GATE 2024 Chemical Engineering, Q48 · Process Control
The correct answer is C, −Gc2Gp1 / [1+Gc2Gp2+Gc1Gc2Gp1].
Question
For the block diagram shown in the figure, the correct expression for the transfer function Gd = y1(s)/d(s) is
- A. −Gp1Gc2 / [(1+Gc1Gc2Gp1)(1+Gc2Gp2)]
- B. −Gc2Gp1 / [1+Gc2Gp2+Gc1Gc2Gp1Gp2]
- C. −Gc2Gp1 / [1+Gc2Gp2+Gc1Gc2Gp1]
- D. 1 / [1+Gc2Gp2+Gc1Gc2Gp1Gp2]
Official answer: −Gc2Gp1 / [1+Gc2Gp2+Gc1Gc2Gp1]
Why
GATE 2024 official key: (C). With y1sp=0, tracing the secondary loop error e2=−Gc1y1−y2, u=Gc2e2, y2=Gp2u+d, y1=Gp1u, and eliminating u and y2 gives y1/d = −Gc2Gp1/(1+Gc2Gp2+Gc1Gc2Gp1).
Explanation cross-checked for consistency. Final answer matches the official IIT answer key.