Consider: if you were given a freeze-frame view of the car in the exact right spot, what controls would you send it to keep it there? It'd be impossible to say without knowing the car's velocity - if the car was in the process of reversing, it should apply forwards acceleration to come to a stop, but if it was in the process of going forwards it should apply reverse acceleration.
The solution is to add Derivative control. This would look like a second set of inputs to the system comprised of the difference between the current measurements and the prior ones.