# MATLAB Programming/Nichols Plot

## IntroductionEdit

This article is on the topic of creating Nichols plots in MATLAB. The quick answer is use the *Nichols* command. However, the Nichols command has several options and the plots generated by the *Nichols* command are not easily reformatted. The default formatting of most MATLAB plots is good for analysis but less than ideal for dropping into Word and PowerPoint documents or even this website. As a result this article presents an alternative that requires more lines of code but offers the full formatting flexibility of the generic *plot* command.

## MATLAB's Nichols CommandEdit

The basic Nichols command is as follows

>> nichols(LTI_SYS)

where

The Nichols command will automatically call *gcf* which will put the Nichols plot on the current figure. If no figure exists then one is created by *gcf*.

If you wish to specify the frequency points at which *LTI_SYS* is plotted then create a frequency vector using *logspace* or *linspace* as follows

>> freqVec = logspace(-1, 3, 5000); >> nichols(LTI_SYS, freqVec * (2*pi))

where

- freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10
^{-1}to 10^{3} - pi is a MATLAB constant equal to the value of and in this case it is used to convert freqVec to rad/sec as it is passed to the
*Nichols*command

- freqVec is a vector of 5000 frequencies, in Hz, spaced evenly on a log scale from 10

### Issues with the *nichols* commandEdit

The main issue with the *nichols* command is reformatting of the plot. The *nichols* command appears to use a normal semilogx plot and then apply patches or something similar to the figure. This can lead to odd behavior when attempting to create multi-line titles, reformat line widths or font sizes, etc. The normal relationship of axes to figure is just not quite present.