The block diagram of a feedback control system is shown in the figure. The overall closed-loop gain G of the system is

G = G1G2 / (1 + G1H1)
G = G1G2 / (1 + G1G2 + G1H1)
G = G1G2 / (1 + G1G2H1)
G = G1G2 / (1 + G1G2 + G1G2H1)

Correct answer: G = G1G2 / (1 + G1G2 + G1G2H1)

Solution

The correct option accounts for the contributions of both the forward path gains and the feedback loop, accurately representing the overall closed-loop gain by including all relevant terms in the denominator.

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