This is because it's somewhat off as described above. Compounded with the 111's slower control response it might end up over-shooting the heading it tries to achieve, which initiates another turn that overshoots again and so on.
It could also be a case of the gyroscopes needing some time to align.
However, it works fine in the 110 even if the desired heading is still a bit off. I've found out that i can set it reasonably well and have it stay level upon engaging the autopilot, because i got used to the amount of offset as it's displayed on the instrument (i let it settle a few times on different headings as a test and i found out it's always off by approximately the same amount of degrees).
Since the desired heading compass card is off, you will need to input a "wrong" desired heading, altered by the same amount of degrees that the system is inaccurate, to compensate for the error and keep the plane from drifting. As an example, let's say you are flying due north and you want to engage the autopilot, it should look something like this:
---330---N---30--- (actual heading)
-----330---N---30--- (desired heading with corrective offset incorporated)
It's about 5-7 degrees offset, but if you set it like this it's almost dead on and takes no time to stabilize (in the 110 at least). From that point on, you ignore the read-out of the desired heading compass card and fly by the actual heading, commanding turns by altering desired heading by the amount of degrees you want to turn (it's like steering the plane with a console/joypad controller from that point on). The read-outs might be different but the differences between headings are the same, so if i want to turn 10 degrees left based on the directional gyro/actual heading, i can simply reduce the desired heading by 10 degrees and it will correctly turn to where i want it.
Hope it helps.
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