在状态空间下直接对结构振动的时滞微分方程离散,并引入适当的增广向量将之转化为不显含时滞项的标准离散形式。在此基础上采用离散的H∞反馈控制理论完成了建筑结构减振控制器的设计,对于地震激励的不确定性有很好的鲁棒性。得到的控制器含有对滞后控制量的线性组合,反映了时滞因素的影响,对大时滞情况也有效。最后通过算例仿真与分析验证了这种控制器的有效性。
This paper presents the application of full-information H∞control theory to the field of vibration attenuation of buildings with control time-delays under seismic excitation. By introducing the extended vectors in state space, the motion equation of original system with time-delays is transformed into standard discrete form that contains no delays. Then a robust controller is designed based on H∞disturbance attenuation theory, considering of the uncertainty of seismic excitation. The deduced controller contains linear combinations of some former steps of control, which reflects the character of controlled systems with time-delays. It is also suitable for the case of large time-delays. Simulation results for a three-story building demonstrate the effectiveness of the control method presented. Furthermore the parameter effects on the performance of the controller are also discussed.