Archive for the math is fun Category

More useful curve fitting – temperature compensation

Posted in Linux, math is fun on February 1, 2011 by makingthingswork

One of my current projects involves making a USB bathroom scale (I’ll post details later).

So as part of the process, I’ve been collecting the data and graphing it to make sure it gives a stable reading. It’s currently sitting in the garage with a 30lb bag of concrete on it, and the readings are not stable — they vary with temperature. Good to know, but how to fix it?

Here’s a day’s worth of data:

Since the weight is constant, the only variation (i’m assuming) is due to the fluctuations in temperature. It looks like a pretty close correlation. OK so far so good.

I exported the datapoints into a text file, looking like this:

258 158
258 157.269
258 157

Then loaded up gnuplot.

First I plotted them against each other, to see if there was a strong linear correlation

gnuplot> plot './tmpwght.txt' using 1:2 with points

It seems pretty linear.. (see the combined graph below). The temperature sensor in the attiny85 has only 1C increments, and the datapoints seem to land on ‘even’ numbers more often than not, creating groups of vertical points on the graph.

I then need to find the slope of the line that best fits the curve. I’m expecting a straight line of best fit, eg y=mx+b style, so i feed that into gnuplot’s “FIT” routines

gnuplot> f(x)=a*x+b
gnuplot> fit f(x) './tmpwght.txt' via a,b
Final set of parameters
a = 1.20761
b = -152.923

so it appears theres about a 1.2:1 correlation between temperature and weight reading (‘a’ from the curve fit). Let’s check the graph

gnuplot> f(x)=a*x+b
gnuplot> a=1.20761
gnuplot> b=-152.923
gnuplot> plot './tmpwght.txt' using 1:2 with points, f(x)

The fit looks good enough to try out. Let’s see if it does what we want.

Now, to adjust the weight reading to compensate for temperature fluctuations.

Since the ratio is based on the raw reading of temperature, we need to multiply the 2 together before we do any shifting: 1.20761 * temperature. Then, we need to make the temperature reading move the opposite way, so when the temp goes up, the number goes down. This is done by subtracting it from another number. I picked 325. This should give us a value that exactly contradicts the effect the temperature had on the weight measurement.

In equation form:
offset = 325 - (1.20761 * temperature)

Then we add that offset to the weight measurement, and we should get a straight line. Let’s see:

Looks pretty straight to me. The parts that aren’t straight can probably be attributed to poor temperature sensor data, which i will try and fix, either by adding a better temp sensor, or polling more frequently and averaging results.

I like math