具有极点约束的不确定压电柔性结构鲁棒H_∞振动控制  

Robust H_∞ Vibration Control for Uncertain Piezoelectric Flexible Structures with Poles Assignment

作　　者：徐亚兰[1] 陈建军[1] 王小兵[1] 谢永强[1] 

机构地区：[1]西安电子科技大学机电工程学院,陕西西安710071

出　　处：《应用基础与工程科学学报》2007年第3期332-341,共10页Journal of Basic Science and Engineering

基　　金：陕西省自然科学基金(D7010418);国防预研基金(51421060505DZ0155);西安电子科技大学青年科研工作站项目资助

摘　　要：以具有范数有界不确定的压电柔性结构为对象,考虑其被控模态参数的不确定性以及剔除残余模态所引起的模型误差,建立了模态空间内结构的不确定线性分式模型;根据所建立的不确定模型,设计了一个对结构进行振动控制的非同位动态输出反馈H∞控制器,并将不确定闭环系统的极点配置在所预设的区域;利用线性矩阵不等式方法,将具有极点约束的不确定压电柔性结构鲁棒H∞振动控制问题转化为一个具有线性矩阵不等式约束和线性目标函数的凸优化问题.仿真结果表明,所建立的模态不确定模型是合理可行的,系统在控制结构低频模态的同时,能很好地抑制在非同位控制中因模型降阶而带来的高阶模态溢出;与单纯的鲁棒H∞控制方法相比较,采用带极点约束的鲁棒H∞控制方法对不确定柔性结构进行振动控制,可保留很好的稳态响应,同时也获得了更理想的动态响应特性.The aim of this study is to investigate the influence of poles assignment on vibration responses of uncertain piezoelectric flexible structures using H∞ control method. Based on the modal state space, the linear fractional representation is developed for the flexible structure with piezoelectric materials as non-collocated actuators and sensors, taking into account norm-bound uncertainties due to modal parameters variation and un-modeled residual modes. In order to obtain the satisfactory dynamic response characteristics, a dynamic output feedback H∞ controller is designed to suppress the vibration due to external disturbances with uncertain closed-loop poles in the desired region using linear matrix inequality method, by which the controller design problem is converted into a linear convex optimization problem. Finally, a comparison between the impulse and frequency responses of closed-loop system for robust H∞ method only and those for robust H∞ method with poles assignment are given by an example. The results show that uncertain H∞ vibration control with poles assignment can suppress the low-frequency modes without exciting the high- and the faster dynamic response is achieved by statesteady characteristics as well. frequency modes in the non-collocated control, the given approach without obviously scarifying

关 键 词：压电柔性结构 不确定模型 线性矩阵不等式 极点配置 

分 类 号：TH113[机械工程—机械设计及理论] TP13[自动化与计算机技术—控制理论与控制工程]