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

and that of the controller is

The transport of the feed along the conveyor requires a transport (or delay) time, T = 1.5 s. (a) Sketch the Bode diagram when K₁ = K₂ = 1, and investigate the stability of the system, (b) Sketch the Bode diagram when K₁ = 0.1 and K₂ = 0.04, and investigate the stability of the system, (c) When K₁ = 0, use the Nyquist criterion to calculate the maximum allowable gain K₂ for the system to remain stable.