Optimal Control of Seismic Response of Structures

提出了一种新的闭开环最优控制律，该律通过最小化二次型时变性能指标和结构系统的动态能量输入的总和而得到。考虑了三种输入能量：地震能、控制力能和两者之和。该控制律不依赖于结构体系的刚度，对在线控制操作简单可靠。详细研究了性能指标中包含的两个加权矩阵对控制效率的影响。利用神经网络的概念，我们开发了一种算法，将所开发的控制律应用到结构系统中，以控制结构的地震反应。该算法由两部分组成。一种是利用反向传播学习过程识别质量、阻尼和刚度矩阵等结构参数的识别模式。另一种是控制模式，其中由响应和控制力矢量组成的时变性能指标以及结构系统的地震能量输入都是最小的。为了实现一种实用的高层建筑主动质量阻尼器（AMD）型控制装置，我们还将该算法应用于一个采用AMD系统的八层建筑模型，验证了该算法控制结构地震反应的可行性。数值算例验证了所提算法的控制效率。

We developed a new closed-open-loop optimal control law that has been derived by minimizing the sum of the quadratic time-dependent performance index and the dynamic energy input to the structural system. Three types of input energy are considered that are the seismic energy, control force energy and the sum of both energy. This control law is simple and reliable for on-line control operations because control force does not depend on the rigidity of structural system. The control efficiency affected by two weighting matrices included in the performance index is investigated in detail. Using the concept of neural network we have developed an algorithm to implement the developed control law into structural system for controlling seismic response of structures. The algorithm consists of two parts. One is an identification mode in which the back propagation learning process is applied to identify the structural parameters such as mass, damping and stiffness matrices. The other is a controller mode in which the time-dependent performance index consisting of response and control force vectors as well as the seismic energy input to the structure system is minimized. To realize a practical control device of active mass damper (AMD) type for high-rise buildings we also implemented this new algorithm into an eight story building model with AMD system and checked feasibility to control seismic response of the structure. Numerical examples are worked out to demonstrate the control efficiency of the proposed algorithms.