Software: Momentum Management

Description

The purpose of this module is to support the three-axis control of a satellite with reaction wheels while using magnetic torque bars for continuous momentum dumping. It is intended to be used in conjunction with an RW feedback controller, while the commanded MTB torques are applied with a feedforward term.

Example Use Cases

• Reaction Wheel De-Saturation: Given set of reaction wheels that a saturated, this module can be used to apply torques using an MTB array to de-saturate these reaction wheels.

Module Implementation

This module computes the torque required to drive the net momentum of the attached reaction wheels to zero. Assuming a satellite has \(n\) reaction wheels, the new angular momentum in the body frame of the reaction wheels is:

\[ \mathbf{h}_{rw} = \sum^{n}_i \mathbf{\hat{g}}_i J_i \Omega_i \]

where \(\mathbf{\hat{g}}_i\) is the spin axis of the \(\mathrm{i^{th}}\) reaction wheel in the body frame, \(\mathbf{J}_i\) is that wheel’s spin axis momentum of inertia and \(\Omega_i\) is the rotation rate of the wheel about the spin axis.

The desired torque required to drive the wheel momentum to zero is then given by a simple proportional control law:

\[ \mathbf{\tau} = -K_p \mathbf{h}_{rw} \]