二阶系统的复特征根对其鲁棒H_∞控制性能的影响  

Impact of Complex Eigenvalues on Their Robust H_∞ Control Performance in Second-Order Systems

作　　者：王占山[1] 王继东[1,2] 刘秀翀 孙鉴[1] WANG Zhan-shan;WANG Ji-dong;LIU Xiu-chong;SUN Jian(School of Information Science & Engineering,Northeastern University,Shenyang 110819,China;School ofElectrical Engineering,North China University of Water Resources and Electric Power,Zhengzhou 450045,China.)

机构地区：[1]东北大学信息科学与工程学院,辽宁沈阳110819 [2]华北水利水电大学电力学院,河南郑州450045

出　　处：《东北大学学报（自然科学版）》2019年第9期1217-1221,1227,共6页Journal of Northeastern University(Natural Science)

基　　金：国家自然科学基金资助项目(61473070,61433004,61627809)

摘　　要：针对具有复特征根的二阶线性系统的鲁棒H∞控制性能进行了研究,特别是探讨了虚部特征根对H∞性能的作用,揭示了当特征根的实部固定不变的情况下,特征根的虚部增加到一定程度就会对H∞性能不起作用,进而针对给定的系统矩阵,在H∞性能的框架下分析了特征根实部和虚部之间的比例关系.同时,比照经典二阶系统的部分成果,探讨了经典二阶系统的阻尼比系数选取范围与H∞性能框架下复特征根参数之间的对照关系,进而从时域的角度给出了阻尼比参数选取的一种合理解释,并形成时频交互综合分析,为极点配置控制理论中的期望极点的选取提供一种理论参考.Robust H ∞ performance is studied for a class of second-order linear systems with complex eigenvalues, especially the impact of imaginary part of complex eigenvalues on the H ∞ performance is studied.It is found that when the real part of the complex eigenvalues is fixed, the impact of the imaginary part of the complex eigenvalues on the H ∞ performance becomes little when the value of the imaginary part exceeds a threshold.Based on this observation, a fixed proportional relation between the imaginary part and the real part of the complex eigenvalues is found for a given system matrix under the framework of H ∞ performance.Referring to the classical control theory of second-order systems in frequency domain, the relationship between the selection ranges of damping ratio and the complex eigenvalue is further discussed in the framework of H ∞ performance, in which a reasonable explanation on the selection ranges of damping ratio is presented.This analysis procedure forms the time-frequency domain interaction synthesis method, which provides a theoretical guidance for the selection and determination of the desired closed-loop poles in the control theory based on the pole placement method.

关 键 词：H∞范数 H∞性能 H∞控制 干扰 阻尼比 时频交互综合分析 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]