Level $(h)$ in a steam boiler is controlled by manipulating the flow rate $(F)$ of the make-up (fresh) water using a proportional (P) controller. The transfer function between the output and the manipulated input is
$$\frac{h(s)}{F(s)}=\frac{0.25(1-s)}{s(2 s+1)} .$$
The measurement and valve transfer functions are both equal to $1.$ A process engineer wants to tune the controller so that the closed-loop response gives decaying oscillations under servo mode. Which one of the following is the $\text{CORRECT}$ value of the controller gain to be used by the engineer?
- $0.25$
- $2$
- $4$
- $6$