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EE 3151 Homework # 2
Fall 2019
Total: 80 points; Due: September 30, 2019
Due Monday
1. For the block diagram shown below, (1) draw the equivalent signal flow graph of the system, (2)
find E(s)/R(s), and (3) find C(s)/R(s).
(15 points)
GA
G1
G
G3
H2
2. For the two feedback systems shown below, (a) Find the closed-loop transfer functions T1 and T2
for each system, (b) Show that T1 = T2 = 100 when Ki = K2 = 100, and (c) Compare the sensitivities
of the two systems with respect to the parameter K1 for the nominal values of K1 = K2 = 100.
(20 points)
T. = Ville
R(S)
K
C (s)
1- 009 9 4, MZ
(1)
0.0099
-.09
R(S)
K1
K2
c(s )
1 +. 094, + , 09 *2 + , 60814 , 42
L. =09 k.
0.09
( 100 ) ( 100)
0.09
LZ =- 09 k z
1 +. 09 ( 160 )
(2)
4 = 1 -(-,0941 - 0942 ) +.008 *. 1/2
3. For a unity feedback control system with controller Gc(s) = K and plant Gp(s) = 1/[s(s+K1)], (a)
calculate the sensitivity of the closed-loop transfer function to changes in K1, and (b) how would
you select a value for K to minimize the effects of K1 variation. (10 points)
4. Construct the signal flow graph for the following set of simultaneous equations: X2 = A21 X1 + A23
X3, X3 = A31 X1 + A32 X2 + A33 X3, X4 = A42X2 + A43X3. Identify the (a) input node, (b) output node, (c)
forward paths, (d) feedback paths, and (e) self-loop. (15 points)...

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- Fall '19
- Dr. Jiann-Shiou Yang