Electric Propulsion and Controller Design for Drag-Free Spacecraft Operation in Low Earth Orbit

A study is presented detailing the simulation of a drag-free follow-on mission to NASA’s Gravity Recovery and Climate Experiment (GRACE). This work evaluates controller performance, as well as thrust, power, and propellant mass requirements for drag-free spacecraft operation at orbital altitudes of 160 - 225 kilometers. In addition, sensitivities to thermospheric wind, GPS signal accuracy and availability of ephemeris data are studied. Orbital dynamics were modeled in Matlab and take into account 2 body gravity effects, J2-J6 non-spherical Earth effects, atmospheric drag and control thrust. A drag model is used in which the drag acceleration is a function of the spacecraft’s relative velocity to the atmosphere, and a “drag parameter,†which includes the spacecraft’s drag coefficient and local mass density of the atmosphere. A MSISE-90 atmospheric model is used to provide local mass densities as well as free stream flow conditions for a Direct Simulation Monte Carlo drag analysis used to validate the spacecraft drag coefficient. The controller is designed around an onboard inertial sensor which uses a freely floating reference mass to measure deviations in the spacecraft position, resulting from non-gravitational forces, from a desired target orbit. Thruster (control actuator) models are based on two different Hall thrusters for providing the orbital along-track acceleration, colloid thrusters for the normal acceleration, and a miniature xenon ion thruster (MiXI) for the cross-track acceleration. The most demanding propulsion requirements correspond to the lowest altitude considered, 160 kilometers. At this altitude the maximum along-track thrust component is calculated to be 98 millinewtons with a required dynamic (throttling) response of 41 mN/s. The maximum position error at this altitude was shown to be in the along-track direction with a magnitude of 3314.9 nanometers and a peak spectral content of 1800 nm/sqrt(Hz) at about 0.1 Hz. At 225 kilometers, the maximum along-track thrust component reduces to 10.3 millinewtons. The maximum dynamic response at this altitude is 4.23 mN/s. The maximum along-track position error is reduced to 367.9 nanometers with a spectral content peak of 40 nm/sqrt(Hz) at 0.1 Hz. For all altitudes, the maximum state errors increase as the mission length increases, however, higher altitude missions show less of a maximum displacement error increase over time than those of lower orbits. The ability of a colloid thruster to control the normal drift is found to be dependent on how frequently the spacecraft state data is updated. Reducing the period between updates from 10 seconds to 1 second reduces the maximum normal state error component from 199 nanometers to less than 32 nanometers, suggesting that spacecraft state update frequency could be a major driver in keeping the spacecraft on the target trajectory. Sensitivity of maximum required thrust and accumulated sensor error to measurement uncertainty is found to be less of a driver than state update frequency. A ‘worst case†thermospheric wind gust was modeled to show the increase on propulsion requirements if such an event were to occur. At 200 kilometers, maximum winds have been measured to be in increase of 650 m/s in the westward direction in the southern pole region. Assuming the majority of the 650 m/s gust occurs over a 4 second time span, the maximum required cross-track thrust at 200 kilometers increases from 1.12 to 2.01 millinewtons. This large increase may drive the thruster choice for a drag-free mission at a similar altitude. For the spacecraft point design considered with a propellant mass fraction of 0.18, the mission lifetime for the 160 km case was calculated to be 0.76 years. This increases 2.27 years at an altitude of 225 km