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How to find the TF of a House Heating System. (New and I need help)

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I would appreciate if somebody could explain me, how can I find the Transfer Function from the Heating System below?
I don't know how to start it, I don't know how to start thinking of starting this.
"In the House Heating System below, we insert a Step change from 0 to a Maximum Heating Power of 100kW.
At the same time, we monitor the increase in Temperature.
The Initial Temperature was 283K and the Final Temperature is 303K.
It took 3.33 hours to reach the Final Temperature.
The Thermal Capacity of the house is C = 15*10^6.
Find the Transfer Function and confirm it with Step in Matlab."
  4 Commenti
Bob
Bob il 29 Mar 2021
L [ C * dTin/dt ] = L [ Win - k*(Tin - Tout) ]

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Star Strider
Star Strider il 29 Mar 2021
This is actually easier to do by hand:
syms C Tin(t) Win k Tout(t) s H(s)
Eqn = C*diff(Tin) == Win - k*(Tin - Tout)
LEqn = laplace(Eqn)
LEqn = subs(LEqn, {laplace(Tin(t), t, s), laplace(Tout(t), t, s)}, {Tin(s),Tout(s)})
LEqn = expand(LEqn/Tin(s))
LEqn = subs(LEqn, {Tout(s)/Tin(s)}, {H(s)})
LEqn = isolate(LEqn, H(s))

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