Attitude-Translation Coupling in Drag-Free Satellites

Abstract

The orbit of a drag-free satellite is determined entirely by gravity because it follows an unsupported proof mass which is shielded from all external surface forces by the satellite. A control system in the satellite senses the relative position of the satellite with respect to the proof mass and actuates reaction jets forcing the satellite to follow the proof mass. A drag-free control system may be added to any type of satellite, and in principle is independent of the satellite's attitude control system. Coupling, however, can occur because both the pickoff, which senses the relative position of the satellite, and the proof mass may be located away from the satellite mass center and the thrusters may be misaligned with respect to the mass center. In passive attitude control systems, misaligned translational control thrusters may produce significant disturbances to the attitude. These attitude motions can in turn be coupled back into the translation control system through an offset of the pickoff with respect to the vehicle mass center. This paper describes the mechanism of this type of coupling and provides design guides for gravity gradient satellites which are made drag free. The discussion begins with a simplified model to illustrate the nature of the coupling and develops the full six-degree-of-freedom equations to examine thoroughly all paths of coupling. It is shown that an important dynamic path for this type of coupling is through the interaction of along-track and radial translations (conventional orbital mechanics perturbation theory). Thrust which is produced in-track due to relative displacement along the orbit produces radial displacement which in turn activates thrusters in the radial direction. The vertical thrust, if misaligned, produces torques which change the vehicle's orientation and thereby produce an error signal in the horizontal direction if the sensor is not located at the satellite mass center. This error signal in turn requests additional horizontal thrust, and may thereby close the loop unstably. Stability boundaries as a function of thruster misalignment, pickoff offset, and attitude-motion damping ratio, are established and the alignment requirements are discussed. The analytical discussion is substantiated with results from a simulation which includes the nonlinear characteristics of thrusters and their modulators.