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“A Logarithmic-Amplitude Polar Diagram”

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

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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:
  [1] R. Zanasi, F. Grossi and L. Biagiotti (2015), doi:10.1016/j.sysconle.2015.06.005
  [2] Roberto Zanasi and Federica Grossi (2014), doi:10.1109/ECC.2014.6862243
  [3] Ulf Jakob F. Aarsnes and Ole Morten Aamo (2016), doi:10.1016/j.jsv.2015.09.017
  [4] O. Aljohani and A. Abu-Siada (2017), doi:10.1109/TDEI.2016.006088


References:
[1] DORF, R.C. BISHOP, R.H. (1998). Modern Control Systems, Eight edition, Menlo Park, California: Addison Wesley.
[2] BRONSTEIN, I.N. SEMENDJAJEW, K.A. (1966). Taschenbuch der Mathematik, Zurich and Frankfurt/Main: Verlag Harri Deutsch.
[3] BÉLANGER, P.R. (1995). Control Engineering: A Modern Approach, Florida: Saunders College Publishing, Harcourt Brace and Company.


BibTeX:
@article{MIC-2001-2-1,
  title={{A Logarithmic-Amplitude Polar Diagram}},
  author={Andresen, Trond},
  journal={Modeling, Identification and Control},
  volume={22},
  number={2},
  pages={65--72},
  year={2001},
  doi={10.4173/mic.2001.2.1},
  publisher={Norwegian Society of Automatic Control}
};

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