开环零极点对消情况下利用根轨迹判定系统稳定性

Assessing system stability by root locus in the condition of open-loop pole-zero cancellation

线性控制系统的稳定性,只与系统闭环极点在[s]平面的分布有关.根轨迹法可以根据开环零、极点分布,描述当某一参数变化时,系统闭环极点在[s]平面上的变化轨迹.因此利用根轨迹可以简便直观地判断控制系统的稳定性.本文从线性定常系统稳定的充分必要条件出发,分析了在系统开环传递函数自身存在开环零、极点对消情况时,直接应用根轨迹判定系统稳定性可能会遇到的问题,并提出了在此种情况下应用根轨迹判稳的几个结论.

The stability of linear control system is only related to the distribution of closed-loop pole of the system on [s]plane. The root locus method, based on the distribution of open-loop polezero, is used to describe the distribution of closed-loop pole of the system on [s] plane when one of the variants changes. Therefore, the root locus method can be used to assess the stability of the control system in a simple and direct way. Starting from the sufficient and necessary condition of linear time-invariant system, this paper analyzes the problems possibly faced if the root locus method is directly used to assess the stability of the system when there is open-loop pole-zero cancellation in the open-loop transfer function of the system. The paper provides a few conclusions of assessing the stability with root locus in the above-mentioned situation.