Scilab Home page | Wiki | Bug tracker | Forge | Mailing list archives | ATOMS | File exchange
Please login or create an account
Change language to: English - Português - 日本語 - Русский
Aide de Scilab >> Systèmes de Contrôle - CACSD > Analyse linéaire > Domaine de fréquence > nyquist


nyquist plot


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



A siso or simo linear dynamical system, in state space, transfer function or zpk representations, in continuous or discrete time.


real scalars (frequency lower and upper bounds (in Hz)).


real (logarithmic discretization step), if not given an adaptative discretization is used.


string vector (captions).


a boolean, default value is %t.


vector or matrix of frequencies (in Hz) (one row for each output of sl).


real matrices of modulus (in dB) and phases (in degree) (one row for each output of sl).


matrix of complex numbers. Frequency response (one row for each output of sl)


Nyquist plot i.e Imaginary part versus Real part of the frequency response of sl. If the symmetry argument is true or omitted the Nyquist plot displays the symmetric graph (positive and negative frequencies).

For continuous time systems sl(2*%i*%pi*w) is plotted. For discrete time system or discretized systems sl(exp(2*%i*%pi*w*fd) is used ( fd=1 for discrete time systems and fd=sl('dt') for discretized systems )

sl can be a continuous-time or discrete-time SIMO system given by its state space, rational transfer function (see syslin) or zpk representation. 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 is a matrix of complex numbers. One row for each response.

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.

Automatic discretization of frequencies is made by calfrq.

To obtain the value of the frequency at a selected point(s) you can activate the datatips manager and click the desired point on the nyquist curve(s).

Graphics entities organization

The nyquist function creates a compound object for each SISO system. The following piece of code allows to get the handle on the compound object of the ith system:

ax=gca();//handle on current axes
hi=ax.children($+i-1)// the handle on the compound object of the ith system

This compound object has two children: a compound object that defines the small arrows (a compound of small polylines) and the curve labels (a compound of texts) and a polyline which is the curve itself. The following piece of code shows how one can customize a particular nyquist curve display.

hi.children(1).visible='off'; //hides the arrows and labels
hi.children(2).thickness=2; //make the curve thicker


//Nyquist curve
clf();    nyquist(h1)
// add a datatip
h_h=ax.children($).children(2);//handle on Nyquist curve of h
datatipSetOrientation(tip,"upper left");

//Hall chart as a grid for nyquist
//two degree of freedom PID
nyquist([Plant;Plant*PID],0.5,100,["Plant";"Plant and PID corrector"]);
hallchart(colors=color('light gray')*[1 1])
//move the caption in the lower right corner

See also

  • syslin — définition d'un système dynamique linéaire
  • bode — Bode plot
  • black — Black-Nichols diagram of a linear dynamical system
  • nyquistfrequencybounds — Computes the frequencies for which the nyquist locus enters and leaves a given rectangle.
  • calfrq — frequency response discretization
  • freq — frequency response
  • repfreq — frequency response
  • phasemag — phase and magnitude computation
  • datatips — Tool for placing and editing tips along the plotted curves



handling zpk representation

Scilab Enterprises
Copyright (c) 2011-2017 (Scilab Enterprises)
Copyright (c) 1989-2012 (INRIA)
Copyright (c) 1989-2007 (ENPC)
with contributors
Last updated:
Thu Feb 14 14:59:54 CET 2019