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Scilab Help >> Control Systems - CACSD > Linear Analysis > Frequency Domain > nicholschart

# nicholschart

Nichols chart

### Syntax

`nicholschart([modules] [,args] [,colors])`

### Arguments

modules

real vector ( modules (in dB))

args

real vector (phases (in degree))

a scalar or a vector, the color indices for isogain and iso phase curves

### Description

plot the Nichols'chart: iso-module and iso-argument contours of `y/(1+y)` in `y` phase/gain plane

`nicholschart` may be used in conjunction with black.

The default values for `modules` and `args` are respectively :

`[-12 -8 -6 -5 -4 -3 -2 -1.4 -1 -.5 0.25 0.5 0.7 1 1.4 2 2.3 3 4 5 6 8 12]`

`[-(1:10) , -(20:10:160)]`

### Remark

Traditionally, the syntax for `nicholschart` is: nicholschart(modules=gains, args=phases, colors=colors), but the following syntax is also allowed: nicholschart(gains, phases, colors).

### Examples

```//Nichols chart
clf()
nicholschart(modules=[-6 -3 -1 1 3 6], args=[-1 -20 20 40 80 160 180]);```

```//Black diagram with Nichols chart as a grid
s=poly(0,'s');
Plant=syslin('c',16000/((s+1)*(s+10)*(s+100)));
//two degree of freedom PID
tau=0.2;xsi=1.2;
PID=syslin('c',(1/(2*xsi*tau*s))*(1+2*xsi*tau*s+tau^2*s^2));
clf();
black([Plant;Plant*PID ],0.01,100,["Plant";"Plant and PID corrector"]);
//move the caption in the lower right corner
ax=gca();Leg=ax.children(1);
Leg.legend_location="in_lower_right";
nicholschart(colors=color('light gray')*[1 1])```