5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given that the transfer functions of the individual blocks are: 1 3 G,(s) = • G,(s) = , H(s) = 2s S+3 using block diagram simplification techniques show that the transfer function of the system is: C(s) R(s) s +s+1 R(s) C(s) G(s) G,(8) H(s)

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5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given
that the transfer functions of the individual blocks are:
1
G,(s) =
S+ 3
G,(1) = 2, H(s) = 2s
using block diagram simplification techniques show that the transfer function of the
system is:
C(s)
1
R(s)
s'+ s+1
R(s)
C(s)
G|(s)
G2(8)
H(s)
Figure Q.5(a)
b) Using Routh's Stability Criteria, determine the range of values of K to ensure that the
system shown in Figure Q.5(b) is stable.
R(s)
K
C(s)
(s + 1)(s + 2)
0.2
Figure Q.5(b)
Transcribed Image Text:5. (a) A system can be represented by the block diagram shown in Figure Q.5(a). Given that the transfer functions of the individual blocks are: 1 G,(s) = S+ 3 G,(1) = 2, H(s) = 2s using block diagram simplification techniques show that the transfer function of the system is: C(s) 1 R(s) s'+ s+1 R(s) C(s) G|(s) G2(8) H(s) Figure Q.5(a) b) Using Routh's Stability Criteria, determine the range of values of K to ensure that the system shown in Figure Q.5(b) is stable. R(s) K C(s) (s + 1)(s + 2) 0.2 Figure Q.5(b)
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