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4th order polynomial coefficients for pressure at temperature readings, Help!!!

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itsbiodiversity:
I am working with an instrument that contains an RTD to account for temperature in precise pressure measurements. The designer used a fourth order polynomial to calculate correction factors a0, a1, a2, a3, and a4. Pressure readings of a standard (STD) versus a unit under test (UUT) are taken at multiple temperatures (3 temperatures) related to an ADC Count Value (3 count settings, directly correlating to temperature). Pressure readings are taken from a low range to a high range at each temperature. Can anyone help direct me to how to calculate these coefficients? I can provide an excel sheet with data if it helps. Thanks so much.  Data presented below for copy/paste, but an excel sheet is shared below.  Any help would be appreciated.

psi   °C   Counts  uut
-15   15   5485   -15.017
-13   15   5485   -13.014
-11   15   5485   -11.011
-9   15   5485   -9.01
-7   15   5485   -7.008
-5   15   5485   -5.006
-3   15   5485   -3.004
-2   15   5485   -2.002
0   15   5485   0
2   15   5485   2.001
3   15   5485   3.002
5   15   5485   5.004
7   15   5485   7.006
9   15   5485   9.007
11   15   5485   11.008
13   15   5485   13.008
15   15   5485   15.008
-15   21   7386   -15
-13   21   7386   -13
-11   21   7386   -11
-9   21   7386   -9
-7   21   7386   -7
-5   21   7386   -5
-3   21   7386   -3
-2   21   7386   -2
0   21   7386   0
2   21   7386   2
3   21   7386   3
5   21   7386   5
7   21   7386   7
9   21   7386   9
11   21   7386   11
13   21   7386   13
15   21   7386   15
-15   28   9471   -14.99
-13   28   9471   -12.991
-11   28   9471   -10.993
-9   28   9471   -8.994
-7   28   9471   -6.996
-5   28   9471   -4.997
-3   28   9471   -2.998
-2   28   9471   -1.999
0   28   9471   0
2   28   9471   1.999
3   28   9471   2.998
5   28   9471   4.997
7   28   9471   6.996
9   28   9471   8.996
11   28   9471   10.996
13   28   9471   12.996
15   28   9471   14.996

ahbushnell:
You can calculate the polynomial or use a lookup table.  Is it a PT100 RTD?  That means it's a nominal 100 ohm resistance.  There is also PT1000 but not common.


I would suggest a lookup table unless floating point is not a problem. 


Omega has information on RTD's.  Here are some links.
https://www.omega.com/en-us/resources/rtd-resistance-elements-principles
https://www.omega.com/en-us/resources/temperature-transmitter-scaling-methodologies
https://www.omega.com/en-us/resources/rtd-hub
European table (more common)
https://assets.omega.com/pdf/tables_and_graphs/thermistor-resistance-europe.pdf
USA table
https://assets.omega.com/pdf/tables_and_graphs/thermistor-resistance-us.pdf


itsbiodiversity:
It is a pt100 rtd.  I corrected the actual RTD measurement already.  This is specifically a correction for the pressure at the multiple temperatures across the range of pressure.  I am not looking to calibrate the RTD, I am looking to use the variation in pressure at temperatures not standard to develop a correction curve.  If the unit reads -15.036 psi at 0 °C, -15 at 20 °C, and -15.001 and 28 °C, for instance, to correct for those values.  The problem I have is that I have data points where the variation differs (see attached excel file).  I hope any of this makes sense.

itsbiodiversity:
You know that is how I'm confused as well.  I am starting to think someone left a vital piece of the puzzle out to make this difficult for future discoverers. 

I hope this helps,
but I am trying to develop the coefficients by comparing the Standard psi to the UUT psi at multiple temperatures. At Standard temperature the coefficient is 1 (a2), it has to be.  I am trying to calculate the other correction coefficients for the cold and warm temperature pressure corrections.

End result, correlation coefficients for psi corrections to the uut at applied ADC temperature and applied PSI to pressure sensor.

itsbiodiversity:
I believe x is (column a) and y is (column d), but at said Temperature (column b) and adc counts (column c).

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