Modern Control Engineering

Problems 397

B–6–25.Consider the system shown in Figure 6–115. The
system involves velocity feedback. Determine the value of
gainKsuch that the dominant closed-loop poles have a
damping ratio of 0.5. Using the gain Kthus determined, ob-
tain the unit-step response of the system.

R(s) 1 C(s)

s

0.2

K

+– +– (s+ 1) (s+ 2)

Figure 6–115

Control system.

B–6–26.Consider the system shown in Figure 6–116. Plot

the root loci as avaries from 0 to q. Determine the value of

asuch that the damping ratio of the dominant closed-loop

poles is 0.5.

+– s+a s (^2) (s^2 + 2)
Figure 6–116
Control system.
B–6–28.Consider the system shown in Figure 6–118. As-
suming that the value of gain Kvaries from 0 to q, plot the
root loci when and 0.5.
Compare unit-step responses of the system for the
following three cases:
(1) K=10, Kh=0.1
(2) K=10, Kh=0.3
(3) K=10, Kh=0.5
Kh=0.1, 0.3,
B–6–27.Consider the system shown in Figure 6–117. Plot
the root loci as the value of kvaries from 0 to q. What value
ofkwill give a damping ratio of the dominant closed-loop
poles equal to 0.5? Find the static velocity error constant of
the system with this value of k.
s+ 1.4
s+ 5
10
s(s+ 1)
ks
s+ 10
+– +–
Figure 6–117
Control system.
R(s) 1 C(s)
s
Kh
K
s+ 1

+

Figure 6–118

Control system.