Logic for scaling more than two coordinates required

hajdeen82 · Jul 11, 2008

Hi

I want to generate a code for a scaling of x,y table,like what we do in analog input scaling of PLC's. Normally for analog inputs we have two co-ordinates. But in my case it is like this

X Y
0 0
325 340
360 360
From this data for each value of X given as input, the corresponding y value should be the output.

Could anyone help please

OZEE · Jul 11, 2008

Well, technically that isn't scaling because it isn't linear. What you have would be more of a computed value. You'll need to figure out what the curve would be, then program that in to a compute command. To calculate the curve equation accurately, you're going to need more points.

Or just put in one big massive array and do a lookup...

hajdeen82 · Jul 11, 2008

hi
in my case i can write a logic if my co-ordinates are only 2 using y=mx+c i.e
X Y
0 0
325 340

The output will be corresponding to the input of X,but i'm looking for some logic where i can insert the 3rd co-ordinate as well

CharlesM · Jul 11, 2008

No help from me

I have seen this done with scales. They call it a 3 point cal. I don't know how to do it but I would like to find out.

Ken Moore · Jul 11, 2008

If you have several x,y points (the more the better) you can use a spread sheet to generate the expression for you. Something like

Y= 2x^2 + 7x - 256

DanYost · Jul 11, 2008

If it is linear between the 3 points (I.E. linear between 0,0 - 325,340 and linear between 325,340 - 360,360) or you aren't too concerned about accuracy, you can just check if the input is over 325. If is is NOT then use y = mx where m=(340/325). If it is greater then use y = ((x-325)*20)/35 + 340.

For increased accuracy (more of a curve) just use more points. Here is how it is done in C:

int i = 1;
float PVSpan, InputSpan;

// Readings is an array of known inputs
// Gallons is an array of known outputs
// Input is the actual input reading

while((Input > Readings) && (Readings != 0)) i ++;

if(Input == Readings)
return Gallons + Offset;

else
{
PVSpan = Gallons - Gallons[i-1];
InputSpan = Readings - Readings[i-1];
if(InputSpan > 0)
return MulDivF((Input - Readings[i-1]), PVSpan, InputSpan) + Gallons[i-1] + Offset;
else
return Gallons[i-1] + Offset;
}

Hopefully that helps. FYI, MulDiv(a, b, c) is (a*b)/c. MulDivF is the same but uses floating point math.

Regards,
Dan

Tom Jenkins · Jul 11, 2008

You are going to need more points, but you can get the equation for any data set using Excel charts.

Enter your data in two columns, highlight them, and insert a chart. Use an X-Y type chart. After you have the chart showing in the spreadsheet click on the data and select "Add Trendline". Check the options for show equation on chart, and show R-squared value (this indicates how close your equation matches the data 1 = perfect). I usually use a polynomial, but you can pick whatever seems to best suit your data. Click OK and voila - your equation shows on the chart. For polynomial you can keep increasing the order until you get a good fit. I also format the numbers to get enough decimal places for accuracy.

Peter Nachtwey · Jul 11, 2008

It looks like Hajdeen82 has the generated the Friday night math quiz.

Let's see if one of the five usual contestants win.
Hint, this has been covered before.

edit
Tom, you are no fun

TConnolly · Jul 11, 2008

After you have the polynomial don't use exponents when programming the polynomial. Expand out the polynomiall using the form

Ax³ + Bx² + C^x + D = (Ax +B)x +C)x + D

Exponential operations take quite a bit longer to execute than successive multiplies.

Mickey · Jul 11, 2008

And some free software to do it for you.

http://curveexpert.webhop.net/

Peter Nachtwey · Jul 11, 2008

Hey guys, I think you missed the point. I think I did at first

Scilab code

A=[1,0,0;1,325,325^2;1,360,360^2];
B=[0;340;360];
x=inv(A'*A)*A'*y

// Verify A*x=B
A*x

-->x
x =

- 9.719D-15 // close to 0
1.4747253
- 0.0013187

-->A*x
ans =

- 9.719D-15 // Close to 0
340.
360.

What I think hajdeen82 wants to do is generate the code so that given 3 points he can find the coefficients of an equation.

I would assume the equation would have the same form as what Alaric posted. So how does one calculate A B and C in ladder?

Tom Jenkins · Jul 11, 2008

Peter Nachtwey said:
Tom, you are no fun

That's funny, my wife says the same thing!

TConnolly · Jul 11, 2008

Alaric said:
Ax³ + Bx² + C^x + D = (Ax +B)x +C)x + D

I see I messed up the the superscript codes in my previous equation. It should read this way:

Ax³ + Bx² + Cx + D = (Ax +B)x +C)x + D

edit:
Here is a snip of code from a control logix add on instruction I wrote to linearize the input from an S type thermocouple transmitter. The transmitter does not do the linearizing. I use four different polynomials depending on the input value, in this case the 4-20mA input was previously scaled to the mV range of the TC.

Code:

[/size]
IF X < 1.874 Then 
Y := (((((((((((((((((2.797863 * X) - 23.41819) * X) + 82.30279) * X) - 159.0859) * X) + 188.8214) * X ) - 152.2486 ) * X) + 102.2374 ) * X) - 80.05041 ) * X) + 184.9495 ) * X);
ElsIf X < 10.4 Then 
	Y := (((((((((((((((((8.211273E-009 * X) - 1.44738E-007 ) * X) + 2.183475E-005) * X) - 0.001291638) * X) + 0.03187964) * X) - 0.4163258) * X) + 3.145946) * X) - 15.34713) * X) + 146.6299) * X) + 12.91507;
ElsIf X < 17.536 Then
	Y := (((((((((0.0002081619 * X) - 0.01441694) * X) + 0.4719687) * X) - 8.536869) * X) + 162.1573) * X) - 80.87801;
Else
Y := (((((((0.6247205 * X) - 42.65694) * X) + 1092.658) * X) - 12358.92) * X) + 53338.75; 
End_IF;

Peter Nachtwey · Jul 11, 2008

There are only three points ( knowns ) so the equation can have only three unknowns.

The equation I provided above will generate coefficients for 'over determined' systems. That is one where there are more points or knowns than coefficients or unknowns.

This still doesn't answer the OPs question about doing it in ladder.

ndzied1 · Jul 11, 2008

Peter Nachtwey said:
What I think hajdeen82 wants to do is generate the code so that given 3 points he can find the coefficients of an equation.

The problem is that hajdeen82 hasn't piped back in here to let us know what he really wants/needs.

My thought was that it is a simple two step scaling.

Below a certain value, follow one slope and above it follow another. My German friends call this a Knee-curve.

It would be nice to know what the process and hardware involved is so a better answer can be given.

Logic for scaling more than two coordinates required

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