5.8.1.40
For the system of Figure 1 let For the system of Figure 1
G
H
C
R
+
-
Figure 1: Standard Closed Loop Conguration
G(s)H(s)=
K(s+2)
s(s+ 1)(s+20)(s+30)
;;
The MATLAB program
%sm5.5.1.40
z1=2
p1 = 0
p2 = 1
p3 = 20
p4 = 30
s=linspace(-19,-4,500)
K=(abs(s+p1).*abs(s +p2).*abs(s+p3).*abs(s+p4))./abs(s + z1);;
figure(1)
plot(s,K)
grid on
axis([-10,-4,2400,2600])
print -deps 58140bo.eps
K=linspace(0,1000,1000);;
gh = zpk([-2],[0 -1 -20 -30],10)
[R,K] = rlocus(gh,K);;
figure(2)
plot(R,'k.')
print -deps 58140rl.eps
Draws the plot of gain versus position along the negativerealaxis, shown
in Figure 2 and the root locus shown in Figure 3
1
-10 -9 -8 -7 -6 -5 -4
2400
2420
2440
2460
2480
2500
2520
2540
2560
2580
2600
Figure 2: Searchfor breakin and break out points
-45 -40 -35 -30 -25 -20 -15 -10 -5 0
-15
-10
-5
0
5
10
15
Figure 3: accurate root locus
2