GainPhaseMargins

GainPhaseMargins[lsys]

gives the gain and phase margins of the linear time-invariant system lsys.

Details and Options

  • The system lsys can be a TransferFunctionModel or a StateSpaceModel.
  • GainPhaseMargins returns {{{ωp1,g1},{ωp2,g2},…},{{ωg1,p1},{ωg2,p2},…}}, where the ωpi are the phase crossover frequencies, the gi are the gain margins, the ωgi are the gain crossover frequencies, and the pi are the phase margins.
  • The gain margins gi are absolute values and the phase margins pi are in radians.
  • The gain margins are the reciprocals of the magnitude of lsys at the phase crossover frequencies.
  • At the phase crossover frequencies, lsys has phase .
  • The phase margins are phase lags needed to make the phase at the gain crossover frequencies.
  • At the gain crossover frequencies, the gain of lsys is unity.
  • The following options can be given:
  • FeedbackType"Negative"the feedback type
    MethodAutomaticmethod to use
    SamplingPeriodNonethe sampling period
  • Explicit settings for the Method option include "Solve" and "NSolve". In each case the methods of Solve or NSolve can be specified as suboptions. The default setting of Automatic switches between these methods, depending on whether lsys is exact or inexact.
  • GainPhaseMargins has the attribute Listable.

Examples

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Basic Examples  (1)

The gain and phase margins of a system:

In[1]:=
Click for copyable input
Out[1]=

Scope  (3)

Generalizations & Extensions  (1)

Options  (2)

Properties & Relations  (2)

See Also

GainMargins  PhaseMargins  StabilityMargins  BodePlot  NyquistPlot  NicholsPlot  TransferFunctionModel

Introduced in 2010
(8.0)