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.
作者
王占山
王继东
刘秀翀
孙鉴
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.)
出处
《东北大学学报(自然科学版)》
EI
CAS
CSCD
北大核心
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)
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
H ∞ norm
H ∞ performance
H ∞ control
disturbance
damping ratio
time-frequency domain interaction synthesis method