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I'm playing around with an arduino, and have build a PID controller that controls the temperature of a light bulb, measured with an NTC. All is working fine

I'm looking to get a bit more theoretical on the subject and have modeled the system in a simulink like environment. I want to be able to determine the transfer function, but am not able to do it on paper and am looking for some help on it.

The system is modeled as:

Qin-Qout=V(t)^2/R-K(T(t)-T0)=C*dT(t)/dt

K and C are determined experimentally 0.77 and 50, the resistance of the light bulb ,R, is 1 Ohm.

A transfer function G(s)=(T(s)-T0)/V(s)=1/(10s+0.154) seems to fit quite well, I'm just not sure how to get from the time based function to the transfer function.

Thanks,

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# Laplace Transform

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