矩阵二阶系统的H_∞观测器设计——一种参数化方法(英文)  

H_∞ observer design for matrix second-order linear systems: a parametric approach

作　　者：武云丽[1] 段广仁[1] 薛雨[1] 

机构地区：[1]哈尔滨工业大学控制理论与制导技术中心,黑龙江哈尔滨150001

出　　处：《电机与控制学报》2005年第3期291-297,共7页Electric Machines and Control

基　　金：supported by the Chinese National Natural Science Foundation under Grant(69925308)

摘　　要：利用一种完全参数化的设计方法,直接在矩阵二阶系统的框架下研究不确定性矩阵二阶系统的H∞观测器设计问题,目标是使观测过程在保持鲁棒稳定并达到期望的动态特性的同时,还能使得外部干扰到误差状态的传递函数的H∞范数小于事先给定的上界数值。基于矩阵二阶系统的Sylvester方程的完全参数化解,通过一组设计参数建立了观测器的所有增益矩阵以及观测器系统矩阵的左特征向量的完全参数化形式。并在此基础上,将H∞范数的上界约束条件转化成一个等价的约束设计参数的条件。该方法能够提供所有的设计自由度,有很强的应用价值。最后通过一个弹簧质量系统表明此方法的有效性。The problem of H∞ observer design for uncertain matrix second-order linear systems is considered in the matrix second-order framework by using a complete parametric design approach. The goal is to design a matrix second-order linear state observer so that the observer process remains robustly stable and achieves the desired dynamical performance, and the transfer function from exogenous disturbances to error state output meets the prescribed H∞norm upper bound constraint. Based on the complete parametric solution to the Sylvester matrix equation of matrix second-order linear systems, complete parameterizations for all the observer gain matrices as well as the left eigenvectors of the observer system matrix are established in terms of a set of design parameters. Also, based on these parametric gain matrices and left eigenvectors, the prescribed H∞ norm upper bound constraint is transformed into an equivalent constraint condition which restricts the design parameters. The proposed approach provides all the degrees of freedom and has great potential in applications. A spring-mass system is utilized to show the effect of the proposed approache.

关 键 词：H∞观测器 二阶系统 参数化方法 SYLVESTER方程 不确定性矩阵 全参数化 H∞范数 设计参数 设计方法 设计问题 动态特性 鲁棒稳定 观测过程 传递函数 误差状态 外部干扰 特征向量 系统矩阵 增益矩阵 约束条件 应用价值 弹簧质量 

分 类 号：TP273.4[自动化与计算机技术—检测技术与自动化装置] TP13[自动化与计算机技术—控制科学与工程]