## Name

black — Black's diagram (Nichols chart)

## Calling Sequence

black( sl,[fmin,fmax] [,step] [,comments] )
black( sl,frq [,comments] )
black(frq,db,phi [,comments])
black(frq,repf [,comments])

## Parameters

- sl
list ( linear system `syslin`

)

- fmin,fmax
real scalars (frequency bounds)

- frq
row vector or matrix (frequencies)

- db,phi
row vectors or matrices (modulus, phase)

- repf
row vectors or matrices (complex frequency response)

- step
real

- comments
string

## Description

Black's diagram (Nichols'chart) for a linear system
`sl`

. `sl`

can be a continuous-time or
discrete-time SIMO system (see `syslin`

). In case of
multi-output the outputs are plotted with different symbols.

The frequencies are given by the bounds
`fmin`

,`fmax`

(in Hz) or by a row-vector
(or a matrix for multi-output) `frq`

.

`step`

is the ( logarithmic ) discretization step.
(see `calfrq`

for the choice of default value).

`comments`

is a vector of character strings
(captions).

`db,phi`

are the matrices of modulus (in Db) and
phases (in degrees). (One row for each response).

`repf`

matrix of complex numbers. One row for each
response.

To plot the grid of iso-gain and iso-phase of
`y/(1+y)`

use chart().

Default values for `fmin`

and
`fmax`

are `1.d-3`

,
`1.d+3`

if `sl`

is continuous-time or
`1.d-3`

, `0.5`

/sl.dt (nyquist frequency)
if `sl`

is discrete-time.

## Examples

s=poly(0,'s')
h=syslin('c',(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01))
clf();black(h,0.01,100);
chart(list(1,0));
h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225))
clf()
black([h1;h],0.01,100,['h1';'h'])
chart(list(1,0));