Finite-time continuous sliding mode magneto-coulombic satellite attitude control

A finite-time continuous sliding mode control is proposed and designed for the attitude control of an earth-pointing magneto-Coulombic satellite actuated using Coulomb shells and orbiting in a circular low earth orbit. A new nonlinear sliding manifold is proposed in terms of errors in quaternions and angular velocity and is used for average finite-time continuous sliding control formulation and closed loop stability analysis of averaged system dynamics. A real and finite-time continuous sliding control is proposed for real-time control of the system. and it is proved that this is reduced to the average finite-time continuous sliding control. Using the Lyapunov theorem, it is proved that the averaged closed loop system is globally stable and converges in finite time to the proposed sliding manifold in the presence of disturbance and destabilizing gravity gradient torque, which is followed by fast and finite-time convergence to the desired orientation and angular velocity (origin) along the sliding manifold. Simulation results of the sliding control are compared against those obtained using proportional-differential control, showing superiority of the sliding control in terms of less charge requirement and better convergence of states of the system. It is also shown that changing the distance between the shells and keeping moments of inertia constant does not alter the results qualitatively or quantitatively except for scaling of charge.