There's a P in PIO...
Yes, and autoPILOT has a 'Pilot' in it.
As I stated earlier, it relates to PIO (but is not strictly PIO since no human hand is on the control.)
The human pilot uses variable gain strategies that can be unexpected or inconsistent, but an autopilot must follow its program.
A fly by wire aircraft is being flown by the autopilot essentially until it degrades to a flight law that is strictly pilot directed. Direct law on Airbus is such a pilot directed mode if I recall the system correctly.
Some of you may also be surprised to learn that the A320 aircraft has encountered lateral PIO on a line flight.
PIO is essentially a cliff like change in aircraft behavior that can be brought on by a number of factors. but incorrect gain in the control loop or excessive time lags at the effectors (control surfaces to you) often set it off.
For those that are curious about the subject, find a copy of "Aviation Safety and Pilot Control" published by National Academy Press, ISBN 0-309-05688-8. It is probably more understandable than the textbooks and is moderately priced.