The attitude control of a 3D rigid pendulum with hierarchical sliding mode method

This paper studies the attitude control problem of 3D rigid pendulum. A 3D rigid pendulum is a reduced model of GEO stationary spacecraft. It consists of a rigid body supported by a fixed and frictionless pivot with three rotational degrees, acted on by a constant gravitational force. Hierarchical sliding mode method is adopted when considering the attitude control of 3D rigid pendulum at equilibrium position. This method divides the system into two subsystems, then we use Lyapunov methods to compute the total amount of control which contains two equivalent components, hence we can guarantee that each subsystem accesses into their own sliding plane. The asymptotic stability of all sliding planes is also proved theoretically, and simulation results show the controller´s validity and its adaptive abilities for outer disturbances.