Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Change language to: Français - Português - 日本語 - Русский

See the recommended documentation of this function

# black

Black-Nichols diagram of a linear dynamical system

### Calling Sequence

```black( sl,[fmin,fmax] [,step] [,comments] )

### Arguments

sl

a continuous or discrete time SIMO linear dynamical system ( see: 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

string

### Description

Black's diagram (Nichols'chart) for a linear system ( see: syslin). `sl` can be a continuous-time or discrete-time SIMO system. In case of multi-output the outputs are plotted with different colors.

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 nicolschart().

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

```//Black diagram
s=poly(0,'s');
sl=syslin('c',5*(1+s)/(.1*s.^4+s.^3+15*s.^2+3*s+1))
clf();black(sl,0.01,10);```

```//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 rigth corner
ax=gca();Leg=ax.children(1);
Leg.legend_location="in_lower_right";
nicholschart(colors=color('light gray')*[1 1])```

• nicholschart — Nichols chart
• bode — Bode plot
• nyquist — nyquist plot
• syslin — linear system definition
• calfrq — frequency response discretization
• datatips — Tool for placing and editing tips along the plotted curves.