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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) INRIA
// 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-en.txt
function evans(n,d,kmax)
// Seuil maxi et mini (relatifs) de discretisation en espace
// Copyright INRIA
smax=0.002;smin=smax/3;
nptmax=2000 //nbre maxi de pt de discretisation en k
//analyse de la liste d'appel
[lhs,rhs]=argn(0)
if rhs <= 0 then // demo
n=real(poly([0.1-%i 0.1+%i,-10],'s'));
d=real(poly([-1 -2 -%i %i],'s'));
evans(n,d,80);
return
end
select typeof(n)
case 'constant' then
if rhs==2 then kmax=0,end
case 'polynomial' then
if rhs==2 then kmax=0,end
//-compat next case retained for list/tlist compatibility
case 'rational' then
if rhs==2 then kmax=d,else kmax=0,end
[n,d]=n(2:3)
case 'state-space' then
if rhs==2 then kmax=d,else kmax=0,end
n=ss2tf(n);
[n,d]=n(2:3);n=clean(n);d=clean(d);
else
error(msprintf(gettext("%s: Wrong type for input argument #%d: A linear dynamical system or a polynomial expected.\n"),"evans",1));
end
if prod(size(n))<>1 then
error(msprintf(gettext("%s: Wrong value for input argument #%d: Single input, single output system expected.\n"),"evans",1));
end
if kmax<=0 then
nm=mini([degree(n),degree(d)])
fact=norm(coeff(d),2)/norm(coeff(n),2)
kmax=round(500*fact),
end
//
//calcul de la discretisation en k et racines associees
nroots=roots(n);racines=roots(d);
if nroots==[] then
nrm=maxi([norm(racines,1),norm(roots(d+kmax*n),1)])
else
nrm=maxi([norm(racines,1),norm(nroots,1),norm(roots(d+kmax*n),1)])
end
md=degree(d)
//
ord=1:md;kk=0;nr=1;k=0;pas=0.99;fin='no';
while fin=='no' then
k=k+pas
r=roots(d+k*n);r=r(ord)
dist=maxi(abs(racines(:,nr)-r))/nrm
//
point='nok'
if dist <smax then //pas correct
point='ok'
else //pas trop grand ou ordre incorrect
// on cherche l'ordre qui minimise la distance
ix=1:md
ord1=[]
for ky=1:md
yy=r(ky)
mn=10*dist*nrm
for kx=1:md
if ix(kx)>0 then
if abs(yy-racines(kx,nr)) < mn then
mn=abs(yy-racines(kx,nr))
kmn=kx
end
end
end
ix(kmn)=0
ord1=[ord1 kmn]
end
r(ord1)=r
dist=maxi(abs(racines(:,nr)-r))/nrm
if dist <smax then
point='ok',
ord(ord1)=ord
else
k=k-pas,pas=pas/2.5
end
end
if dist<smin then
//pas trop petit
pas=2*pas;
end
if point=='ok' then
racines=[racines,r];kk=[kk,k];nr=nr+1
if k>kmax then fin='kmax',end
if nr>nptmax then fin='nptmax',end
end
end
//draw the axis
x1 =[nroots;matrix(racines,md*nr,1)];
xmin=mini(real(x1));xmax=maxi(real(x1))
ymin=mini(imag(x1));ymax=maxi(imag(x1))
dx=abs(xmax-xmin)*0.05
dy=abs(ymax-ymin)*0.05
if dx<1d-10, dx=0.01,end
if dy<1d-10, dy=0.01,end
legs=[],lstyle=[];lhandle=[]
rect=[xmin-dx;ymin-dy;xmax+dx;ymax+dy];
f=gcf();
cur_im_dr= f.immediate_drawing;
f.immediate_drawing = 'off';
a=gca()
a.data_bounds=[rect(1) rect(2);rect(3) rect(4)]
if nroots<>[] then
xpoly(real(nroots),imag(nroots))
e=gce();e.line_mode='off';e.mark_mode='on';
e.mark_size_unit="point";e.mark_size=7;e.mark_style=5;
legs=[legs; _("open loop zeroes")]
lhandle=[lhandle; e];
end
if racines<>[] then
xpoly(real(racines(:,1)),imag(racines(:,1)))
e=gce();e.line_mode='off';e.mark_mode='on';
e.mark_size_unit="point";e.mark_size=7;e.mark_style=2;
legs=[legs;_("open loop poles")]
lhandle=[lhandle; e];
end
dx=maxi(abs(xmax-xmin),abs(ymax-ymin));
//plot the zeros locations
//computes and draw the asymptotic lines
m=degree(n);q=md-m
if q>0 then
la=0:q-1;
so=(sum(racines(:,1))-sum(nroots))/q
i1=real(so);i2=imag(so);
if prod(size(la))<>1 then
ang1=%pi/q*(ones(la)+2*la)
x1=dx*cos(ang1),y1=dx*sin(ang1)
else
x1=0,y1=0,
end
if md==2,
if coeff(d,md)<0 then
x1=0*ones(2),y1=0*ones(2)
end,
end;
if maxi(k)>0 then
xpoly(i1,i2);
e=gce();
legs=[legs;_("asymptotic directions")]
lhandle=[lhandle; e];
axes = gca();
axes.clip_state = "clipgrf";
for i=1:q,xsegs([i1,x1(i)+i1],[i2,y1(i)+i2]),end,
axes.clip_state = "off";
end
end;
//lieu de evans
[n1,n2]=size(racines);
plot2d(real(racines)',imag(racines)',style=2+(1:n2));
legend(lhandle,legs,1);
xtitle(_("Evans root locus"),_("Real axis"),_("Imaginary axis"));
f=gcf();
if(cur_im_dr=="on") then f.immediate_drawing = 'on';end
if fin=='nptmax' then
warning(msprintf(gettext("%s: Curve truncated to the first %d discretization points.\n"),"evans",nptmax))
end
endfunction
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