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So I'm trying to identify the model of a simple system (I'm pouring hot water (m [kg/s] into a water tank and displace the colder water inside) in order to tune a PID controller. I performed a doublet test and have the resulting data in this file (first column is time, second one the inout, third one the output). This is the plotted data:

enter image description here

Now I want to fit a function to this in order to derive the parameters $K_p$, $\tau_p$, and $\theta_p$ (which can be used to calculate the tuning parameters for a PID controller). However, I don't really know how to approach this. I've found a script but for some reason, the result is unusable ("optimized function" is pretty much just a straight line).

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