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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 1984-2011 - INRIA - Serge STEER
// This file must be used under the terms of the CeCILL.
// This source file is licensed as described in the file COPYING, which
// you should have received as part of this distribution. The terms
// are also available at
// http://www.cecill.info/licences/Licence_CeCILL_V2.1-en.txt
function nyquist(varargin)
// Nyquist plot
//!
rhs=size(varargin);
if rhs == 0 then
//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));
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";
return;
end
symmetry=%t
if type(varargin(rhs))==4 then //symmetrization flag
symmetry=varargin(rhs)
rhs=rhs-1
end
if type(varargin(rhs))==10 then
comments=varargin(rhs);
rhs=rhs-1;
else
comments=[];
end
fname="nyquist";//for error messages
fmax=[];
if or(typeof(varargin(1))==["state-space" "rational"]) then
//sys,fmin,fmax [,pas] or sys,frq
refdim=1; //for error message
sltyp=varargin(1).dt;
if rhs==1 then
[frq,repf,splitf]=repfreq(varargin(1),1d-3,1d3);
elseif rhs==2 then //sys,frq
if size(varargin(2),2)<2 then
error(msprintf(_("%s: Wrong size for input argument #%d: A row vector with length>%d expected.\n"),fname,2,1))
end
[frq,repf]=repfreq(varargin(1:rhs));
elseif or(rhs==(3:4)) then //sys,fmin,fmax [,pas]
[frq,repf,splitf]=repfreq(varargin(1:rhs));
else
error(msprintf(_("%s: Wrong number of input arguments: %d to %d expected.\n"),fname,1,5))
end
elseif type(varargin(1))==1 then
//frq,db,phi [,comments] or frq, repf [,comments]
refdim=2;
sltyp="x";
splitf=[];
splitf=1;
select rhs
case 2 then //frq,repf
frq=varargin(1);
repf=varargin(2);
if size(frq,2)<2 then
error(msprintf(_("%s: Wrong size for input argument #%d: A row vector with length>%d expected.\n"),fname,1,1))
end
if size(frq,2)<>size(varargin(2),2) then
error(msprintf(_("%s: Incompatible input arguments #%d and #%d: Same column dimensions expected.\n"),fname,1,2))
end
case 3 then //frq,db,phi
frq=varargin(1);
if size(frq,2)<>size(varargin(2),2) then
error(msprintf(_("%s: Incompatible input arguments #%d and #%d: Same column dimensions expected.\n"),fname,1,2));
end
if size(frq,2)<>size(varargin(3),2) then
error(msprintf(_("%s: Incompatible input arguments #%d and #%d: Same column dimensions expected.\n"),fname,1,3));
end
repf=exp(log(10)*varargin(2)/20 + %pi*%i/180*varargin(3));
else
error(msprintf(_("%s: Wrong number of input arguments: %d to %d expected.\n"),fname,2,4))
end
else
error(msprintf(_("%s: Wrong type for input argument #%d: Linear dynamical system or row vector of floats expected.\n"),fname,1));
end;
if size(frq,1)==1 then
ilf=0;
else
ilf=1;
end
[mn,n]=size(repf);
if and(size(comments,"*")<>[0 mn]) then
error(msprintf(_("%s: Incompatible input arguments #%d and #%d: Same number of elements expected.\n"),fname,refdim,rhs+1));
end
//
repi=imag(repf);
repf=real(repf);
// computing bounds of graphic window
mnx=min(-1,min(repf));// to make the critical point visible
mxx=max(-1,max(repf));
if symmetry then
mxy=max(0,max(abs(repi)));
mny=min(0,-mxy);
else
mxy=max(0,max(repi));
mny=min(0,min(repi));
end
dx=(mxx-mnx)/30;
dy=(mxy-mny)/30;
rect=[mnx-dx,mny-dy;mxx+dx,mxy+dy];
fig=gcf();
immediate_drawing=fig.immediate_drawing;
fig.immediate_drawing="off";
ax=gca();
if ax.children==[] then
ax.data_bounds=rect;
ax.axes_visible="on";
ax.grid=color("lightgrey")*ones(1,3)
ax.title.text=_("Nyquist plot");
if sltyp=="c" then
ax.x_label.text=_("Re(h(2iπf))");
ax.y_label.text=_("Im(h(2iπf))");
elseif sltyp=="x" then
ax.x_label.text=_("Re");
ax.y_label.text=_("Im");
else
ax.x_label.text=_("Re(h(exp(2iπf*dt)))");
ax.y_label.text=_("Im(h(exp(2iπf*dt)))");
end
else
rect= ax.data_bounds
mnx=rect(1,1);
mxx=rect(2,1)
mny=rect(1,2)
mxy=rect(2,2)
end
// drawing the curves
splitf($+1)=n+1;
ksplit=1;sel=splitf(ksplit):splitf(ksplit+1)-1;
R=[repf(:,sel)]; I=[repi(:,sel)];
F=frq(:,sel);
for ksplit=2:size(splitf,"*")-1
sel=splitf(ksplit):splitf(ksplit+1)-1;
R=[R %nan(ones(mn,1)) repf(:,sel)];
I=[I %nan(ones(mn,1)) repi(:,sel)];
F=[F %nan(ones(size(frq,1),1)) frq(:,sel)];
end
Curves=[]
kf=1
if symmetry then
for k=1:mn
xpoly([R(k,:) R(k,$:-1:1)],[I(k,:) -I(k,$:-1:1)]);
e=gce();e.foreground=k;
e.display_function = "formatNyquistTip";
e.display_function_data = [F(kf,:) -1*F(kf,$:-1:1)];
Curves=[Curves,e];
kf=kf+ilf;
end
else
for k=1:mn
xpoly(R(k,:),I(k,:));
e=gce();e.foreground=k;
e.display_function = "formatNyquistTip";
e.display_function_data = F(kf,:);
Curves=[Curves,e];
kf=kf+ilf;
end
end
clear R I
kk=1;p0=[repf(:,kk) repi(:,kk)];ks=1;d=0;
dx=rect(2,1)-rect(1,1);
dy=rect(2,2)-rect(1,2);
dx2=dx^2;
dy2=dy^2;
// collect significant frequencies along the curve
//-------------------------------------------------------
Ic=min(cumsum(sqrt((diff(repf,1,"c").^2)/dx2+ (diff(repi,1,"c").^2)/dy2),2),"r");
kk=1;
L=0;
DIc=0.2;
while %t
ksup=find(Ic-L>DIc);
if ksup==[] then break,end
kk1=min(ksup);
L=Ic(kk1);
Ic(1:kk1)=[];
kk=kk+kk1;
if min(abs(frq(:,ks($))-frq(:,kk))./abs(frq(:,kk)))>0.001 then
if min(sqrt(((repf(:,ks)-repf(:,kk)*ones(ks)).^2)/dx2+..
((repi(:,ks)-repi(:,kk)*ones(ks)).^2)/dy2)) >DIc then
ks=[ks kk];
d=0;
end
end
end
if ks($)~=n then
if min(((repf(:,ks(1))-repf(:,n)).^2)/dx2+((repi(:,ks(1))-repi(:,n)).^2)/dy2)>0.01 then
ks=[ks n];
end
end
// display of parametrization (frequencies along the curve)
//-------------------------------------------------------
kf=1
if ks($)<size(repf,2) then last=$;else last=$-1;end
for k=1:mn,
L=[];
for kks=ks
xstring(repf(k,kks),repi(k,kks),msprintf("%-0.3g",frq(kf,kks)),0);
e=gce();e.font_foreground=k;
L=[e L];
if symmetry&(abs(repi(k,kks))>mxy/20) then //not to overlap labels
xstring(repf(k,kks),-repi(k,kks),msprintf("%-0.3g",-frq(kf,kks)),0);
e=gce();e.font_foreground=k;
L=[e L];
end
end
L=glue(L);
A=[];
if size(ks,"*")>1 then
dr=repf(k,ks(1:last)+1)-repf(k,ks(1:last));
di=repi(k,ks(1:last)+1)-repi(k,ks(1:last));
dd=1500*sqrt((dr/dx).^2+(di/dy).^2);
dr=dr./dd;
di=di./dd;
// we should use xarrows or xsegs here.
// However their displayed arrow size depends
// on the data bounds and we want to avoid this
if symmetry then
xx=[repf(k,ks(1:last)) repf(k,ks(last:-1:1))+dr($:-1:1) ;
repf(k,ks(1:last))+dr repf(k,ks(last:-1:1))]
yy=[repi(k,ks(1:last)) -repi(k,ks(last:-1:1))-di($:-1:1) ;
repi(k,ks(1:last))+di -repi(k,ks(last:-1:1))]
else
xx=[repf(k,ks(1:last)) ;
repf(k,ks(1:last))+dr]
yy=[repi(k,ks(1:last));
repi(k,ks(1:last))+di]
end
xpolys(xx,yy)
//xarrows([repf(k,ks(1:last));repf(k,ks(1:last))+dr],..
// [repi(k,ks(1:last));repi(k,ks(1:last))+di],1.5)
A=gce();
A.children.arrow_size_factor = 1.5;
A.children.polyline_style = 4;
A.children.foreground=k;
end
kf=kf+ilf;
glue([Curves(k) glue([L A])]);
end;
if comments<>[] then
legend(Curves, comments);
end
fig.immediate_drawing=immediate_drawing;
endfunction
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