I was trying to solve a question from the 2004 GATE IN paper,

question 4.16

I solved it this way,

my attempt

Now, the book is giving a different solution, I'm pretty sure my way is correct since they pulled the "standard form" out of nowhere. I don't think that formula is applicable here. But please tell me if I am wrong.

gate madeeasy solution

Also while I understand that I performed those algebraic manipulations to find how the disturbance and error is related in the frequency domain, I am not comfortable with the fact that I had to assume input R(s) was 0. I mean practically we would care about how the disturbance D affects the output C or error E in the presence of some non zero input R right? If I don't take input to be zero I can't seperate terms and find the transfer function. So I was wondering if the superposition principle is strong enough such that this result is useful even in the case of both D and R bring present?

  • \$\begingroup\$ Already got the answer? \$\endgroup\$ – Unknown123 May 5 at 5:22
  • \$\begingroup\$ No I still have the question unanswered in my mind. If I ever find a satisfactory solution, I'll come back here and add an answer myself. Do you know of the solution? \$\endgroup\$ – Aditya P May 5 at 6:52

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