Okey, so that is how it works.
I have an idea for a, I believe, better tuning scheme.
In stead of doing a shortcut in system identification (which relay tuning is by sampling the Nyquist plot), find the the "true" model:
where L is the length to the rotational center, A_F is the thrust coefficient for the motors and w_max is the maximum angular rate of the motors.
By baking all the constants together and replacing the two squared throttles as a differential throttle we get:
And the parameter beta is observable as long as u_d is not equal to zero.
Then it-s just to make an observer for it of personal choice. Anything from a least squares (batch processing) to gradient descent to Kalman Filter (recursive) would to the trick.
And when beta has been identified, any way of calculating controller gains can be used. Since we now "know" the system.
I was planning on testing this om my system quite soon, but perhaps you will have use of it before me.
What do you think about this approach? Then any control signal (more or less) in will identify the system.