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authorShashank2017-05-29 12:40:26 +0530
committerShashank2017-05-29 12:40:26 +0530
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+// Scilab ( http://www.scilab.org/ ) - This file is part of Scilab
+// Copyright (C) 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 [kp,s]=krac2(sys)
+ //The denominator of the closed loop system is den(s)+K*num(s). So the
+ // the closed loops poles verify K(s)=-den(s)/num(s)
+ //The real axis breakaway points occurs at the extrema of the K(s)
+ // so at the point where K'=dK/ds = 0
+ // K'=-(den'*num-den*num')/num^2
+ // K'= 0 --> den'*num-den*num'=0
+ // http://www.scribd.com/doc/21374148/An-Introduction-to-Control-Systems
+ select typeof(sys)
+ case "rational" then
+ case "state-space" then
+ sys=ss2tf(sys);
+ else
+ error(msprintf(gettext("%s: Wrong type for input argument #%d: Linear state space or a transfer function expected.\n"),"krac2",1))
+ end
+ if size(sys,"*")<>1 then
+ error(msprintf(gettext("%s: Wrong size for input argument #%d: Single input, single output system expected.\n"),"krac2",1))
+ end
+ num=sys.num
+ den=sys.den
+ s=roots(derivat(num)*den-derivat(den)*num,"e")
+ //collect the real roots only
+ i=find(abs(imag(s))<=10*%eps)
+ if i==[] then kp=[],s=[];return,end
+ s=s(i)';
+ s=s(horner(num,s)<>0);
+
+ kp=-real(freq(den,num,real(s)));
+ i=find(kp>=0);
+ kp=kp(i)
+ s=s(i)
+endfunction