Nonlinear attitude control of a 3D rigid pendulum using hierarchical sliding mode techniques

This paper studies the attitude control problem of a 3D rigid pendulum. The 3D rigid pendulum is a reduced model of Geo-stationary(GEO) 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. An improved hierarchical sliding mode method is proposed for nonlinear attitude control of the 3D rigid pendulum at arbitrary position. This method divides the system into two subsystems, and then we use Lyapunov law to obtain the total control input which contains equivalent control components of each subsystem, we can guarantee that each subsystem accesses into their own sliding planes. The asymptotic stability of all sliding planes is also proved theoretically, and simulation results show the controller´s validity.