Mathematical model of angular motion of nanosatellites with inertial actuators

The problem of developing a nanosatellite attitude control system using three reaction wheels mounted along the main central axes of inertia is discussed in the paper. The law of controlling a nanosatellites attitude is based on a PD - controller. The stability of the process of controlling the nanosatellite attitude using the Lyapunov function method has been analyzed. It allows us to prove that the obtained control law provides the asymptotic stability of nanosatellite angular motion. Hereafter, the function of control voltage for electric motors of reaction wheels taking into account their specifications is obtained based on the developed mathematical model of reaction wheel dynamics. Numerical calculations of controlled angular motion have been carried out for the nanosatellite CubeSat3U with actuators on the basis of a commercial DC motor. Several cases of controlling the satellites rotation by different angles are considered in the course of the numerical experiments. The results of numerical experiments showed the adequacy of the developed mathematical model