Calibration - resistance
270 Ohm - 253 = -6%
1k2 Ohm - 1188 = -1%
15kOhm - 15000 = 0%
120kOhm - 114503 = -5%
With 5% resistors, I think this is pretty good; probably the error is distributed between my measurement and the resistor error
Programming the temperature gradient
As stated in my previous post, I was modelling the temperature gradient in the egg as a linear model, represented by thermal resistance and thermal capacity. I 'guestimated' the time constants in a simulation in LTSpice:
Good results, now I have to program this circuit in the microcontroller. I didn't want to dive into theory of differential equation solving by hand, so I calculated a 'crude' solution; every two seconds I calculate the current through the resistors based on the calculated 'temperature/voltages' of the previous sample. I then use these currents to calculate the new voltages on the capacitors.
This is a bit inaccurate, especially for fast changing temperatures, but I guess that won't be a problem in this case. To proof whether my method made sense I first programmed it in a spreadsheet (see formula in box: calculate currents, integrate this over capacitor):
I checked these values (also after 300 seconds) and they corresponded nicely with the values from the simulation. This is what it became in code:
#define RTH_WHITE 25.0
#define CTH_WHITE 4.0
#define RTH_YOLK 17.0
#define CTH_YOLK 3.0
#define TSTART_EGG 20.0
struct egg_s
{
float tyolk;
float twhite;
};
void CalculateTyolk(struct egg_s *egg, float twater)
{
float tyolk_new, twhite_new;
twhite_new = egg->twhite + ((((twater - egg->twhite)/RTH_WHITE)-((egg->twhite - egg->tyolk)/RTH_YOLK))*(1/CTH_WHITE)*2);
tyolk_new = egg->tyolk + (((egg->twhite- egg->tyolk)/RTH_YOLK) * (1/CTH_YOLK) * 2);
egg->tyolk = tyolk_new;
egg->twhite = twhite_new;
}
Preliminary results
I tested this code last weekend, and it worked reasonably well for the amount of estimation I used. The problem I found was that the cooking point was at 108 degrees Celsius... The Netherlands are below sea level, but pressure is not that high.... One of the reasons is the 'simple' beta value calculation I used: here a plot of the values, again from a spreadsheet; the plot shows the error. The simplified formula is good around 25 degrees, but not at the extremes. I can change the formula to 'shift' the error to another point, and I'm going to check what the temperature sensors' resistance is at those extremes.
Energy usage
Click on the image to see in real size; in the status bar you can see that one sample costs 217microjoule, with an average usage of 31uA.