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GATE 2025 Chemical Engineering, Q25 · Process Control

The correct answer is A, (αs + 1)e^(−θs) / [(τ₁s + 1)(τ₂s + 1)²].

Question

Choose the transfer function that best fits the output response to a unit step input change shown in the figure, where the output response shows an initial delay, then rises and overshoots before settling to the new steady state.

Figure for Q25 (Process Control, Transfer Functions): Choose the transfer function that best fits the output response to a unit step input change shown in…
  • A. (αs+1)e−θs/[(τ1s+1)(τ2s+1)2](αs + 1)e^{−θs} / [(τ₁s + 1)(τ₂s + 1)²]
  • B. (αs+1)e−θs/[(τ1s+1)(τ2s+(αs + 1)e^{−θs} / [(τ₁s + 1)(τ₂s + 1)]
  • C. (αs+1)/[(τ1s+1)(τ2s+1)2](αs + 1) / [(τ₁s + 1)(τ₂s + 1)²]
  • D. (αs+1)2e−θs/[(τ1s+1)(τ2s+1)2](αs + 1)²e^{−θs} / [(τ₁s + 1)(τ₂s + 1)²]

Official answer: (αs+1)e−θs/[(τ1s+1)(τ2s+1)2](αs + 1)e^{−θs} / [(τ₁s + 1)(τ₂s + 1)²]

Why

GATE 2025 official key: (A). The S-shaped step response with an inflection point and no initial overshoot matches a lead/lag numerator combined with dead time over a second-order-plus-repeated-pole denominator.

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

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