nyquist(sl) nyquist(sl, fmin, fmax) nyquist(sl, fmin, fmax, step) nyquist(sl, frq) nyquist(frq, db, phi) nyquist(frq, repf) nyquist(.., comments) nyquist(.., 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
real matrices of modulus (in dB) and phases (in degree) (one row for each output of
matrix of complex numbers. Frequency response (one row for each output of
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
For continuous time systems
plotted. For discrete time system or discretized systems
sl(exp(2*%i*%pi*w*fd) is used (
for discrete time systems and
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
The frequencies are given by the bounds
(in Hz) or by a row-vector (or a matrix for multi-output)
step is the ( logarithmic ) discretization step.
calfrq for the choice of default value).
comments is a vector of character strings
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
Default values for
sl is continuous-time or
0.5/sl.dt (nyquist frequency)
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
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($+i-1)// the handle on the compound object of the ith system
This compound object has two children: a compound object that defines the small arrows (a compound of small polylines) and the curve labels (a compound of texts) and a polyline which is the curve itself. The following piece of code shows how one can customize a particular nyquist curve display.
hi.children(1).visible='off'; //hides the arrows and labels hi.children(2).thickness=2; //make the curve thicker
//Nyquist curve s=poly(0,'s') h=syslin('c',(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01)); h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225)) clf(); nyquist(h1) // add a datatip ax=gca(); h_h=ax.children($).children(2);//handle on Nyquist curve of h tip=datatipCreate(h_h,[1.331,0.684]); datatipSetOrientation(tip,"upper left");
//Hall chart as a grid for nyquist 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(); 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 ax=gca();Leg=ax.children(1); Leg.legend_location="in_upper_left";
- syslin — определение линейной системы
- 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
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