After flying for an hour or so autopilot starts to sway / oscillate left and right along the GPS course while using NAV
(86) Autopilot oscillation - YouTube
Use NAV on auto pilot for extended period of time, if you increase sim rate the plane flies wider and wider arcs as you increase sim rate.
This is something I noticed a couple of months ago, but blamed sim rate, I have now noticed it during normal speed flight.
Microsoft Store version
Auto pilot heading doesn’t do this - I have experienced this on multiple aircraft
Check your general options, set your Flight model to Modern… Don’t use Legacy.
I’ve not tried the Legacy flight model, always been set to Modern
Did you check it just to be sure anyway? MSFS is notorious for changing settings on its own without you knowing.
This is a known problem that’s particularly bad with the Citation Longitude. There are multiple past threads on the problem, but it’s never been resolved on Asobo’s end.
As mentioned, if you switch to HDG mode it won’t oscillate – however it also won’t compensate for wind, so you will have to adjust the heading manually. 
I’ve heard it’s most pronounced under heavy crosswinds at high altitude, so switching off live weather and disabling winds may or may not help (I have not tested this myself).
I’ve checked and still on Modern flight model.
I’ve always avoided live weather / traffic etc as it seems to cause stutters and crashes.
I don’t like switching to heading mode really, would rather it worked 
I did try and find topics on this, but only found one on A320neo and it was closed out as “resolved”
If you search specifically for “Citation Longitude oscillation” several threads should show up:
https://forums.flightsimulator.com/search?q=citation%20longitude%20oscillation
Sorry not used these forums much so far and was searching “autopilot oscillates” need to get better at searching
No worries, the search is sometimes weirdly specific to which keywords you do/don’t use. 
What is most common in this situation is drift because of wind speeds, while Autopilot will make sure you stay on course and arrive at the destination you have set it doesnt correct for windspeed pushing it off the path, sure it will correct so it stays on course and so it reaches the correct destination set but doesnt correct so it stays on a straight line.
Seen as the FMS and Garmin detect the wind, that is a very frustrating bug that I wouldn’t have though is too hard to fix.
Does seem odd that it only appears to happen after the flight has been in progress for a while though.
Maybe linked to flight data accumulation? or Memory issues? I don’t know theorising in my head here.
thanks for all your replies 
I’m going to try this:
Unfortunately this won’t work for people on Xbox. Asobo would have to go in and fix it for us
On Xbox, the Citation Longitude autopilot makes you sea sick. 
It continuously oscillates left and right at higher speeds and altitudes (I don’t know whether speed or altitude is the main factor here, that would require more testing). It’s annoying. And it’s quite disappointing that after all this time it has never been fixed, especially being part of the most expensive edition.
It appears to me like sim auto pilot update speed.
Say it only checks the course every 2 seconds, and then over corrects, overshoots then another 2 seconds to correct.
It is then exacerbated by increasing sim rate but still 2 second update, and before you know it you’re doing S curves and out of fuel
It appears to me like sim auto pilot update speed.
Say it only checks the course every 2 seconds, and then over corrects, overshoots then another 2 seconds to correct.
It is then exacerbated by increasing sim rate but still 2 second update, and before you know it you’re doing S curves and out of fuel
The Autopilot system uses a Proportional, Integral, Derivative (PID) control loop equation. Basically, it looks at where you are and stears the plane to towards where it is supposed to be. The oscillation or swaying that you see is the result of the PID controller not being properly tuned. It goes past the nav course then it has to turn back to try to get back on course and passes it again. In controls this problem can be fixed by adjusting the values of the controller to get the desired result. It isn’t hard to fix if you know how to tune a PID controller.