Question

The overall closed loop transfer function C(s)R(s) represented in the figure, will be

A
(G1(s)+G2(s))G3(s)1+(G1(s)+G2(s))(H1(s)+G3(s))
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B
(G1(s)+G3(s))1+G1(s)H1(s)+G2(s)G3(s)
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C
(G1(s)G2(s))H1(s)1+(G1(s)+G3(s))(H1(s)+G1(s))
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D
G1(s)G2(s)H1(s)1+G1(s)H1(s)+G1(s)G3(s)
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Solution

The correct option is A (G1(s)+G2(s))G3(s)1+(G1(s)+G2(s))(H1(s)+G3(s))Blocks G1 and G2 are in parallel ∴G1+G2 To the above result H1 is in negative feedback ∴G1+G21+(G1+G2)H1 To the above result of G3 is in series ∴(G1+G2)G31+(G1+G2)H1 To the above result feedback is '1' ∴C(s)R(s)=(G1+G2)G31+(G1+G2)[H1+G3] =(G1(s)+G2(s))G3(s)1+(G1(s)+G2(s))(H1(s)+G3(s))

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