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 gain of the transfer function between the plant output and an additive load disturbance input of frequency $2\pi /T_u$ in closed loop with a $\text{P}$-controller designed according to the Ziegler-Nichols tuning rule as given above is
- $-1.0$
- $0.5$
- $1.0$
- $2.0$