Static input allocation for reaction wheels desaturation using magnetorquers

Considering a set of reaction wheels and an array of magnetorquers, we revisit the classical “cross product control law” solution for achieving attitude stabilization and momentum damping. In particular, we highlight the existence of a quasi-cascade structure for which asymptotic stability can be obtained by selecting a sufficiently high gain of the attitude stabilizer. However, we show how the classical solution renders the actuators more inclined to saturate. This is the reason underlying the introduction of a revisited version of this control law which stabilizes the overall system regardless of the aggressiveness of the attitude stabilizer by transforming the quasi-cascade into a real cascade. We then discuss how both strategies are such that the attitude control is affected by the momentum damping task although it should be treated as a secondary goal. To overcome this drawback, we propose a new allocation-based controller which makes the attitude dynamics completely independent of the momentum damping of the reaction wheels while preserving the possibility of considering non-aggressive attitude controllers. Finally, several simulation results enrich these discussions and highlight the pros and cons of the different control strategies.