# nichols

Nichols chart of frequency response

## Syntax

nichols(sys)
nichols(sys,w)
nichols(sys1,sys2,...,sysN)
nichols(sys1,sys2,...,sysN,w)
nichols(sys1,'PlotStyle1',...,sysN,'PlotStyleN')
[mag,phase,w] = nichols(sys)
[mag,phase] = nichols(sys,w)

## Description

nichols creates a Nichols chart of the frequency response. A Nichols chart displays the magnitude (in dB) plotted against the phase (in degrees) of the system response. Nichols charts are useful to analyze open- and closed-loop properties of SISO systems, but offer little insight into MIMO control loops. Use ngrid to superimpose a Nichols chart on an existing SISO Nichols chart.

nichols(sys) creates a Nichols chart of the dynamic system sys. This model can be continuous or discrete, SISO or MIMO. In the MIMO case, nichols produces an array of Nichols charts, each plot showing the response of one particular I/O channel. The frequency range and gridding are determined automatically based on the system poles and zeros.

nichols(sys,w) specifies the frequency range or frequency points to be used for the chart. 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 must be in rad/TimeUnit, where TimeUnit is the time units of the input dynamic system, specified in the TimeUnit property of sys.

nichols(sys1,sys2,...,sysN) or nichols(sys1,sys2,...,sysN,w) superimposes the Nichols charts of several 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 nichols(sys1,'PlotStyle1',...,sysN,'PlotStyleN').

See bode for an example.

[mag,phase,w] = nichols(sys) or [mag,phase] = nichols(sys,w) returns the magnitude and phase (in degrees) of the frequency response at the frequencies w (in rad/TimeUnit). The outputs mag and phase are 3-D arrays similar to those produced by bode (see the bode reference page). They have dimensions

(number of outputs) × (number of inputs) × (length of w)

## Examples

collapse all

Plot the Nichols response with Nichols grid lines for the following system:

$H\left(s\right)=\frac{-4{s}^{4}+48{s}^{3}-18{s}^{2}+250s+600}{{s}^{4}+30{s}^{3}+282{s}^{2}+525s+60}.$

H = tf([-4 48 -18 250 600],[1 30 282 525 60]);
nichols(H)
ngrid

The context menu for Nichols charts includes the Tight option under Zoom. You can use this option to clip unbounded branches of the Nichols chart.

## Tips

You can change the properties of your plot, for example the units. For information on the ways to change properties of your plots, see Ways to Customize Plots.

See bode.