A liquid vessel has an inlet and an outlet streams. The outlet stream flows through a valve having a resistance R. To control the level at a specified value a PI (Proportional-Integral) controller placed on the inlet stream is used. You have been tasked with the design of the control system.

Data: Assume that the outflow can be expressed as (/) where is the level in the surge vessel and is the valve resistance to flow. Control valve transfer function = 1 Transmitter transfer function = 1 Surge vessel area 5 m2 Liquid level 2 m Liquid flowrate 5 m3 /min.

Question: Determine the characteristic equation of the block diagram transfer function Assume that the transfer function of the PI controller is given by = (1 + (1/I))