The attitude stabilization of hanging equilibrium of the 3D axially symmetric rigid pendulum with hierarchical sliding mode control

3D rigid pendulum is an reduced model of GEO stationary spacecraft, and researches on the dynamics and control methods of it have great significance of the development for nonlinear system control theory. Being acted on by gravitational force, the 3D axially symmetric rigid pendulum rotates around a fixed point, if the angular velocity rotated around the axis of symmetry is zero, the system is referred as a spherical 2D pendulum; and if the angular velocity is a non-zero constant, the system is referred as a Lagrange top. This paper concentrates on hanging equilibrium control problem of a Lagrange top, and then we design a hierarchical sliding mode controller with sliding mode variable structure method. Simulation results show that this method is feasible and effective for the hanging equilibrium control of the 3D Rigid Pendulum.