Full-Matrix MIMO QFT controller design for drag-free satellites in dual formation

In order to suppress the non-gravitational acceleration interference generated by formation control in the gravity measurement band, relative position control method for loose formation flying drag-free satellites applied to Earth gravimetry mission is investigated. Firstly, a relative dynamic model with J2 perturbation effect is derived based on a formation center of mass, which is located at the middle position of the two satellites. Then, the frequency domain constraints for tracking performance, robust stability and input disturbance suppression are specified based on the quantitative feedback theory (QFT). Different from the general diagonal matrix QFT controller, a fully populated robust controller matrix is designed through taking the highly-coupled multiple-input-multiple-output (MIMO) system characteristics into account. Not only loop-shaping, channel decoupling and steady convergence for closed control loop are realized, but also the power spectral density of disturbance generated by formation control is suppressed in scientific measurement band. Finally, the time domain numerical simulation is carried out to illustrate the effectiveness and robustness of the proposed controller.