建筑结构的准滑模控制研究

Keeping Chattering Effect Sufficiently Low with New Quasi-Sliding Mode Control for Building Structure

结合饱和函数和继电特性连续函数的优点,提出了含饱和函数的指数趋近律形成的控制律和含继电特性连续函数的指数趋近律形成的控制律。基于这两种控制律,采用准滑模控制方法对地震作用下建筑结构的振动控制问题进行了研究。以一个多层剪切型建筑结构模型为例验证所提控制方法的有效性,算例数值分析结果表明,所提出的准滑模控制方法,控制效果明显,能有效地减小结构的地震峰值响应,且在控制参数ε值较大的情况下,控制系统的抖振很小。

Abstract： Existing sliding-mode control methods for reducing seismological response of building structure, such as those of Cai et al and Zhao et al , suffer, in our opinion, the shortcoming that it is almost very difficult to avoid excessive chattering effect. Therefore we propose new quasi-sliding mode control laws that can not only reduce seismological response but can also avoid undue chattering effect. In the full paper, we explain in detail the application of the quasi-sliding mode control methods to the control of seismologically excited structural systems. In this abstract, we just add some pertinent remarks to listing the following three topics of explanation： （1） the motion equation, （2） the determination of switching surfaces, （3） the design of control laws; under topic 3, we derive eq. （6） for the quasi-sliding mode control law involving saturation function and derive eq. （8） for that involving relay function. Finally we give numerical simulations for MDOF （Multiple-Degree-of-Freedom） shear building model containing an active brace system. The results of seismological response are shown in Figs. 2, 3 and Tab. 1 for control law eq. （6） and control law eq. （8）; they show that, like Refs. 5 and 6, seismological responses can be markedly reduced. The results for chattering effect are given in Fig. 4; Fig. 4（a） is for Refs. 5 and 6, Fig. 4（b） is for control law eq. （6）, and Fig. 4（c） is for control law eq. （8） ; Fig. 4 shows preliminarily that our quasi-sliding mode control laws can keep the chattering effect sufficiently low but, in this ease, Refs. 5 and 6 cannot do so.