“A Logarithmic-Amplitude Polar Diagram”

Authors: Trond Andresen,
Affiliation: NTNU, Department of Engineering Cybernetics
Reference: 2001, Vol 22, No 2, pp. 65-72.

Keywords: Logarithmic polar diagram, Nyquist criterion, stability, logarithmic spiral

Abstract: 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.

PDF PDF (966 Kb)        DOI: 10.4173/mic.2001.2.1

DOI forward links to this article:
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  title={{A Logarithmic-Amplitude Polar Diagram}},
  author={Andresen, Trond},
  journal={Modeling, Identification and Control},
  publisher={Norwegian Society of Automatic Control}