Consider a plant with the transfer function $G(s)=1/(s+1)^3.$ Let $K_u$ and $T_u$ be the ultimate gain and ultimate period corresponding to the frequency response based closed loop Ziegler-Nichols cycling method, respectively. The Ziegler-Nichols tuning rule for a $\text{p}$-controller is given as : $K=0.5\;K_u.$
The values of $K_u$ and $T_u,$ respectively, are
- $2\sqrt{2}$ and $2\pi$
- $8$ and $2\pi$
- $8$ and $2\pi /\sqrt{3}$
- $2\sqrt{2}$ and $2\pi /\sqrt{3}$