Consider three identical non-interacting first order processes in series, each having unit gain and a time constant of 2 min. Tuning of a proportional controller using closed loop Ziegler-Nichols technique is considered. Which one of the following is the ultimate period of sustained cycling (in min per cycle)?

Question

Accepted Answer

The correct answer is C, 4π / √3. GATE 2026 official key: (C). For 3 identical first-order lags in series, 3·arctan(ωτ) = 180° gives ωτ = √3, ω = √3/τ. With τ = 2 min, the ultimate period Pu = 2π/ω = 4π/√3 min/cycle.