@Rariusz Thank you. I hope that you can understand why your latest reponse contains the details which ought to have been provided originally.
As is not uncommon for such kinds of nonlinear optimization problem with an oscillatory aspect, there are many local minima which are "close" to globally optimal for some reasonable objective metrics. That might be a problem.
So, in just a few minutes a worksheet of mine produces a similar plot for ode_x2 which compares quite closely to your simulation, for a fit to the theta(t) data from the third column. It uses a continuous approximation for V(t) using the data from the second column. It took me about 15 minutes to write.
But... depending on the run, and depending on the ranges I supply for the parameters, I can get several sets of results for the parameters. All produce a reasonable fit (plot) for the simulation of theta(t) and diff(theta(t),t). But the frequency of oscillation of the simulated i(t) varies a great deal, from slow to very fast.
If there is some physical reason (constraints on the motor design, etc) why a low/medium/high frequency of oscillation is needed for the simulated i(t) , or some tighter ranges for the parameters, then now would be a great time to mention it.
Additionally, it's not clear whether you need to match the highly/fast varying data for diff(theta(t),t) with a highly varying/fast simulation of that dependent quantity, or whether you would be satisfied with a a simulation that approximated a smoothed curve of that data (fourth column).