Robust sliding mode control applied to double inverted pendulum system

A three hierarchical sliding mode control is presented for a class of an underactuated system which can overcome the mismatched perturbations. The considered underactuated system is a double inverted pendulum (DIP), can be modeled by three subsystems. Such structure allows the construction of several designs of hierarchies for the controller. For all hierarchical designs, the asymptotic stability of every layer sliding mode surface and the sliding mode surface of subsystems are proved theoretically by Barbalat's lemma. Simulation results show the validity of these methods.