Minimal realizations from MFDs and attitude control of spinning satellite using gyrotorquers

The questions related to the matrix traction descriptions (MFDs) and the minimal realizations of the transfer matrix of a spinning satellite system and control system design using output feedback are considered. The control torques are generated using gyrotorquers and the output variables are the attitude angles. Two minimal state space representations of the system, namely, a controller-form and an observer-form realization are obtained form a right and a left MFD of the transfer matrix, respectively. Using these canonical realizations, analytical expression for the feedback matrices of the controller and the observer as functions of the system parameters are obtained. The poles of the closed-loop system are invariant with respect to the spin rate of the satellite. Simulation results are presented to show that precise attitude control is accomplished in the closed-loop system using output feedback.