H∞ Control Design for a Rigid-Flexible Spacecraft under a Fuel Slosh Influence

Abstract

The spacecraft Attitude Control System (ACS) performance and robustness depend on the interactioneffects between the fuel slosh motion, the panel's flexible motion, and the spacecraft rigid motion, mainly duringtranslational and/or rotational maneuvers. In regards to satellite pointing accuracy flexibility and fuel, slosh is thetwo most important effects that should be considered in the satellite ACS design since their interactions can damage the ACS performance and robustness. Once, the lowest vibration frequencies, normally of the sloshing modeare about six times less than of the ACS bandwidth. Therefore, there is a strong possibility that this mode can destabilize the ACS pointing accuracy. This phenomenon is called spillover because the control effort spills over outside the control bandwidth. As a result, the designer needs to explore the limits between the conflicting requirements of performance, that is, increase of the bandwidth without introduction noise in the ACS keeping the systemrobustness to parameters variation. In this paper, one applies the H infinity control method which can deal withthese two design requirements (performance and robustness) considering the controller error pointing that may belimited by the minimum time necessary to suppress disturbances that affect the satellite attitude acquisition. Theequations of motions are obtained considering the Lagrange method for small flexible deformations and a mechanical model of liquid sloshing which allows modeling and investigating the longitudinal dynamic characteristics of apartially filled liquid tank during a pitch maneuver, satisfying performance and robustness requirements.