Control System Toolbox Function Reference

nyquist

Compute Nyquist frequency response of LTI models

Syntax

nyquist(sys)
nyquist(sys,w)

nyquist(sys1,sys2,...,sysN)
nyquist(sys1,sys2,...,sysN,w)
nyquist(sys1,'PlotStyle1',...,sysN,'PlotStyleN')

[re,im,w] = nyquist(sys)
[re,im] = nyquist(sys,w)

Description

nyquist calculates the Nyquist frequency response of LTI models. When invoked without left-hand arguments, nyquist produces a Nyquist plot on the screen. Nyquist plots are used to analyze system properties including gain margin, phase margin, and stability.

nyquist(sys) plots the Nyquist response of an arbitrary LTI model sys. This model can be continuous or discrete, and SISO or MIMO. In the MIMO case, nyquist produces an array of Nyquist plots, each plot showing the response of one particular I/O channel. The frequency points are chosen automatically based on the system poles and zeros.

nyquist(sys,w) explicitly specifies the frequency range or frequency points to be used for the plot. To focus on a particular frequency interval [wmin,wmax], set w = {wmin,wmax}. To use particular frequency points, set w to the vector of desired frequencies. Use logspace to generate logarithmically spaced frequency vectors. Frequencies should be specified in rad/sec.

nyquist(sys1,sys2,...,sysN) or nyquist(sys1,sys2,...,sysN,w) superimposes the Nyquist plots of several LTI models on a single figure. All systems must have the same number of inputs and outputs, but may otherwise be a mix of continuous- and discrete-time systems. You can also specify a distinctive color, linestyle, and/or marker for each system plot with the syntax

nyquist(sys1,'PlotStyle1',...,sysN,'PlotStyleN')

See bode for an example.

When invoked with left-hand arguments

[re,im,w] = nyquist(sys)
[re,im] = nyquist(sys,w)

return the real and imaginary parts of the frequency response at the frequencies w (in rad/sec). re and im are 3-D arrays with the frequency as last dimension (see "Arguments" below for details).

Arguments

The output arguments re and im are 3-D arrays with dimensions

For SISO systems, the scalars re(1,1,k) and im(1,1,k) are the real and imaginary parts of the response at the frequency .

For MIMO systems with transfer function , re(:,:,k) and im(:,:,k) give the real and imaginary parts of (both arrays with as many rows as outputs and as many columns as inputs). Thus,

where is the transfer function from input to output .

Example

Plot the Nyquist response of the system

H = tf([2 5 1],[1 2 3])
nyquist(H)

You have two zoom options available from the right-click menu that apply specifically to Nyquist plots:

• Tight --Clips unbounded branches of the Nyquist plot, but still includes the critical point (-1, 0)
• On (-1,0) -- Zooms around the critical point (-1,0)

Also, click anywhere on the curve to activate data markers that display the real and imaginary values at a given frequency. This figure shows the nyquist plot with a data marker.

See Also
bode        Bode plot

evalfr      Response at single complex frequency

freqresp    Frequency response computation

ltiview     LTI system viewer

nichols     Nichols plot

sigma       Singular value plot

norm

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