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nyquist
nyquist plot
Calling Sequence
nyquist( sl,[fmin,fmax] [,step] [,comments] [,symmetry]) nyquist( sl, frq [,comments] [,symmetry]) nyquist(frq,db,phi [,comments] [,symmetry]) nyquist(frq, repf [,comments] [,symmetry])
Arguments
- sl
a continuous or discrete time SIMO linear dynamical system ( see: syslin).
- fmin,fmax
real scalars (frequency lower and upper bounds (in Hz)).
- step
real (logarithmic discretization step), if not given an adaptative discretization is used.
- comments
string vector (captions).
- symmetry
a boolean, default value is %t.
- frq
vector or matrix of frequencies (in Hz) (one row for each output of
sl
).- db,phi
real matrices of modulus (in dB) and phases (in degree) (one row for each output of
sl
).- repf
matrix of complex numbers. Frequency response (one row for each output of
sl
)
Description
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 symetric 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 (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
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($+i-1)// the handle on the compound object of the ith system
This compound object has two children: a compound object that defines the small arrows (a compound of small polylines) and the curve labels (a compound of texts) and a polyline which is the curve itself. The following piece of code shows how one can customize a particular nyquist curve display.
hi.children(1).visible='off'; //hides the arrows and labels hi.children(2).thickness=2; //make the curve thicker
Examples
//Nyquist curve s=poly(0,'s') h=syslin('c',(s^2+2*0.9*10*s+100)/(s^2+2*0.3*10.1*s+102.01)); h1=h*syslin('c',(s^2+2*0.1*15.1*s+228.01)/(s^2+2*0.9*15*s+225)) clf(); nyquist(h1) // add a datatip ax=gca(); h_h=ax.children($).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 rigth corner ax=gca();Leg=ax.children(1); Leg.legend_location="in_upper_left";
See Also
- syslin — linear system definition
- 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.
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