nichols (Control System Toolbox)

Compute Nichols frequency response of LTI models

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

computes the frequency response of an LTI model and plots it in the Nichols coordinates. Nichols plots 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 plot.

nichols(sys)

produces a Nichols plot of the LTI model sys. This model can be continuous or discrete, SISO or MIMO. In the MIMO case, nichols produces an array of Nichols plots, 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)

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 radians/sec.

nichols(sys1,sys2,...,sysN) or nichols(sys1,sys2,...,sysN,w) superimposes the Nichols 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

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

See bode for an example.

When invoked with left-hand arguments,

[mag,phase,w] = nichols(sys)
[mag,phase] = nichols(sys,w)

return the magnitude and phase (in degrees) of the frequency response at the frequencies w (in rad/sec). The outputs mag and phase are 3-D arrays similar to those produced by bode (see bode). They have dimensions

Remark

If sys is an FRD model, nichols(sys,w), w can only include frequencies in sys.frequency.

Example

Plot the Nichols response of the system

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

nichols(H); ngrid

Algorithm

See bode.