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.TH evans 1 "April 1993" "Scilab Group" "Scilab Function"
.so ../sci.an
.SH NAME
evans - Evans root locus
.SH CALLING SEQUENCE
.nf
evans(H [,kmax])
.fi
.SH PARAMETERS
.TP
H
: list (linear system \fVsyslin \fR)
.TP
kmax
: real (maximum gain desired for the plot )
.LP
.SH DESCRIPTION
Gives the Evans root locus for a linear system in state-space or
transfer form H(s) (\fVsyslin\fR list). This is the locus of the roots of
\fV1+k*H(s)=1+k*N(s)/D(s)\fR, in the complex plane. For a selected
sample of gains \fVk <= kmax\fR, the imaginary part of the roots of
\fVD(s)+k*N(s)\fR is plotted vs the real part.
.LP
To obtain the gain at a given point of the locus you can
simply execute the following instruction :
\fVk=-1/real(horner(h,[1,%i]*locate(1)))\fR and click the desired point
on the root locus. If the coordinates of the selected point are
in the real 2 x 1 vector \fVP=locate(1)\fR this \fVk\fR
solves the equation \fV k*N(w) + D(w) =0\fR with \fVw=P(1)+%i*P(2)=[1,%i]*P\fR.
.SH EXAMPLE
.nf
H=syslin('c',352*poly(-5,'s')/poly([0,0,2000,200,25,1],'s','c'));
evans(H,100)
P=3.0548543 - 8.8491842*%i; //P=selected point
k=-1/real(horner(H,P));
Ns=H('num');Ds=H('den');
roots(Ds+k*Ns) //contains P as particular root
// Another one
xbasc();s=poly(0,'s');n=1+s;
d=real(poly([-1 -2 -%i %i],'s'));
evans(n,d,100);
//
xbasc();n=real(poly([0.1-%i 0.1+%i,-10],'s'));
evans(n,d,80);
.fi
.SH SEE ALSO
kpure, krac2, locate
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