A control system for a chemical concentration control system is shown in Figure P9.11. The system receives a granular feed of varying composition, and we want to maintain a constant composition of the output mixture by adjusting the feed-flow valve. The transfer function of the tank and output valve is
$$
G(s)=\frac{5}{5 s+1},
$$
and that of the controller is
$$
G_c(s)=K_1+\frac{K_2}{s} .
$$
The transport of the feed along the conveyor requires a transport (or delay) time, $T=1.5 \mathrm{~s}$. (a) Sketch the Bode diagram when $K_1=K_2=1$, and investigate the stability of the system. (b) Sketch the Bode diagram when $K_1=0.1$ and $K_2=0.04$, and investigate the stability of the system. (c) When $K_1=0$, use the Nyquist criterion to calculate the maximum allowable gain $K_2$ for the system to remain stable.