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Question

The signal flow graph of a system is shown in the figure. The transfer function C(s)R(s) of the system is


A
6s2+29s+6
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B
6ss2+29s+6
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C
s(s+2)s2+29s+6
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D
s(s+27)s2+29s+6
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Solution

The correct option is D s(s+27)s2+29s+6
P1=1
Δ1=1+3s+24s=s+27s
G(s)=P1Δ11(loop gain)+pair of non-touching loops
L1=3s,L2=24s,L3=2s
L1 and L3 are non-touching
G(s)=(s+27)s1(3s24s2s)+2s×3s
=(s+27)s1+29s+6s2
C(s)R(s)=s(s+27)s2+29s+6

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