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Find the transfer function Y(s) of the system given below.
X(s)

1. G₁ + G₂
  1 - HG₁ 1 - HG₂
2. G₁ + G₂
  1 + HG₁ 1 + HG₂
3. G₁ + G₂
  1 + H(G₁+ G₂)
4. G₁ + G₂
  1 - H(G₁+ G₂)

Correct Option: C

Y(s) = Y₁ (s) + Y₂ (s)
Y₁ (s) = (X – HY)G₁ = XG₁ – HG₁ Y
Y₂ (s) = (X – HY)G₂ = XG₂ – HG₂ Y
Y(s) = XG₁ – HG₁ Y + XG₂ – HG₂ Y
Y = X(G₁ + G₂) – H(G₁ + G₂ )Y
Y + Y(G₁ + G₂ )H = (G₁ + G₂ )X
Y(1 + (G₁ + G₂ )H) = (G₁ + G₂ )X

	Y(s)	=	G₁ + G₂
	X (s)		1 + H(G₁ + G₂)

Find the transfer function	Y(s)	of the system given below.
	X(s)