Solution 5.8.1.2
G
H
+
R
CΣ
Figure 1: Standard Closed Loop Conguration
For the system of Figure 1 let
GH =
K(s+1)
s(s+2)
The rst step is to plot the poles and zeros of GH.Thepoles of GH are
not the closed loop pole locations, but they can be used to nd the closed
loop poles. The closed loop zeros can be found immediately: they are the
zeros of G and the poles of H.Thezeros of GH also help in nding the
poles of the closed loop system.
The rootlocus is shown in Figure 2. Note that there is root locus between
the pole ats =0andthezero ats = ;1andto the left of the pole ats = ;2.
In this simple case the entire root locus is on the real axis.
-1-2
Re(s)
Im(s)
Figure 2: Root Locus
1