Model reference adaptive method for microsatellite active magnetic control

The paper deals with the problem of the magnetic attitude control for microsatellite in LEO, with three torquerods along with the principal axes of inertia. The resulting attitude dynamics is nonlinear and the actuation torque is always perpendicular to the local Earth magnetic field. The linearization of the attitude dynamics with respect to a nominal attitude, yields a linear periodic system that is useful to develop a linear control algorithm in order to keep the attitude stable. Several methods have been developed using the theory of the linear periodic equations to obtain stable attitude control algorithms. This work presents a novel strategy based on a method of the Direct Adaptive Control theory. Using the dipole model of the Earth magnetic field, the paper shows that the linearized dynamics is represented by coefficients that are analytically computed. As a result, the attitude equations have coefficients that are bounded by maximum and minimum values. Consequently, we are under the conditions to apply a control algorithm, which performs an adaptive law to track the slow variations of the dynamic parameters. A useful control technique exploits the Model Reference Adaptive Control. The method consists in using a LTI system as a reference system and constructing a control law in order to nullify the output error of a system with unknown-bounded dynamic parameters. The approach shown in the paper uses the average on the attitude linearized equations in an orbital period as the model reference system. Using a Lyapunov approach, it is demonstrated that the resulting adaptive control is stable and is able to keep the attitude within some degrees. Numerical testes are shown to support the theoretical results of the work.