Bronkhorst Multibus - Manual (Page 10)

BRONKHORST ®
Page 10 Operational instructions for digital multibus instruments 9.17.023
2.4 C
ALIBRATION WITH MATHEMATICAL FUNCTIONS
2.4.1 General information
Depending on instrument and sensor type an instrument output signal is calculated with one of the following
mathematical methods:
• polynomial function
• look-up table (2 dimensions)
• look-up table with temperature compensation (3 dimensions)
2.4.2 Polynomial functions
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.
2.4.2.1 General form of a polynomial function
In mathematics, a polynomial is an expression of finite length constructed from variables (also known as in
determinates) and constants. The general form of a polynomial function of the n-th degree is as follows:
n
n
X a X a X a X a a y ⋅ + + ⋅ + ⋅ + ⋅ + = ..... 3
3
2
2 1 0
n is a non negative integer and 'a
0
' to 'a
n
' are polynomial constant coefficients. When you have 'n + 1' measure-points,
they can be approximated by means of a 'n th ' degree polynomial function.
2.4.2.2 Polynomial function of sensor signal
By means of a calibration at Bronkhorst several measured calibration points will be used to obtain a polynomial
function. The form of this function of the 3 rd degree is:
3 2 X d X c X b a Y ⋅ + ⋅ + ⋅ + =
In which 'Y' is the normalized measured value (0-1) and 'X' is the value of the sensor signal. Characters 'a - d' are
polynomial parameters, which can be obtained by a mathematical program. The polynomial parameters are calculated
in such a way that the fit error between the calibration points and the polynomial function is minimized.
2.4.3 Look-up tables
It is also possible to linearize a sensor signal is using a so called look-up table. A look-up table is a table filled with
calibration points. The embedded software inside the digital instrument calculates a continuous smooth function
which fits exactly through these calibration points. Using this method it is possible to describe any monotone rising
sensor signal curve with high accuracy.
2.4.4 General form of 2-dimensional look-up tables
The general form of a 2-dimensional look-up table is as follows:
index X Y
0 x
0
y
0
1 x
1
y
1
2 x
2
y
2
3 x
3
y
3
… … …
n x
n
y
n
In which 'Y' is the real flow value, 'X' is the value of the sensor signal and ‘index’ represents the position in the look-up
table. A Bronkhorst digital instrument can store look-up tables with a maximum of 21 calibration points.