1. Consider the liquid level, PI control system in the following figure. The liquid level is measured and the level transmitter output is sent to a feedback controller that controls liquid level h by adjusting flow rate 92. A second inlet flow rate 91, is the disturbance variable. The liquid density p and the cross-sectional area of the tank A are constant. The flow-head relation is linear, 93 = h/R. The level transmitter, I/P transducer, and pneumatic control valve have negligible dynamics. An electronic controller with input and output in % is used (full scale=100%). P 11 92 LC 1/P h 93 a) Draw a block diagram for the system (10 Points) b) What is the closed-loop transfer function for set-point changes? (20 Points) c) Assume: A=3 ft? R=1.0 min/ft? K&=0.2 ft3/min psi, Ko=4 mA/A, K=5.33, Kyp=0.75 psi/mA, and 5=3min. Suppose that the system is initially at the nominal steady state with a liquid level of 2 ft. If the set point is suddenly changed from 2 to 3 f how long will it take the system to reach 2.5 ft and 3ft. (20 Points)