I would venture that
as
@Tom.G suggested
y = mx + b is the right approach.
I'd make y be output milliamps
and x be input bars.
so as to make the independent variable, pressure, plot on the X axis
and the dependent one , milliamps, on the y axis.
x and m and b are not simple single term constants though.
Look at the units - we have to get from psi to ma,
so m will be the product of at least two individual m's -
one for units conversion let's call it m
units
and another for controller gain which is 1/(proportional band) let's call it m
gain
and m's sign will reflect direct or reverse acting..
Next, since controllers operate on an error signal, namely difference between input and setpoint,
input x will be that difference namely (pressure - setpoint)
so x = (bars - setpoint)
lastly b will take care of the 4ma offset in controller output.
But there's a sneaky little fact not mentioned in the problem statement, namely,
... in the absence of directions to the contrary you set up controllers so they have 50% output at zero error
that way they'll control somewhere around mid output and not bang against a limit.
so our b term also takes care of the fact that at zero error, ie x = zero,. the controller's output will be 50% or 12 ma.
meaning b is 12 ma not the 4 you'd likely think. .
y = m
units X m
gain X (input - setpoint) + 12 milliamps
so let's step through what we know
David J said:
A 5 to 20 bar reverse acting proportional pressure controller has an output of 4 – 20 mA.
..
He didn't state at what proportional band that relation holds so let us assume it's at pb of 100%, meaning it take a fullscale change at input to cause a fullscale change at output.
So, m
units = Δoutput / Δinput = 16 ma / 15 bar
Furthermore, since it's reverse acting, ie increasing input causes decreasing output,
Δ's in numerator and denominator have opposite signs
meaning m
units must be negative.
So m
units = -(16/15) ma / bar .
The set point is 11 bar. Determine:
aha ! Error then will be (pressure -11) bars and that's x .
x = (bars - 11)
(a) The measured value pressure which gives an output of 15 mA when the proportional band setting of the controller is 40%
Great ! He's told us pb is 0.4 which is 1/(controller gain),
That makes m
gain =2.5 ,
and m = m
units X m
gain = -16/15 X 2.5 = = -8/3
and x = pressure - 11
Now y = mx + b
and y = 15
so
15 = -8/3 X (bars-11) + 12
(15-12) X 3/8 = -(bars - 11)
9/8 = 11 - bars
bars = 11 - 9/8 = 9.875
(b) The proportional band setting which will give an output of 8 mA when the measured value is 14 bar and the desired value is 11 bar
okay,
y = 8
x is (bars - setpoint) = (14-11) = 3
b is 12 as before
solving y = mx + b for m
8 = m X 3 + 12
(8 -12 ) / 3 = m = -4/3
since m = m
units X m
gain
m
gain = m / m
units = ( -4/3 ) / (-16/15) = 5/4 ,
so pb = 1/m
gain = 1/(5/4)= 0.8 = 80%
[ it's latei= --- i hope i didnt bungle my arithmetic. ]Does above make sense ?
There's no step that is complicated. Just you have to be meticulous.
let me know if you find a mistake.
old jim