地震作用下主动减震结构的时滞离散最优控制

对地震作用下线性时滞结构的离散最优控制方法进行研究,按时滞量为采样周期的整数倍和非整数倍两种情况,将时滞连续控制系统离散为形式上不包含时滞的标准离散形式,采用连续时间形式的性能指标函数,按照离散最优控制方法进行控制设计。所得出的控制律表达式中,除了含有当前的状态反馈外,还包含有前若干步控制项的组合。最后结合一个三自由度建筑结构模型进行仿真计算,结果表明,算法中采用连续时间形式的性能指标函数优于离散形式的性能指标函数,此方法易于保证控制系统的性能和稳定性,而且可以看到,控制系统的时滞量并非越短越好。

DISCRETE-TIME OPTIMAL CONTROL METHOD FOR SEISMIC-EXCITED BUILDING STRUCTURES WITH TIME DELAY

The paper is concerned with discrete-time optimal control method for linear systems with time-delay. Using zero-order holder, the continuous-time differential equation with time delay can be transformed into standard discrete-time form without time delay. The controller is designed considering two cases that the time delay is integer and non-integer times of the sampling period, respectively. Since the optimal controller is obtained directly from the differential equation with time-delay, the proposed control method is able to guarantee stability of the controlled structures. Simulation results demonstrate that the continuous time performance index is superior to that of discrete-time and the present control method ensures the stability of the controlled structures as well as the desired reduction in the maximum responses.