Non-linear level measurements

Greetings!

I have a assignment where i have to solve a non-linear level measurement with the use of trend line. I have a tank table showing liters on different levels.

The level is close to linear up to about half the tank, then it flats out more and more. I was not able to make a 2nd polynomial scaling that worked in all of the curve.

If i split the table in two on the middle, and run a polynomial trend line of the two halves seperatly i got something that worked on the entire tank. Minus the very lowest and highest points (doesnt matter, filter that out)

If tank level is below half, run the ladder formula with first set of coefficients and constant, if over half run the second set in the ladder formula.

Is this a efficient solution or am i overthinking this? Whats your best practice for non-linear scaling?

Look-up table with linear interpolation between points.

Yes, lookup table => FGEN instruction (for Logix 5000; FB and ST; not ladder):



https://literature.rockwellautomati...[{"num":170,"gen":0},{"name":"XYZ"},52,245,0]

Im using a basic ladder program, no function or function blocks like that. I have to write all the calculations..

do as L D[AR2,P#0.0] says


say 10% = 7mA and 15% = 8ma


If analog input = 7mA then level =10%
If analog input = 8mA then level =15%


If analog input >7 and < 8 then divide the amount between 7 and 8 into the amount between 10 and 15

Many years ago we had a similar problem, the vessel was non linear i.e. a cone from bottom to half way up we created a table and split it into 100 segments, each segment in the table contained the diameter of the vessel, from that we could calculate the volume of each segment and add them up.
It will depend if the vessel is round or square though.

Varri said:

Is this a efficient solution or am i overthinking this? Whats your best practice for non-linear scaling?

Click to expand...

Greetings in return!


Maybe this is overthinking, but unless there is a lookup table instruction (e.g. FGEN in Logix 5000 for ST or FB), then any solution is going to go through these steps something like this.



I assume there a single level measured value, and there is a break point in level between the two polynomials. That single measured value needs to be broken into two values, either

• the single level value between 0 and the break point for the first polynomial and 0 for the second polynomial, when the single value is at or below the break point,
• OR
• the break point for the first polynomial, and [the single value minus the break point] for the second polynomial, when the single value is above the break point.

Then pass each of the two values as the independent argument to each polynomial to evaluate the volume in each section, then add the volumes.

The lookup table approach will do more or less the same thing, although it is using linear interpolation between the pre-computed volumes of two of several break points; it will end up spending more code and CPU finding which two break points to use, and less code and CPU interpolating, so efficiency is probably a wash.


The most important thing to do is to document clearly whichever path is taken. In fact, I would probably code it both ways, and choose the method for which the comments and code were the most easily understood.


That said, from the OP it appears that the volumes at individual levels are already available, so transcribing those into a lookup table algorithm is the quickest solution in terms of programming time; that argues that the polynomial approach is indeed overthinking. It's also easier to test.



One thing I will mention is that, in the case of a conical top above a prism bottom, where any horizontal cross-section of the top conical section is congruent that of the bottom prism, the top volume polynomial will be cubic in level, regardless of the shape of the horizontal cross-section.

It is disheartening to see that this thread has followed a profession and appropriate set of replies.

So, now I need to know if there is a cat on top of the vessel, and if the vessel is next to railroad tracks, and if when a train goes by the cats mate is on the train.

I_Automation said:

It is disheartening to see that this thread has followed a profession and appropriate set of replies.

Click to expand...

I don't see the point you are trying to make.

So, now I need to know if there is a cat on top of the vessel, and if the vessel is next to railroad tracks, and if when a train goes by the cats mate is on the train.

Click to expand...

Not very useful. You can't hear the cats growling, howling and screeching as the train goes by.



However, it would be good to know the surface area of the vessel at each level if doing level control. The gains change as a function of the level.

Peter Nachtwey said:

However, it would be good to know the surface area of the vessel at each level if doing level control. The gains change as a function of the level.

Click to expand...

That is available as dV/dh, which is a corollary of either the lookup table method (numerical) or the polynomial method (analytical).

I would calculate the volume as a function of height in Excel. Graph it and generate a polynomial equation, and use that poly equation in the plc.

OP did a polynomial, and did not think the results were good enough; maybe it needs more coefficients. Perhaps a Chebyshev approach would be better; I suspect the level vs. volume plot is not too far off a sine curve.

g.mccormick said:

I would calculate the volume as a function of height in Excel. Graph it and generate a polynomial equation, and use that poly equation in the plc.

Click to expand...

+1

For complex functions you generally need to use at least third order equations. The closer R2 is to 1 the more accurate the equation. I generally format the trend equation results in scientific notation and go out to at least five decimal places.

L D[AR2,P#0.0] is the best/easiest solution so far.
The OP's PLC probably isn't very sophisticated so simple algorithms are are probably best.



Third order polynomials can have two inflection points. Third order polynomials must be used with care. I would not try to fit one third order polynomial to the whole range.


When provided an accurate table of volume vs level, trying to fit a polynomial to the data is simply wrong because at the polynomial and the table will not match at levels where the volume is known. Using a table and linear interpolation between the points will at least be accurate at the levels where the levels are known.


There is a big difference between doing some sort of regression and interpolation with good data.


I would use third order interpolation between the middle two of four points but that is probably too difficult to implement on a simple PLC.

The answer was @#2