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Is it me or does AS hug the wrong side of a turn?

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AS works fairly well on the freeway (best lane is the middle lane on a 3-lanes each way freeway so there's little merging into and out of the lane by others, etc.). But since I got the car in June, AS always moves to the outside of a turn, especially when the road turns right. It gets fairly close to the left lines (over the weekend it actually was turning so wide that it actually ran over a couple of line reflectors on the road centerline (no glare, overcast but otherwise good visibility). I find that when it goes to the left side of a right turn, it stays in that uncomfortable position throughout the turn, and when the road straightens, it over-corrects by moving past the center to the right side, and then re-centers itself. Granted, these are tighter turns at lower speeds (turns normally done at 45mph or so vs 70mph turns on an interstate).

Because of this, I sometimes inadvertently disengage AS because I'm turning the wheel before the car wants to. At a minimum, I would expect it to stay centered, but a more realistic path would be to slightly hug the inside of each turn (starting the turn earlier rather than later).

Is all of this normal? If so then AS is really only for almost completely straight freeways (while I don't have FSD, I would assume AS and FSD acts the same in these types of scenarios).

As a side note, I do occasionally get phantom braking, but I assume that will happen the same whether you have AS on or just adaptive cruise control on.
 
FSD beta on two lane country roads like to stay very close to the center double yellow. It makes me uncomfortable. To me it should stay in the middle or just off to the right. If it were any closer to the center lines it would hit the rumble strips. It does well for me but it makes me on edge.