Hierarchical Sliding Mode Control to Swing up a Pendubot

To swing up a Pendubot, a pendulum robot, this paper presents a hierarchical sliding mode controller with limited control torque. The structure characteristic of the Pendubot system is that it can be treated as two subsystems. Thus, the hierarchical structure of the sliding mode surfaces is designed as follows. The sliding mode surfaces of the two subsystems are defined at first. The sliding mode surface of one subsystem is selected as the first layer sliding mode surface. The second layer sliding mode surface is constructed by the first layer sliding mode surface and the sliding mode surface of the other subsystem. The hierarchical sliding mode control law is deduced in terms of Lyapunov stability theorem. Asymptotic stability of the entire sliding mode surfaces is proven theoretically and control parameter boundaries of the two subsystems are also given theoretically. Finally, simulation results show the validity of this control method and its robustness for external disturbances.