On-Off Quantization of an MPC Policy for Coupled Station Keeping, Attitude Control, and Momentum Management of GEO Satellites

This paper introduces a novel on-off quantization scheme used with a control architecture based on model predictive control (MPC) to simultaneously perform station keeping, attitude control, and momentum management of a nadirpointing geostationary satellite equipped with three reaction wheels and four on-off electric thrusters. The MPC policy includes an inner-loop SO(3)-based attitude control law to maintain a nadir-pointing attitude, and an outer loop for station keeping and momentum management. The continuous thrust command generated by the MPC policy is quantized as a single on-off pulse every feedback period in such a way that the predicted error in the states induced by quantization is minimized. This quantization scheme introduces very limited change in behavior and performance compared to results with the non-quantized MPC policy, and uses significantly less on-off pulses compared to other approaches in the literature, such as pulse-width modulation. The tuning parameters of the proposed quantization scheme are discussed in detail and their effects on closed-loop performance are analyzed numerically.