控制效果较好,当时滞较小时,采用较大的控制增益可以获得更好的控制效果。该结果可用于设计考虑时滞影响的结构振动主动控制算法。
A kind of dynamic equation of control system with double time delays was solved by a modified precise integration method.The accuracy of the method was proved by numerical examples in which time histories of system response and the distribution of response peaks of the system with variational time delays were calculated when feedback control gains take different values.The influences of different values of time delays and feedback control gains on the distribution of stable areas of the system were investigated.The influences of different feedback gains and variational time delays on system response were analysed,which shows that the influence of time delays gets more distinct as feedback gains increase.The result is of certain guiding significance for designing active structural vibration control algorithm considering the influence of time delay.
A kind of dynamic equation of control system with double time delays was solved by a modified precise integration method.The accuracy of the method was proved by numerical examples in which time histories of system response and the distribution of response peaks of the system with variational time delays were calculated when feedback control gains take different values.The influences of different values of time delays and feedback control gains on the distribution of stable areas of the system were investigated.The influences of different feedback gains and variational time delays on system response were analysed,which shows that the influence of time delays gets more distinct as feedback gains increase.The result is of certain guiding significance for designing active structural vibration control algorithm considering the influence of time delay.
引文
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[2]胡海岩,王在华.非线性时滞动力系统的研究进展[J].力学进展,1999,29(4):501-512.HU Hai-yan,WANG Zai-hua.Review on nonlinear dynamic systems involving time delays[J].Advances in Mechanics,1999,29(4):501-512.
[3]胡海岩.振动主动控制中的时滞动力学问题[J].振动工程学报,1997,10(3):273-279.HU Hai-yan.On dynamics in vibration control with time delay[J].Journal of Vibration Engineering,1997,10(3):273-279.
[4]Pyragas K.Continuous control of chaos by self-controlling feedback[J].Physics Letters A,1992,170(6):421-428.
[5]Ali M S,Hou Z K,Noori M N.Stability and performance of feedback control systems with time delays[J].Computers&Structures,1998,66(2-3):241-248.
[6]孙清,刘正伟,伍晓红,等.含双时滞振动主动控制系统的稳定性分析[J].西安交通大学学报,2010,44(1):112-116.SUN Qing,LIIU Zheng-wei,WU Xiao-hong,et al.Stability analysis of the vibration active control system involving double time delay[J].Xi'an Jiaotong University,2010,44(1):112-116.
[7]陈龙祥,蔡国平.旋转运动柔性梁的时滞主动控制实验研究[J].力学学报,2008,40(4):520-527.CHEN Long-xiang,CAI Guo-ping.Experimental study on active control of a rotating flexible beam with time delay[J].Chinese Journal of Theoretical and Applied Mechanics,2008,40(4):520-527.
[8]周星德,陈政道,杜成斌.框架结构主动控制最优时滞研究[J].计算力学学报,2007,24(2):246-249.ZHOU Xing-de,CHEN Zheng-dao,DU Cheng-bin.Research on optimal time-delay of active vibration control of frame structures[J].Chinese Journal of Computational Mechanics,2007,24(2):246-249.
[9]钟万勰.结构动力方程的精细时程积分法[J].大连理工大学学报,1994,34(2):131-135.ZHONG Wan-xie.On precise time-integration method for structural dynamics[J].Journal of Dalian University of Technology,1994,34(2):131-135.
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