Satellite attitude control using a novel Constrained Magnetic Linear Quadratic Regulator

This paper addresses a novel Constrained Magnetic Linear Quadratic Regulator (CM-LQR) scheme that generates a control torque vector on a plane approximately perpendicular to the local geomagnetic field. This control torque nearly precisely guarantees the production of an equivalent mechanical torque. The main ideas in the proposed method are (1) excluding the actuator dynamics from the system dynamics, and (2) incorporating the designed dynamics in the problem formulation using an algebraic mathematical constraint. In this way, a common time-variant system is transformed into a time-invariant system. The proposed CM-LQR generates the control torque via adjusting a time-variant control weighting matrix according to the geomagnetic field feedback. Unlike previous methods, our proposed control torque has a negligible parallel projection to the local geomagnetic field, and thus, it can be utilized fully by the magnetorquers. The hybrid Genetic Algorithm (GA) and Sequential Quadratic Programming (SQP) methods are applied to find an optimum state weighting matrix. Moreover, numerical simulation is performed to evaluate the performance and agility of the closed-loop control system. In addition, the obtained results are compared with a conventional magnetic LQR attitude controller to confirm that the presented scheme results in more agility and lower steady-state error in the attitude maneuver of the magnetically actuated satellites.