Consider three identical non-interacting first order processes in series, each having unit gain and a time constant of $2$ min. Tuning of 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)?
- $4 \sqrt{3} \pi$
- $\dfrac{\sqrt{3} \pi}{4}$
- $\dfrac{4 \pi}{\sqrt{3}}$
- $\dfrac{\pi}{4 \sqrt{3}}$
