P9.11 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 transport of the feed along the conveyor requires a transport (or delay) time, T = 1.5 s.

(a) Sketch the Bode plot when K1 = K2 = 1, and investigate the stability of the system.

(b) Sketch the Bode plot 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.

Feed Desired Controller concentration Ge(s) 0000000 Conveyor Measurement of concentration FIGURE P9.11 R(s) K+ Controller K Conveyor Tank 5 S 5s+1 Y(s) Composition Chemical concentration control.