Don't get your question !

Can you please explain "feedback control given to the system is less than the required amount" ?

-Sanjay

Sorry for the crisp details.

I am currently working in a team that builds a nano-satellite. We use 3 magnetorquers (square copper coils) as actuators to control the satellite. To stabilize the satellite,we are using a PID controller which will give(theoretically)  the amount of torque(T1 ) that will be needed to control the satellite given the satellite's current orientation.

           T = M X B  where  M= magnetic moment 

                                           B= Magnetic Field

                                           T= Torque Generated.

Here, T1 & B are known. M is calculated by   ( B x T1) / |B|^2 . Since M is known and          M= niA where       n= Number of turns in the coil

                  i = Amount of current passing through the coil,

                 A = Area of the coil,

i is calculated and sent to the coils. Since a current carrying conductor suspended in a magnetic field experiences torque, A torque(T2) is generated which is perpendicular to both B and M(cross product rule) .

Ideally T1 and T2 should be the same but they aren't. From the simulations I've observed that the T1 given by the controller is not perpendicular to B. But the actual torque that will be acting on the satellite (physically)  will always be perpendicular to B. Therefore the effective torque that will be acting on the satellite is Tsin(x) where x is the angle between theoretical T and B. Essentially the component perpendicular to B when T is resolved into Tsinx and Tcosx. 

In this situation, I require 'T' N/m2 to act on the satellite but effectively 'Tsinx'  N/m2 is acting on the satellite. How do I improvise my system such that the satellite is stabilized .

Thanks, Revathi..

Since the angle "x" is something that the satellite has to "put up with", you can only improvise the control by pumping in more current (i).

My first guess will be to improve upon the integral component. A systematic way to retune all three components (P-I-D) will be to follow the well known Ziegler-Nichols tuning rules, that are popular, reliable, and available at quite a few places on the web.

Just do a Google search and get them !!

-Sanjay

Hello Revathi

Did you get a solution to your problem? If yes, could you please share it. We are also working on a similar project and are facing the same issue ourselves.