  Among various satellite actuators, magnetic torquers have been widely
equipped for stabilization and attitude control of small satellites. Although
magnetorquers are generally used with other actuators, such as momentum wheels,
this paper explores a control method where only a magnetic actuation is
available. We applied a nonlinear optimal control method, Nonlinear Model
Predictive Control (NMPC), to small satellites, employing the generalized
minimal residual (GMRES) method, which generates continuous control inputs.
Onboard magnetic actuation systems often find it challenging to produce smooth
magnetic moments as a control input; hence, we employ the Pulse Width
Modulation (PWM) method, which discretizes a control input and reduces the
burden on actuators. In our case, the PWM approach discretizes control torques
generated by the NMPC scheme. This study's main contributions are investigating
the NMPC and the GMRES method applied to small spacecraft and presenting the
PWM control system's feasibility.
