Page 306 - Modern Control Systems

280 Chapter 4 Feedback Control System Characteristics

5. An advantage of using feedback is a decreased sensitivity of the system
to variations in the parameters of the process. True or False
6. The loop transfer function of the system in Figure 4.39 is
G c(s)G{s) = 5 ° , .
v
c W
' TS + 10
The sensitivity of the closed-loop system to small changes in T is:
T
a. S 7{s) = TS
TS + 60
T
T
b. S T(s) =
TS + 10
T/„\
c. S T(s) -
TS + 60
T
d. S T(s) = -
TS + 10
7. Consider the two systems in Figure 4.40.
*(•*> — * 0 K, + Y(s)
0.0099

(i)
+
/~\
/f(.v) A K, * Y(s)
l
1
0.09 4—1
(H)
FIGURE 4.40 Two feedback systems with gains /C, and K 2.
These systems have the same transfer function when K\ = K 2 = 100. Which system is
most sensitive to variations in the parameter K{> Compute the sensitivity using the nom-
= = 100.
inal values K x K 2
a. System (i) is more sensitive and $£, = 0.01

b. System (ii) is more sensitive and Sjc, = 0.1
c System (ii) is more sensitive and S£ 1 = 0.01
d. Both systems are equally sensitive to changes in K x.
8. Consider the closed-loop transfer function
A, + kA 2
T(s) =
A 3 + *A 4 '
where A l5 A 2, A 3, and A 4 are constants. Compute the sensitivity of the system to
variations in the parameter k.
k{A 2A 3 - A XA A)
3 Sk
* (A 3 + kAt){A x + kA 2)
k(A 2A 3 + A,A 4)
b Sk
* ' (A 3 + kA 4)(Ai + kA 2)