Optimal Hybrid Magnetic Attitude Control: Disturbance Accommodation and Impulse Timing

A recently proposed hybrid attitude control scheme, which optimally combines magnetic torques with impulsive thrusting using a continuous/discrete linear quadratic regulator, is modified to accommodate disturbances. Accounting for the presence of disturbances in the design procedure, previous results on necessary conditions for optimality of impulse application times are modified accordingly. In addition, the special case of a multiorbit mission with repeating impulse patterns is considered, showing that an elegant extension of the optimality conditions would significantly reduce the computational cost by limiting the design space to only the first orbit: this extended condition is obtained by summing over all orbits within the control interval, the original conditions being computed at each repeating impulse time. Finally, numerical examples are presented, confirming the superiority of the proposed disturbance-accommodating controller in terms of steady-state performance (even when the disturbance estimates are partly incorrect) and the validity of the extended optimal timing theory in the linear region.