This is a good description of the problem, but I would hazard to say that it’s less about the PID controller and more about what the PID controller is solving for and what it’s using for feedback.
In a system like this I’m imagining that the controller has some sense as to what the passengers in the seats are doing. The controller is probably then solving for a braking curve that minimizes deceleration in the passenger while also minimizing stopping distance.
A good human driver does this naturally. They will feather their braking to the point just before feeling themselves break away from the back seat. If they break too hard and release too hard and the passenger lurches, it’s uncomfortable and anxiety producing.
(Edit: @VeronicaConnor goes over this in more detail above.)
