Documentation

# ngrid

Superimpose Nichols chart on Nichols plot

## Syntax

```ngrid ```

## Description

`ngrid ` superimposes Nichols chart grid lines over the Nichols frequency response of a SISO LTI system. The range of the Nichols grid lines is set to encompass the entire Nichols frequency response.

The chart relates the complex number H/(1 + H) to H, where H is any complex number. For SISO systems, when H is a point on the open-loop frequency response, then

`$\frac{H}{1+H}$`

is the corresponding value of the closed-loop frequency response assuming unit negative feedback.

If the current axis is empty, `ngrid` generates a new Nichols chart grid in the region –40 dB to 40 dB in magnitude and –360 degrees to 0 degrees in phase. If the current axis does not contain a SISO Nichols frequency response, `ngrid` returns a warning.

## 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 right-click menu for Nichols charts includes the Tight option under Zoom. You can use this to clip unbounded branches of the Nichols chart.

## See Also

#### Learn how to automatically tune PID controller gains

Download code examples