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NyquistGridLines

is an option to NyquistPlot that specifies contours of constant magnitude and phase of a closed-loop system.

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Basic Examples  
Scope  
Applications  
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NyquistGridLines

NyquistGridLines

is an option to NyquistPlot that specifies contours of constant magnitude and phase of a closed-loop system.

Details

  • The following settings can be given:
  • Noneno contours drawn
    Automaticcontours chosen automatically
    {magnitude,phase}contours specified by magnitude and phase are drawn
  • magnitude values are the absolute values.
  • phase values are given in radians.
  • The following settings can be given for magnitude and phase:
  • Noneno contours drawn
    Automaticcontours chosen automatically
    {c1,c2,…}draw the contours ci
    {{c1,style1,r1},…}contours with specified styles and regions
  • The default setting for stylei is Dashed for magnitude contours and Dotted for phase contours.
  • The setting specifies that a point should be included if yields True.
  • The default value of is True&.

Examples

open all close all

Basic Examples  (1)

Show the closed-loop magnitude and phase contours:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{10}}, (6 + s)*(1 + 2*s + s^2)}, s], NyquistGridLines -> Automatic]

Scope  (9)

Choose contours automatically:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> Automatic]

Show the specified magnitude and phase contours:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> {{0.1, 0.15, 0.2, 0.25}, {-1, -0.3, 0.3, 1}}]

Use different contour styles:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> {{0.1, {0.15, Green}, {0.2, Yellow}, {0.25, Red}}, {{-1, Directive[Dotted, Red]}, {-0.3}, 0.3, {1, Directive[Dotted, Red]}}}]

Specify different regions:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> {{0.1, {0.15, Green}, {0.2, Yellow}, {0.25, Red}}, {{-1, Directive[Dotted, Red], #1^2 + #2^2 > 0.1^2&}, {-0.3, Automatic, #1^2 + #2^2 > 0.25^2&}, {0.3, Automatic, #1^2 + #2^2 > 0.25^2&}, {1, Directive[Dotted, Red], #1^2 + #2^2 > 0.1^2&}}}]

Specify contours with magnitude -12 dB, -13 dB, -15 dB, and -18 dB:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> {10^(#/20)& /@ {-12, -13, -15, -18}, None}]

Specify contours with phase from -60 to 60 degrees in increments of 10:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> {None, Range[-60, 60, 10] Degree, RegionFunction -> (True&)}]

The contours depend on the feedback type:

Wolfram Language code: GraphicsRow@Table[NyquistPlot[TransferFunctionModel[{{{s}}, 3 + 3*s + s^2}, s], NyquistGridLines -> Automatic, FeedbackType -> f, PlotLabel -> Style["Feedback Type: " <> ToString@f, Italic]], {f, {"Negative", "Positive", None}}]

The contours are shown only in the finite regions:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{3*(4 + s)}}, 4 + s^2}, s], PlotRange -> 10, NyquistGridLines -> Automatic]

A discrete-time system:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{-1 + z}}, 1 - 3*z + z^2}, z, SamplingPeriod -> 1], NyquistGridLines -> Automatic]

Applications  (1)

Estimate closed-loop magnitude and phase values at various frequencies:

Wolfram Language code: NyquistPlot[TransferFunctionModel[{{{1 + 6*s}}, (1 + s)*(1 + 3*s)}, s], Mesh -> {{0.1, 0.7, 1}}, MeshStyle -> Directive[PointSize[Medium], Red], NyquistGridLines -> Automatic]
Wolfram Research (2010), NyquistGridLines, Wolfram Language function, https://reference.wolfram.com/language/ref/NyquistGridLines.html.

Text

Wolfram Research (2010), NyquistGridLines, Wolfram Language function, https://reference.wolfram.com/language/ref/NyquistGridLines.html.

CMS

Wolfram Language. 2010. "NyquistGridLines." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/NyquistGridLines.html.

APA

Wolfram Language. (2010). NyquistGridLines. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/NyquistGridLines.html

BibTeX

@misc{reference.wolfram_2026_nyquistgridlines, author="Wolfram Research", title="{NyquistGridLines}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/NyquistGridLines.html}", note=[Accessed: 12-June-2026]}

BibLaTeX

@online{reference.wolfram_2026_nyquistgridlines, organization={Wolfram Research}, title={NyquistGridLines}, year={2010}, url={https://reference.wolfram.com/language/ref/NyquistGridLines.html}, note=[Accessed: 12-June-2026]}