Feedback control scheme proportionalonly controller bias pr

Feedback control scheme, proportional-only controller & bias problem.

Consider the pressure vessel below. Draw a feedback control scheme to control the pressure in the tank. Define the control variables and elements. The pressure transmitter, PT77, has a range of 0 to 100 psig. The controller will be a proportional-only controller its bias value is set at mid-scale, and its set point is 10 psig. Obtain the correct action of the controller and the proportional band required so that when the pressure in the tank is 30 psig, the valve will be wide open.

Solution

The forces acting are the total pressures caused by the internal pressure p and the total tension in the walls T.
F=pA=pDLF=pA=pDL

T=tAwall=ttLT=tAwall=ttL

FH=0FH=0

F=2TF=2T

pDL=2(ttL)