A logarithmic-amplitude polar diagram

被引:7
作者
Andresen, T [1 ]
机构
[1] Norwegian Univ Sci & Technol, Dept Engn Cybernet, N-7034 Trondheim, Norway
关键词
logarithmic polar diagram; Nyquist criterion; stability; logarithmic spiral;
D O I
10.4173/mic.2001.2.1
中图分类号
TP [自动化技术、计算机技术];
学科分类号
0812 ;
摘要
A polar diagram where the amplitude of the transfer function is on a logarithmic scale, is presented. This gives a one-size-fits-all diagram with no need for zooming in and out, and no need for additional reasoning about infinite-radius encirclements when there are poles on the imaginary axis-as opposed to what is usually neccessary with the standard polar (Nyquist-) diagram. All properties needed for stability considerations are upheld, such as encirclements, gain and phase margins. The path for s in the loop transfer function is carefully chosen with regard to possible poles on the imaginary axis. Small excursions into the right half plane in the form of arcs of different-sized logarithmic spirals result in corresponding large but finite arcs that do not overlap in the logarithmic polar plots.
引用
收藏
页码:65 / 72
页数:8
相关论文
共 3 条
[1]  
BELANGER PR, 1995, CONTROL ENG MODERN A
[2]  
BRONSTEIN IN, 1966, TASCHENBUCH MATH
[3]  
Dorf R., 1998, MODERN CONTROL SYSTE