Controller to reaction wheel interface

A typical controller generally gives control torques which should be applied about the axis of a satellite. How exactly is this torque applied using a reaction wheel?

For example if control torques are a,b,c then will equating a,b,c to $I(\omega_{cur}-\omega_{prev})/step$ (where $I$ is moment of inertia, $\omega_{prev}$ and $\omega_{cur}$ are previous and current angular velocities) give me the new angular rate at which the wheel should rotate, or should I equate it with -a,-b,-c?

And also if I want continuous attitude control while dumping the momentum of reaction wheel using a magnetorquer, is it required that the net torque from magnetorquer and reaction wheel be equal to control torque?

• I don't quite understand your question. Are you asking for the equation of motion of angular momentum? – ChrisR May 29 '17 at 4:00
• Usually any control system gives a torque which needs to be applied on the system and not directly the angular velocity of reaction wheel which needs to be set. So i wanted to know if the equation above will get me the required conversion. – user97213 May 29 '17 at 5:01
• Right. Wouldn't that depend on the set of wheels you're using and the mass of your spacecraft? – ChrisR May 29 '17 at 5:05
• Yeah consider for 3 reaction wheels on 3 orthogonal axis and it does depend on Moment of Inertia (indirectly on mass). – user97213 May 29 '17 at 10:22
• You shouldn't try to base the control on the torque as values of torques involved will be so small that your problem will be ill-conditioned numerically. Your control variables should be angles and angular velocities (0th and 1st derivative) and only use angular acceleration, and torque (2nd derivative) where you can't get away with lower derivatives (say, power supply to the RW motor) deriving these ad-hoc from φ,ω for immediate use. – SF. May 29 '17 at 12:48

Some reaction wheels provide only "speed control", in which the interface admits only the speed that the wheel needs to track. If the AOCS designed a controller that would output torque, then the command to the wheel would need to be converted somehow, one possibility being similar to your suggestion, but with $\omega_{next}$ and $\omega_{cur}$ instead of the previous spin rate. A designer could also build the control under the premise that it will not control wheels in torque mode.