Control Allocation Methods for Constrained and Over Actuated Satellite Attitude Control Systems

Jonathon M. Childress

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The research presented in this thesis compares the numerically simulated performance of various control allocation methods applied to the constrained and over actuated control system of the Air Force Research Laboratory, Space Vehicle Directorate's satellite simulator, the REBEL. The REBEL prototype reaction wheel array design has not yet evaluated the implementation of control allocation methods in its attitude control system. As a result, three different control allocation methods are formulated and applied to the simulation: the simple pseudo inverse, the redistributed pseudo inverse, and the redistributed pseudo inverse with adaptive weighting (a newly developed control allocation variant.) The equations of motion (kinematics and kinetics) for a satellite simulator utilizing a reaction wheel array as an attitude control system are also derived and implemented in the simulation. The control law for a basic high level controller is defined and applied to the simulation as well. A single simulated maneuver is executed with the control system utilizing each of the control allocation methods independently. This single maneuver is evaluated in detail to provide insight into the control allocation methods' functionality. A set of multiple maneuvers is also executed for each control allocation method and the resulting performance metrics are averaged. Based on these results, conclusions are drawn about the different control allocation methods' potential for implementation on REBEL. The results indicate that redistributed pseudo inverse and the redistributed pseudo inverse with adaptive weighting both show promise as potential control allocation methods REBEL could utilize.