建筑结构基于平衡降阶的时滞离散最优控制

DISCRETE TIME-DELAY OPTIMAL CONTROL OF STRUCTURES USING THE BALANCED REDUCTION SCHEME

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,然后将该离散系统进行平衡降阶,取前几个可控度大的状态组成优势子系统,大大降低了离散系统的维数。在此基础上采用离散时间最优控制理论完成了建筑结构减振控制器的设计,所得出的控制律表达式除了含有当前的状态反馈,还包含前若干步控制项的组合,反映了时滞因素的影响,对大时滞情况亦有效。最后通过数值算例验证了这种控制器的有效性,特别是在不牺牲控制效果的基础上,显著降低了控制器的阶数。

The time-delay discrete equations are derived directly form the differential vibration equations of structures in state space which are transformed to a standard form containing no explicit time-delay terms by introducing an expanded state vector. The balanced reduction method is then applied to the discrete system and a dominant subsystem is formed based on the eigenmodes of the state subspace with higher controllability, and so the order of the discrete system is reduced considerably. The controller is designed with the discrete time-delay optimal control theory, which contains the control terms of the current state and a few previous states which reflect the influence of time-delay. The proposed means considerably reduce the order of the controller without causing essential difference in the control effect. A numerical example shows the effectiveness of the proposed method, which is so even if time-delays are rather large.