I wrote down this model in June 2020 and gave it to a few people on the FRC Discord, and it’s been used successfully by (at least) team 5687. You can see their code here, which mostly implements this model. I figured that I should probably get around to posting it (I’ve been meaning to for about a year), in case it’s useful to anyone else.
I’m not totally sure what you mean. The model takes a control input \mathbf{u} because it’s designed to model the system under control inputs so that it can be used to design a controller.