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Need help interpreting questions

Can some one explain to me how to interpret these kind of questions? I am preparing for a 3 hour electrical test with Valero.

What is the proportional band if a step change in the level of 3" causes an output change of the controller to go from 12 psi to 7.2 psi, in the first instant of time?

Given:
LT: 0"-12"@ 3psi - 27 psi
Controller:
Output = 3 psi - 27 psi
MPR = .5
Set Point = 7"

Start with the needed result and work backward. You are often given more information than required, or need to massage (intermediate calculations) the information given.

Since you are asked for Proportional Band (PB), start with that equation, which is PB(%) = 100/GAIN. To obtain gain, you need to determine the input and output changes (GAIN = OUTPUT/INPUT). In this case, the output would be level change, while the input would be pressure change to the level control valve (assuming a linear relationship between supply pressure and valve position).

Assuming the question is stating that level drops by 3" (to 4" from initial setpoint of 7"), the gain is [(7-4)/(12-7.2)] = 0.625, which makes the Proportional Band = (100/0.625) = 160%.

Fundamentally, that means the valve will not travel full stroke to move from 0-100% of the level control range (since PB > 100%).