Discussion
The transfer function y(s)/Td (s) for the following system (shown in fig) is :
Answer: D
The transfer function is G2(s) / [1 + G1(s)G2(s)H(s)], which is option D reading the G(s) printed in the options as G2(s), the only block the disturbance passes through.
Set R(s) = 0 and follow the loop. The disturbance Td enters just before G2, and the output is fed back with a minus sign through H to G1:
\[ \begin{aligned} y &= G_2\,(Td - G_1 H y) \\ y\,(1 + G_1 G_2 H) &= G_2\,Td \\ \frac{y}{Td} &= \frac{G_2}{1 + G_1 G_2 H} \end{aligned} \]
Option C has a minus in the denominator, which would be positive feedback, and the figure shows negative feedback. Option B (zero) would hold only if the disturbance had no path to the output, and option A is not the form of any loop gain here. The options do not define G(s); this explanation takes it to mean G2(s), the reading under which the key is right.
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