I think that the mistake is to try to use a simple equation for a system with
several nested loops. Normally such loops are provided with multiple sources of
feedback. This makes each individual loop more ideal-like and easier to cascade.
E.g. in high performance servo controls for cnc. I do not know what happens in a
helicopter dynamically. I do not think that it so simple as to control the loops
individually and hope they do not interact. I guess in a plane of a certain size
an unexplained oscillation with a period of a few seconds would be called a
phugoid. All I could say is get a better controls book, f.ex. one about CNC
controls by Prof. B.C.Kuo and examine the control loops in it. The first type of
PID equation is never used afaik. It is seriously flawed. Also in a helo in
forward motion the tail rotor is 'shaded' and tends to waver in the turbulence
behind the fuselage. Helos that fly very stably on heading seem to have the kind
of ducted fan tail rotor. Also one can see most normal (non ducted tail non gyro
controls) helos that fly fast forward have the tail pointing out from straight
and 'leaning' into the travel wind. I suppose that the direction of leaning out
gives a kind of negative feedback that stabilizes the oscillation you saw. Maybe
a pilot could help to explain more here. I am not a pilot at all.

Peter P.


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