Page 307 - Modern Control Systems

Skills Check 281

k(Aj + kA 2)
=
** * (A 3 + kA 4)
k^JcAd_

Consider the block diagram in Figure 4.39 for Problems 9-12 where G c(s) = K x and
K
W, - s + K XK 2
9. , The closed-loop transfer function is:
KK\
a. 7 » =
s + K X(K + K 2)
KK X
b. T(s) =
s + K X{K + K 2)
KK X
c. T(s) =
s - K X{K + K 2)
KK X
J TY«.\ —
s 2 + K xKs + K XK 2
10. The sensitivity Sk, of the closed-loop system to variations in #1 is:
a. Sl(s) =
(s + K t(K + K 2)f
2s
b S
- " ^ = s + K X(K + K 2)
c Sl(s) =
5 + K X{K + K 2)
/
T _ *,(* + ¾ )
d. SUs) =
{s + K,(K + K 2)Y
T
11. The sensitivity S K of the closed-loop system to variations in K is:
s + K xK 2
T
a. S K{s) =
5 + K x(K + K 2)
Ks
b. $£(*)
(5 + ^ ( K + K 2 )) 2
c S' K(s)
* + #1*2
K,(s + A ^ )
T
d. S K(s) =
(5 + * , ( * + K 2)) 2
12. The steady-state tracking error to a unit step input R(s) = \/s with T d{s) = 0 is:
K
a. €c X K + K 2
K 2
b. e,
K + K 2
K 2
K }(K + K 2)

d €ss
* K + K 2