Function Reference

nichols

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 the bode reference page). They have dimensions

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
  

The right-click menu for Nichols plots includes the Tight option under Zoom. You can use this to clip unbounded branches of the Nichols plot.

Algorithm

See bode.

See Also
bode        Bode plot

evalfr      Response at single complex frequency

freqresp    Frequency response computation

ltiview     LTI system viewer

ngrid       Grid on Nichols plot

nyquist     Nyquist plot

sigma       Singular value plot

ngrid

norm