User`s guide

rlocfind
11-180
11rlocfind
Purpose Select feedback gain from root locus plot
Syntax [k,poles] = rlocfind(sys)
[k,poles] = rlocfind(sys,p)
Description rlocfind returns the feedback gain associated with a particular set of poles on
the root locus.
rlocfind works with both continuous- and discrete-time SISO
systems.
[k,poles] = rlocfind(sys) is used for interactive gain selection from the
root locus pl ot of the SISO system
sys generated by rlocus. The function
rlocfind puts up acrosshair cursoron t h e root locus plott hat youuse to select
a particular pole location. The root locus gain associated with this point is
returned in
k and the column vector poles contains the closed-loop poles for
this gain. To use this command, the root locus o f the SISO open-loop model
sys
must be present in the current figure window.
[k,poles] = rlocfind(sys,p) takes a vector p of desired root locations and
computes a root locus gain for each of these locations (that is, a gain for which
one of the closed-loop roots is near the desired location). The
jth entry of the
vector
k gives the computed gain for the pole location p(j),andthejth column
of the matrix
poles lists the resulting closed-loop poles.
Example Determine a feedback gain such that the closed-loop poles of the system
have damping r atio ζ =0.707.
h = tf([2 5 1],[1 2 3]);
rlocus(h) % Plot the root locus
k = rlocfind(h) % Select pole with ζ=.707 graphically
Algorithm [k,poles] = rlocfind(sys,p) calculates the gain k from the following
formula.
k = abs(d(p)/n(p))
hs()
2s
2
5s 1++
s
2
2s3++
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