Satellite attitude control using only magnetorquers

Since magnetic control systems are relatively reliable, lightweight, and energy efficient, magnetic torque was found to be attractive for small, inexpensive satellites. Magnetorquers are often used with a gravity gradient boom to control a spacecraft's attitude. However, attempts at using only magnetorquers in all three axes have been unsuccessful, because control torque can only be generated perpendicular to the geomagnetic field vector. This study presents a method to control small satellites only using magnetorquers. If the spacecraft is isoinertial, employing Krstic's backstepping concept (1991), dynamics equation is divided into two parts in geomagnetic frame: the outer loop and the inner loop. The outer loop controller is regarded as a regulation system which is controlled by the virtual control input. The outer loop is a nonlinear and periodical system, and its stability is supported by La Salle's and Floquet's theorems. The inner loop controller is designed for a tracking system and produces the signal to track the virtual control. Considering disturbance torque, a sliding mode controller is designed in the inner loop. Simulation results show that three axis control can be achieved with magnetorquers as the sole actuators. The control system has a good performance not only in detumbling phase but also in attitude acquisition phase.