### “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 (966 Kb) DOI: 10.4173/mic.2001.2.1

**DOI forward links to this article:**

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**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}

};