Multiplexed MPC attitude control of a moving mass satellite using dual-rate piecewise affine model

Abstract

This paper proposes a Multiplexed MPC algorithm for the dual-rate piecewise affine (PWA) model to control the attitude of a low-Earth-orbit (LEO) moving mass satellite. Although still facing an inherent inertial disturbance problem, the moving mass technology is a promising way to counter the strong aerodynamic torques in LEO. To make the satellite attitude fully actuated, a magnetorquer is used to cooperate with the moving mass system, resulting in a two-input control system. Through a strategy that updates inputs asynchronously, the proposed algorithm effectively balances the inertial disturbances caused by mass motions, the system's dynamic performance, and the controller's computational complexity. Error attitude kinematic and dynamic equations are derived, to convert the tracking problem into an equivalent regulation problem. The PWA approximation is used to transform the nonlinear attitude control equations described by error modified Rodrigues parameter to a linear state-space model for MPC design. Then, a new form of Multiplexed MPC, namely dual-rate PWA-MMPC, is developed for this dual-rate PWA model, which updates two control inputs at different rates. Despite only finding sub-optimal solutions to the original problem by stability analysis, this algorithm outperforms other control strategies through its ability to coordinate multiple inputs, deal with constraints, and reduce computational complexity. Hardware-in-the-loop simulations are conducted to demonstrate the effectiveness of the proposed methodology for the attitude control.