Solution Manual of Principle of Control System by Bakshi ebook pdf

3.3 Transfer Function
Solution : The s-domain network is shown in the Fig. 3.1.
Applying KVL to the two loops,
R I (s) I (s) sL I (s) sL V(s)1 1 1 2 = 0
i.e. I (s) [R sL] I (s) sL1 1 2 = V(s) ... (1)
I (s) R 1 sC
I (s) sL I (s) sL I (s)2 2 2 2 1 = 0
I (s)1 =
sL
s LC
2 2
2 2
2 2
s LC sL2
2 2 1
I (s)
V(s) 2 =
s LC
s LCR s R R C R s L C s L R C sL s L C
2
3 2 2 2
s LC (R R ) s (R R C L) R
2
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3 Transfer Function and Impulse Response
1(s)
R2R1
sL
Q.2
Solution : The s-domian network is shown in the Fig. 3.2 (a).
T.F. = E (s) E (s)
Z Z Z
(R R )+ sR R (C C ) 2 1 1
1 2 1 2 1 2



Principles of Control Systems 3 - 2 Transfer Function and Impulse Response
TECHNICAL PUBLICATIONS - An up thrust for knowledge TM
E (s)i
5.3 Rules for Block Diagram Reduction
Q.11
Solution : Shifting take off point after G 2 and seperating feedback paths we get,
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5 Block Diagram Representation of
Control Systems
G1 G2
2 2 1 2 1
G1 G (1 + G )
1 + G H + G H + G G H H + G G H + G G G H H
3 2
3 3 2 2 2 3 2 3 1 2 1 1 2 3 1 3
R(s) C(s)
Series
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Q.12
Solution : No series, parallel combination and no minor feedback loop exists. So shifting
take off point before the block of s
s + 10


.
Principles of Control Systems 5 - 2 Block Diagram Representation of Control Systems
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–
–
+
(s + 11) (s 3) (s 4) + s(2s + 7) (s + 8)3
C(s)
R(s) =
2
Q.4
Solution : As there are two inputs, consider each input separately. Consider R(s), assuming Y(s) = 0.
C(s)
R(s) =
1 2 1 i.e. C(s) =
R(s) G G
1 2 1
Now consider Y(s) acting with R(s) = 0.
Now sign of signal obtained from H1 is negative which must be carried forward, though
summing point at R(s) is removed, as R(s) = 0, so we get,
Key Point While finding equivalent G, trace forward path from input summing point to
output in direction of signal. While finding equivalent H, trace the feedback path from output
to input summing point in the direction of signal.
Now equivalent G = G 2 , tracing forward path from input summing point to output.
Equivalent H = G H1 1 tracing feedback path from output to input summing point.
While sign of the final feedback is positive at the input summing point.
Principles of Control Systems 5 - 3 Block Diagram Representation of Control Systems
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–
+ + C(s)
G2
3_1
5_1
6_1
7_1
8_1
10_1
11_1
12_1
14_1