地震作用下建筑结构基于平衡降阶的时滞离散H_∞控制

BALANCED-REDUCTION-BASED H_∞ CONTROL FOR VIBRATION ATTENUATION OF SEISMIC-EXCITED BUILDINGS WITH CONTROLLER DELAYS

在状态空间下直接对结构振动的时滞微分方程进行离散,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,然后将该离散系统平衡降阶,大大降低了离散系统的维数。在此基础上采用离散的H∞全信息反馈控制理论完成了建筑结构减振控制器的设计,得到的控制器含有对当前和滞后控制量的线性组合,反映了时滞因素的影响,对大时滞情况亦有效。最后通过算例仿真与分析验证了该控制器的有效性,它在不牺牲控制效果的前提下,大大降低了控制器的维数。

The application of full-information H∞ control theory to vibration attenuation of buildings with control time-delays under seismic excitation was presented. By introducing the extended vectors in state space, the motion equation of original system with time-delays was transformed into the standard discrete form that contains no delays. Then by using balanced-reduction method for this discrete system, the dimension can be significantly reduced. Thusly, a robust controller was designed based on H∞ disturbance attenuation theory, concerning the uncertainty of seismic excitation. The vibration-reduction controller contains linear combination 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. Moreover, the dimension of the controller can be reduced without discounting the control efficiency.