Fixed-Time Attitude Control of Satellite Using Combined Magnetic and Magneto-Coulombic Actuators

This paper presents a novel fixed time attitude control for a satellite system actuated by hybrid actuators. The hybrid actuators considered in this paper are a combination of magnetic and magneto-Coulombic actuators which provide torques along the three body axes at every instant of time. The magneto-Coulombic torque is generated with the help of spherical charged shells which are placed along the different body axes. These charged shells interact with Earth's magnetic field to produce the Lorentz force which in turn produces the required magneto-Coulombic torque for actuating the satellite. Whereas, the magnetic torque is produced by magnetorquers on interaction with the current flowing through them with the Earth's magnetic field. However, the magneto-Coulombic torque as well as the magnetic torque, if used independently for actuation purposes results in an under-actuation problem because the magneto-Coulombic torque is constrained in a plane containing the local magnetic field and velocity vectors, and magnetic torque lies in a plane perpendicular to the local magnetic field vector. This problem is tackled and addressed in this paper by using the combination of magneto-Coulombic and magnetic actuators, which yields a fully actuated satellite system thereby resulting in a three-axis attitude control or full controllability at all periods of time. The control formulation in this paper is derived from sliding mode control theorem which is a popular robust control algorithm. The sliding manifold considered in this paper is a non-singular terminal sliding manifold designed in such a way that it ensures finite-time convergence to the origin of the sliding surface. Finite-time stability of the satellite is proved using the Lyapunov theorem. The expression of convergence time is derived using the Lyapunov theorem and is found to be independent of the initial conditions of the state variables when the satellite system dynamics is modeled in the state-space formulation. As the convergence time is independent of the initial conditions of state variables, therefore the control algorithm is termed as fixed-time attitude control algorithm. Numerical simulations are used to validate the effectiveness of the fixed time attitude control algorithm.