Bronkhorst E-7000 - Manual (Page 63)

BRONKHORST HIGH-TECH B.V.
9.17.004 page 63
4.11 Calibration with polynomial functions
4.11.1 General information
A normally calibrated device will have a linearized transfer function. This means that real flow/pressure and
setpoint are proportional to the output signal.
A polynomial function is a method of approximation which mathematically describes a continues transfer
function.
By means of a few samples, a polynomial function can be obtained.
After determining the polynomial function, the original calibration points and an infinite amount of values in
between, can be calculated with high accuracy.
In a system where pressure- and/or flow meters and -controllers should be readout and set with high
accuracy, these polynomial functions often are used for approximation of their transfer function. For instance
the function which describes the relation between output signal and measured flow.
4.11.2 General form
The general form of a polynomial function of the n-nd degree is as follows:
Y = a0 + a1 · X + a2 · X
2
+ a3 · X
3
+ ……+ an · X
n
Where 'a0' to 'an' are polynomial parameters, which can be calculated.
When you have 'n + 1' measure-points, they can be approximated by means of a 'n-nd' degree polynomial
function.
4.11.3 Polynomial functions of sensor signal and setpoint
By means of a calibration at Bronkhorst High-Tech B.V. several measure points will be used to obtain a
polynomial function.
The form of this function is:
Y = a + b · X + c · X
2
+ d · X
3
In which 'Y' is the measured value and 'X' is the value of output signal.
Characters 'a - d' are polynomial parameters, which can be obtained by a mathematical program. These
parameters can be filled in and the polynomial function is completed.
4.11.4 Presentation of parameters
Parameters 'a - d' are polynomial function parameters, which can be obtained with a mathematical program
out of measured calibration points.
All parameters will be presented in scientific notation with 5 significant digits, where the last digit is obtained
by rounding-off.
Example (unscaled):
a = -2.1899 E-03
b = +9.7442 E-01
c = +8.9309 E-02
d = -5.9906 E-02
Polynomial function for sensor signal:
Y = -2.1899 · 10
-3
+ 9.7442 · 10
-1
· X + 8.9309 · 10
-2
· X
2
- 5.9906 · 10
-2
· X
3