Whose reallity? I calculate system models by comparing the PV with the control signal. Trial and error is not the only way. One can put some of that control theory you learned in college to use. As a bare minimum one can use the ISE or ITAE to give one an idea of how good the tuning is. Graphs of the PV as a function of the control signal are a must. Otherwise reality .....
If you have RSLogix you can do a pretty good job with the RSTrends, an excel spreadsheet ( I prefer Mathcad ) and a little knowledge.
First and second order systems can be modeled pretty easily by just looking at some graphs of the PV as a function of the control signal. I know this is covered in many test books. Basically that is all a tranfer function is. Things get messy when the mechanical guys design non-linear systems, one with too many poles, and with dead time.
We use least squared system identification to calculate a model. Actually we try to fit the data to many models and then play them back using the recorded control signal and then we compare the estimated values with the actual values. The model that generates estimated values closest to the actual values is the model we choose.
Control class in university is just to get you exposed. You have to spend much more time than just a few hours a week to get good. I do this for a living so I have many hours invested.
The point of the different spread sheets is that it show that tuning different types of systems require different techniques. What 'winds up my integrator' are all the people on the forums that think that just because they can tune a system that all system are the same and can be tuned the same way.
If you remember there are
type 0 systems ( velocity and temperature )
type 1 systems ( position )
type 2 systems ( I can't think of any now )
First order lag ( 1 real pole )
Second order lag ( 2 read poles )
Second order underdamped ( 1 complax pair of poles )
Now start mixing and matching and there are many different combinations. Each combination has a different set of formulas for calculating the closed loop gains. Yes, you can calculate the closed loop gains. You don't have to guess if you have the model.