What is the stability proof for a PI controller in a formation flying system?

[fernandoz]

I have two satellites flying in formation geverned by the equations of motion including J2 and drag. Now, one of the satellites has more drag than the other so they become appart. I designed a controller (proportional integral) which meassures the along track position between them and gives Thrust values so the error, which is the difference in the along ttrack position between different orbits, will be zero (that means they will still fly in formation)
I have to give a stability proof for the controller, someone can help me? (the equations governing the system are nonlinear, of course).

thanks!

 

[RobertT]

There are various techniques to design a controller. If you want guaranteed performance try searching for Ragazzini's method and of course I'm assuming you are trying to design a discrete controller.

 

[RobertT]

If you insists on using a PI controller to see if it's stable you'll have to get the locus plot of the system (plant + controller) and see where the poles are located in the s-plane.

If you are puzzled as to why the poles' locations determine stability then you'll have to study ODE (as a good starting point) and its connection to Laplace transform.