AUTOPILOT PROS & CONS

Doesn't anybody do proper modelling of the aircraft behaviour (such as
is done for airliner flight simulators, in order to derive the
equations which are then solved in the sim) and check that the control
loop parameters of the AP provide a sufficient margin?

No. It's not done.

There have been too many cases of APs going unstable under certain
conditions.

I have a Twin Comanche with a Piper Autocontrol autopilot (single
axis), and I can esily force it into a divergent pitch oscillation
mode. All I have to do is let go of the controls in a trimmed
airplane, let it fall off into a spiral past about 30 degrees
(eventually it will, no matter how well trimmed and how smooth the
air), and then just turn on the autopilot in wing level mode. You
know, like pilots who lose it in IMC are told to do. The autopilot
will keep the wings level, but the plane will go into a divergent pitch
oscillation.

Gotta love it.

Michael