I am a computer engineering student and currently having my undergraduate thesis. My thesis is about temperature control system of a chicken egg incubator. I searched over the internet and found this research. Please verify if i can use this transfer function for my temperature control system of an chicken egg incubation system with desired temperature of 37.8 °C.

Inside the research, the researcher calculated the transfer function from the equation Q = CT and the netwon's law of cooling and arrived at this transfer function.

Modeling the incubation temperature control system

Question 1. Is this transfer function applicable to my chicken egg incubation system?

Question 2. Is there other things to be added or considered for calculating the transfer function of a thermal system aside from what the researcher calculated?

Question 3. The paper tells us that Tau is the time it takes to achieve the maximum temperature of the incubator. I turned on the 200W heat rod in my incubator and the time it took to reach 37.8 °C is 240s. Isn't that very fast? Cause i did a simulink of this transfer function and the transient response(rise time, overshoot, settling time) is very fast compared to the real scenario. I tried 940s and its closer to the real system than 240s.


1 Answer 1


The transfer function you provide is merly a model of the egg incubation system it is not a controller. In addition a lot of assumptions are made, for instance, heat does spread evenly through the egg incubator. Heat is lost evenly throughout the egg incubator, et cetera.

The model is derived from basic heat equations, this is described in the article. Tau is the so called time constant of the system, read: https://en.wikipedia.org/wiki/Time_constant. What the time constant is depends on the thermal resistance and the heat capacity or your egg incubation system.

You can derive the time constant by of your egg incubation system by an experiment. Put a temperature sensor inside the incubation chamber and change the heat from (lets say) 20 degrees to 38.5 degrees. Monitor how the temperature changes. The time at which the temperature has reached 66% of its end value (w.r.t. to its starting value) is your time constant. In this case, it would reach 66% = 32.21 degrees ((38.5-20) * 0.66 + 20).

  • $\begingroup$ we tried the derivation of time constant with that method and found Tau = 4 minutes but it seems like wrong. its very fast. With PID, using that transfer function, we found rise time of 15 minutes. Do you know anything about this or you cant based on these post and my given? $\endgroup$
    – paulj
    Oct 15, 2016 at 17:26
  • $\begingroup$ Well if that is what you measure it must be correct right? Maybe you just have a very good heather? Or the chamber is really small compared to the one which they use in the article. Could be numerous reason why it might be faster. $\endgroup$
    – WG-
    Oct 16, 2016 at 23:00

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