# Will this magnetorquer configuration effectively desaturate a reaction wheel?

I'm trying to run a Matlab simulation for desaturation of a reaction wheel using magnetorquers.

But there is still something that I'm not entirely sure of :

I know that when the reaction wheel reaches its max speed ( in terms of rpm), it becomes saturated and will have 0 acceleration. Assuming that you stop the reaction wheel motor after saturation, will the angular velocity generated by the reaction wheel still cause it to turn? I think this is true as it would then justify using magnetorquers to externally counteract this angular velocity, but I am not entirely sure.

Also, this is my current plan to desaturate the reaction wheel:

When the reaction wheel is saturated, a control signal will be sent to active a P controller with the control law : m=-Kp(href-hw) where m is the magnetic moment of the magnetorquer, hw is the momentum of the reaction wheel and href is a reference momentum. This P controller would then be connected to a magnetorquer ( Let's call the this torque tmag).

tmag would then be added into the dynamic equations for the satellite.

Would this work?

Thanks!

• "Assuming that you stop the reaction wheel motor after saturation, will the angular velocity generated by the reaction wheel still cause it to turn?" Why wouldn't it keep turning? Shouldn't it keep turning if you stop prior to saturation as well? How is this situation different from plain inertia? – called2voyage Sep 21 '16 at 16:41
• For the record, I did upvote. I love having a Matlab question. I'm just a little unclear on your scenario. – called2voyage Sep 21 '16 at 16:41
• I'm a little confused because on earth frictional forces would cause the wheel to stop rotating after awhile, but that would not happen in space since there is no friction, or gravity. – John Sep 21 '16 at 16:43
• That's not quite true. There can still be friction in space where surfaces are in contact for reasons other than gravity. The question is what are the possible sources of friction on the reaction wheel. My guess is that it is not enough to keep from spinning for a while. – called2voyage Sep 21 '16 at 16:45
• Ah, so it would mean that the reaction wheel wouldn't stop spinning even after the motor is stopped. Which is why one would need to desaturate it, especially when it reaches saturation. In that case, would my proposed Matlab plan for the desaturation controller work? – John Sep 21 '16 at 16:48