Feedback Control of Attitude using Quaternions

I have a quaternion state space model of an aircraft and I can apply moments in the body frame to control its attitude.

So I have a quaternion state, a desired quaternion state and want use an lqr regulator to control the system.

My question is how do I define the error for the feedback controller? Is it ok to just just use the difference between each of the quaternion vector elements?

[Ryan G]

The main issue I see doing this is how do you determine the control to move when you have a quaternion error. For example, in an airplane, I know if my roll, phi, has an error I want to move the ailerons to remove the error and my control system is designed knowing this. If I have a quaternion error I would have to map the quaternions to the surfaces to determine where I what surfaces a I want to move based on a quaternion error.

You may be able to sort this out with the resulting command signals from the LQR. I haven't personally done it though.

[Deepana]

I guess there s a separate formulae for quaternion error calculation..i used separate formulae for error caln for attitude feedback control.