The overall transfer function of the system in figure is

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The overall transfer function of the system in figure is—

1. G/1 – GH
2. 2G/1 – GH
3. GH/1 – GH
4. 2G/1 – H

Correct Option: B

From given figure
Y₁ = U + X₂H …(i)
Y₂ = U + X₁H …(ii)
and
X₁ = GY₁ = G (U + X₂H) = GU + GX₂H
X₂ = GY₂ = G (U + X₁H) = GU + GX₁H
Now,
Y = X₁ + X₂
or
Y = GU + GX₂H + GU + GX₁H
or
Y = 2GU + GH (X₁ + X₂)
or
Y = 2GU + GHY
or
Y – GHY = 2GU
or
Y/U = 2G/1 – GH