LINEARIZER (Cont’d)
The computer program in Appendix “C” outputs the display and process
(input) scaling points (the location of each linear segment) as a percentage of
the full scale input (eg. 0-3.333 VDC @ 0-24 ft.) and full scale display (eg.
0-1608.4 cu. ft.). To obtain the actual input and display scaling points,
multiply the respective percent of full scale values by the respective full scale
range for the input and display. “Pro 2” is then used to enter these values into
the IM unit. Certain linear sections of a given curve may have a slope which
exceeds the measuring resolution of the instrument. The effect will be an
erratic display in that part of the curve, if not corrected (generally, if slope 2
counts/mV). Correcting for this condition consists of three steps: increase
digital filtering to level 1 or level 2, decrease display resolution to 2 or 5 and/or
add dummy right hand zeros by programming 10 or 100 for “round”.
LINEAR SEGMENTING EXAMPLE
An example utilizing the program in Appendix “C” and the linearizing
feature of the IMD is given below.
It is desired to indicate the volume of a hopper used to store dry material
(sand, stone, etc.) at a brick manufacturing facility. The bottom portion of the
hopper is cone-shaped, therefore, as the level of the cone increases, the
volume increases at a non-linear rate. This relationship is expressed
mathematically by the following formula:
V=
1
|| r
2
h
3
Where ...
V = volume (of a cone) r = radius h = height
The upper portion of the hopper is a cylinder where the relationship
between the volume and the height is linear.
The indicator’s segment-linearizing option is employed to satisfy this
application. The upper portion of the hopper needs only one segment (two
scaling points). The remaining eight segments can be used for the lower
portion (cone-shaped). An ultra-sonic level transmitter with a 0-5 VDC output
corresponding to 0-36 feet is used.
The ±20 VDC range of the IMD is selected to cover the full range of the
transducer (refer to “Selecting The Input Range” section). The total height of
the hopper is 36 feet. The cone-shaped portion (non-linear) is 0-24 ft (0-3.333
VDC) with the remaining 12 ft. being linear. A resolution of 0.1 cu. ft. is desired.
The following display and process percentage tables were derived from the
computer program in Appendix “C” (Reference Appendix C section for more
details). The display and process percentage tables listed below are for the
non-linear portion only.
Number of linear segments = 8 Curve fitting error (%) = 0.4
Display Values Process Values
( % of Range) (% of Range)
0.00 0.00
1.25 25.50
6.49 41.00
15.33 54.00
27.70 65.50
43.66 76.10
63.19 86.00
86.41 95.40
100.00 100.00
Now, using the above percentages, the actual process (input) signal and display
scaling points can be calculated. For the display (output) values, simply multiply
each display percent by the full volume of the cone portion only (1608.4 cu. ft. for
the above example). For example, 1.25% x 1608.4 cu. ft. = 20.0 cu. ft., 43.66% x
1608.4 cu. ft. = 702.3 cu. ft., etc. The volume of the cylinder is calculated
separately then added to the cone to yield total hopper volume.
-27-
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