建筑结构振动的一种常分数阶控制策略

A constant fractional-order control strategy for building structure vibration

为了在实际控制中取得更优的效果,结构阻尼采用分数阶表示,以建筑结构为研究对象,设系统的阻尼为位移向量的α阶导数,提出一种变异阶次控制器的设计方法。具体过程为:首先,假设原运动方程中的阻尼项为系统位移向量的β阶导数,并对该运动方程进行控制器设计;其次,考虑控制对象为含α阶导数的运动方程,为达到控制目的,采取基于输出相同的处理方式;再次,根据第3代基准建筑物定义的性能指标,通过搜索的方式确定最优参数β,分数阶阶次在0和2之间均有阻尼效果,搜索范围为[0,2]。仿真结果表明,存在不同于α的β值可获得更优的控制效果,同时,针对不同的性能指标,最优β的选取亦不同。最后,通过一个仿真实例说明该控制方法的可行性。

In order to achieve a better control effect, the fractional-order was used to describe the damping force, which was supposed to be anα-order derivative of the displacement vector, and a variational-order controller design method was developed. The detailed process is as follows：First, it is assumed that the damping force in the original equation of motion is aβ-order derivative of the displacement vector and the controller is designed according to this assumption. Second, considering the equation of motion that includes anα-order derivative as the control object, a control strategy based on systemic output is applied to ensure that the designed controller can be used for the original model. Third, the optimal parameter β is determined with the search method according to the third generation of the benchmark building control performance index. In this study, there was a damping effect when the fractional-order ranged from 0 to 2 , and the search scope was between 0 to 2 . The simulation results show that optimal parameters can be found to obtain a better control effect when β is different from α. Meanwhile, the selection of the optimal β varied with different performance indices. Finally, a simulation example verified the feasibility of the proposed control strategy.