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GATE 2024 Chemical Engineering, Q22 · Process Control

The correct answer is B, (−0.5, 0.5).

Question

Consider the block diagram in the figure with control input u, disturbance d and output y. The disturbance path is Gd =1/(s+1)2,= 1/(s+1)², the manipulated-variable path (process) is Gp =2/(0.5s+1)2,= 2/(0.5s+1)², and the feedforward controller is Gf =K[(αs+1)/(βs+1)]2.= K[(αs+1)/(βs+1)]². For perfect disturbance rejection (feedforward controller cancels the effect of d on y), the ordered pair (K, α/β)α/β) is

Figure for Q22 (Process Control, Feedforward Control): Consider the block diagram in the figure with control input u, disturbance d and output y. The distu…
  • A. (0.5, 2)
  • B. (−0.5, 0.5)
  • C. (−2, 2)
  • D. (2, 0.5)

Official answer: (−0.5, 0.5)

Why

GATE 2024 official key: (B). Perfect feedforward cancellation requires Gf·Gp + Gd =0⇒= 0 \Rightarrow Gf = −Gd/Gp =−[1/(s+1)2]/[2/(0.5s+1)2]=−(0.5s+1)2/[2(s+1)2].= −[1/(s+1)²]/[2/(0.5s+1)²] = −(0.5s+1)²/[2(s+1)²]. Matching forms gives K =−0.5,α=0.5,β=1,= −0.5, α = 0.5, β = 1, so α/β=0.5.α/β = 0.5.

Explanation cross-checked for consistency. Final answer matches the official IIT answer key.

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