基于特征方程幅相特性的时滞线性系统状态反馈镇定  

State feedback stabilization of LTI systems with input time delay based on amplitude and phase property of characteristic equation

作　　者：曾启杰[1] 章云[1] 唐斌[1] 陈贞丰[1] 

机构地区：[1]广东工业大学自动化学院,广州510006

出　　处：《控制与决策》2012年第11期1676-1680,共5页Control and Decision

基　　金：国家自然科学基金项目(U0735003;60974047;61104105);广东省自然科学基金项目(8351009001000002;9451009001002702)

摘　　要：研究具有输入时滞的线性时不变(LTI)系统的状态反馈控制镇定问题.由于时滞的引入,闭环系统特征方程变成一个超越方程.从时滞系统的特征根求解出发,从特征方程的实部和虚部系数中提取两个与系统矩阵和反馈矩阵相关的向量,其幅值和相角关系正好反映了特征根轨迹穿越虚轴的情况,且得到的判据将时滞参数与系统其他参数进行了分离,可方便地应用于镇定控制器的设计.最后通过仿真实例表明了该算法的正确性和有效性.This paper investigates the state feedback stabilization of linear time-invariant（LTI） systems with input time delay.The existence of time delay transforms the closed-loop characteristic equation into a transcendental equation.By investigating the eigenvalues of the time-delay system,two vectors related to the system parameters and the feedback gain respectively can be obtained from the real part and the imaginary part of the transcendental equation.The amplitude and phase relations of these two vectors indicate the crossing situation of the root locus on the imaginary axis.Furthermore,the time delay is dependent on the system parameters and the feedback gain explicitly in this criterion,so that the state feedback stability controller can be designed more expediently.Finally,numerical examples illustrate the correctness and effectiveness of the proposed algorithm.

关 键 词：线性系统 镇定 时滞 特征方程 

分 类 号：TP273[自动化与计算机技术—检测技术与自动化装置]