振动系统的特征结构配置设计

DESIGN OF EIGEN-STRUCTURE DISPOSITION FOR VIBRATION SYSTEMS

考虑了振动系统特征结构配置设计问题,其目的是设计比例加微分反馈控制律使得闭环振动系统具有期望的特征值和特征向量。基于一类矩阵方程的参数化解,给出了该比例加微分反馈特征结构配置设计参数化方法。该参数化方法提供的自由参量为振动控制系统设计提供了全部自由度,可适当选取这些参量来满足某些性能指标,如鲁棒性等。此外,该特征结构配置参数化方法直接基于振动系统参数矩阵,无须对振动系统进行变换并将其转化一阶线性系统。最后,通过数值例子验证了所提振动系统比例加微分反馈特征结构配置参数化方法的有效性。

Design of eigen-structure disposition of vibration systems is investigated in this paper.Its aim is to find a proportional plus differential feedback law so that a closed-loop vibration system has the desired eigenvalues and eigenvectors.Based on parametric solutions for a type of matrix equations,a parametric method for this eigen-structure disposition problem is propose.This parametric method offers all the design degrees of freedom,which can be further selectod to satisfy certain design performances,such as robustness.In addition,this method utilizes system matrices of vibration systems,and does not involv in transforming a vibration system to its first-order linear system.Finally,a numerical example shows the effectiveness and simpleness of the proposed parametric method.