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

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.