基于向量分析的频域稳定性判据及其应用

Frequency domain stability criterion and its application based on vector analysis

稳定性是控制系统性能分析的首要问题,频域稳定性判据以其方便直观的特性获得了广泛应用。本文基于特征矢量分析,利用系统极点分布与特征多项式相频特性幅角增量的关系,推导了一种关系直接、概念清楚的频域稳定性判据表达形式,改善了目前采用复变函数幅角映射理论论述Nyquist判据时不够直观易懂的不足。针对判据应用中出现的开环幅相频率图的画法和稳定性判断方法进行了论述,化繁为简,并给出了实例互为印证。

Stability identification is an important part in control system performance analysis.Frequency domain stability criterion is in widely used by reason of its convenience and illustrative property.Based on characteristic vector analysis,a kind of frequency domain stability criterion was put forward with the relationship of system pole distribution and eigenpolynomial phase-frequency characteristic argument increment.This criterion which characterized by direct relationship and obvious conception improved profound Nyquist criterion illustrated by principle of argument of complex analysis.Some amplitude and phase frequency drawing technique of open loop system was indicated and stability identification method was also discussed in detail.The criterion was verified by some examples in this paper.