I just selected a region of your data that makes a model that “could” work.
The “could” is in quotes because your test data is quite “dirty”, meaning that you have a lot of disturbances going on while you are making the test.
In order to get a proper model (and better PID tuning) try to do the test without such disturbances. The disturbances are clearly observable at the end of your est where you do not have any movements on the process input, yet the process output displays fluctuations that are not correlated to the input. These are disturbances, you must identify them and try to reduce them at least temporarily as much as possible for the test.
