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// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
// Copyright (C) 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 [fmin,fmax]=nyquistfrequencybounds(H,bounds)
//find frequencies that reaches the nyquist bounds on real an imag part
fname="nyquistFrequencyBounds" //for error messages
if or(size(bounds)<>[2 2]) then
error(msprintf(_("%s: Wrong size for argument #%d: (%d,%d) expected.\n"),fname,2,2,2))
end
if or(bounds(2,:)<bounds(1,:)) then
error(msprintf(_("%s: Wrong value for input argument #%d: second row must be greater than first one.\n"),fname,2))
end
if and(typeof(H)<>["state-space" "rational"]) then
error(msprintf(_("%s: Wrong type for input argument #%d: Linear dynamical system expected.\n"),fname,1))
end
if size(H,"*")<>1 then
error(msprintf(_("Wrong type for argument #%d: SISO expected.\n"),fname,1))
end
if typeof(H)=="state-space" then
H=ss2tf(H)
end
dom=H.dt
if dom==[]|dom=="d" then dom=1,end
eps=1d-10
frq=[];
orient=[]
if dom=="c" then
c=2*%i*%pi
function f=arg2freq(y)
f=y/c;
endfunction
Hr=(H+horner(H,-%s))/2;
Hi=(H-horner(H,-%s))/2;
else
c=2*%i*%pi*dom
function f=arg2freq(y)
f=log(y)/c;
endfunction
Hr=(H+horner(H,1/%z))/2;
Hi=(H-horner(H,1/%z))/2;
end
// computing frequencies that make the nyquist locus to cross
// the real part lower bound
f=arg2freq(roots(numer(Hr-bounds(1,1))));
f=real(f(real(f)>0&abs(imag(f)./abs(f))<eps));
//keep only those that give imaginary parts inside the bounds
im=imag(repfreq(H,f));
f=f(im<=bounds(2,2)&im>=bounds(1,2))
if f<>[] then
orient=[orient imag(repfreq(derivat(Hr),f))<0]
frq=[frq;f];
end
// computing frequencies that make the nyquist locus to cross
// the real part upper bound
f=arg2freq(roots(numer(Hr-bounds(2,1))));
f=real(f(real(f)>0&abs(imag(f)./abs(f))<eps));
//keep only those that give imaginary parts inside the bounds
im=imag(repfreq(H,f));
f=f(im<=bounds(2,2)&im>=bounds(1,2))
if f<>[] then
orient=[orient imag(repfreq(derivat(Hr),f))>0]
frq=[frq;f];
end
// computing frequencies that make the nyquist locus to cross
// the imaginary part lower bound
f=arg2freq(roots(numer(Hi-%i*bounds(1,2))));
f=real(f(real(f)>0&abs(imag(f)./abs(f))<eps));
//keep only those that give real parts inside the bounds
re=real(repfreq(H,f));
f=f(re<=bounds(2,1)&re>=bounds(1,1))
if f<>[] then
orient=[orient real(repfreq(derivat(Hi),f))>0]
frq=[frq;f];
end
// computing frequencies that make the nyquist locus to cross
// the imaginary part upper bound
f=arg2freq(roots(numer(Hi-%i*bounds(2,2))));
f=real(f(real(f)>0&abs(imag(f)./abs(f))<eps));
//keep only those that give real parts inside the bounds
re=real(repfreq(H,f));
f=f(re<=bounds(2,1)&re>=bounds(1,1))
if f<>[] then
orient=[orient real(repfreq(derivat(Hi),f))<0]
frq=[frq;f];
end
if frq==[] then
//check if there is at least one point inside the bounds
r=repfreq(H,%pi)
if real(r)<bounds(1,1)|real(r)>bounds(2,1)|imag(r)<bounds(1,2)| ...
imag(r)>bounds(2,2) then
fmin=[];fmax=[]
else
fmin=0;fmax=%inf
end
else
//looking for the lowest frequency for which the locus enters the
//area and the highest for which the locus leaves it.
[frq,k]=gsort(frq,"g","i");
orient=orient(k)
if ~orient(1) then
//locus starts inside the area
frq=[0;frq]
end
if orient($) then
//locus ends inside the area
frq=[frq;%inf]
end
fmin=frq(1)
fmax=frq($)
end
endfunction
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