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Very stable temperature control
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joeqsmith:
I was asked about the control system in a PM.  Would rather keep discussions in a public forum so others may benefit.

I posted about how I monitor the temperature in my previous post.   The PC uses this feedback to run a simple PI controller (D set to zero).  Output from the PI drives a power supply in voltage mode which in turn powers the Peltiers.   The voltage is limited to a safe operating area.   Similar to the video posted, the Peltiers are different for the two stages.  Lower power on the cold side.   It's nothing too complex.

If the goal is to run below -40 with any sort of volume and loading, I would still suggest a more conventional system.   Faster ramp times, more efficient, maybe longer life depending how you plan to use your system.  The datasheets for the Peltiers talk about their life and how they are cycled. 
HendriXML:

--- Quote from: 3roomlab on June 29, 2019, 06:25:00 am ---
--- Quote from: HendriXML on June 28, 2019, 10:02:28 am ---
The best way to use this setup is to start with boiling water and let it then cool down. The regulation will than eventually kick in. To keep the temperature stabile it needs about 2 W

--- End quote ---

if you have the temperature at x watts, you can likely estimate the RC time.
overall heat leakage (water temp - ambient temp) / watts = "C/W"
the water "thermal mass" = ((liters)*4200) = J/K
the container also have a thermal mass est about 100s of J/K
the heater and circuit also have a mass est about 50s of J/K
the 1RC time is approx = "C/W value" x "J/K value"
look like the RC is going to be in 000s of seconds

000s second damped op amp? 2RC ? or faster? 0.5RC ?

--- End quote ---
I had to think about this for a while. I see the usage of the capacitor as adding a way to store state. In this circuit it should store the avg difference voltage that is needed to counterbalance the temp leakage. By oscillating a few times it will approximate  that voltage. This will happen without problems because the heating power is low to the thermal capacity and the cooling power is even lower. Except when the capacitor gets near its max and min voltages too soon while heating and cooling. When that's the case it's "memory function" is not entirely effective anymore.
So I guess the calculation of the value of C should mainly take that into account. It is like the rough analysis I did before, but without the conclusion is should be much less than 68uF. It should be around 68uF, so the  the capacitor is kept in a more effective range of it's charging and discharging curve.
So I think half the capacitor voltage at half of the temp difference would be a good rule of thumb, when doing exact calculations -due to missing parameters- is impossible. There is for example unknown thermal resistance to the thermal mass. (And the most power will be used to heat the mass a bit more.)
If my reasoning seems broken, please let me know.
HendriXML:
Also I think the circuit can be improved by hooking up C3 after R16. Charging C3 with more voltage than what will ever be used by the following stage is not helpful in getting the balancing voltage in that cap.
It wouldn't surprise me if that would make a 10uF as C3 stabilizing as well.
HendriXML:
The modification did not mean only a 10uF cap could be used. It wasn't the heating that unbalanced things. It is the slow spread of heat to thermal mass in the cooling down cycle part. That part of the cycle is also the part that was taken in the RC analysis. Don't know whether the analysis was correct, but it seems to work.
Kleinstein:
Moving the capacitor to the other side of the resistor makes sense. It is a way to implement anti-windup. It helps for the initial approach, but no more in the final approach, when the heater no longer goes into saturation. 
The change should not effect the choice of the capacitor values.
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