Hierarchical Sliding Mode Control for Series Double Inverted Pendulums System

This paper proposes a hierarchical sliding mode controller for series double inverted pendulums system. This provides a simple method to control a class of under-actuated systems with three subsystems by sliding mode control. Firstly, the given system is divided into three subsystems according to its structure characteristic. Then, the 1^st -level sliding mode surface is defined for every subsystem and the 2^nd-level sliding mode surface is constituted by them. Based on the two levels structure, the equivalent control of each subsystem is deduced and the total control law is derived by the Lyapunov stability theorem. The asymptotical stability of the entire sliding mode surfaces is proved theoretically. Finally, simulation results show the validity of this control strategy. And the influence of the controller parameter changes for the performances is also discussed