Research ArticleIntegral backstepping sliding mode control for underactuated systems: Swing-up and stabilization of the Cart-Pendulum System

•A sliding mode controller combined with integral backstepping is proposed.•The controller is designed for underactuated Cart-Pendulum System.•Robustness to mismatched uncertainty and chattering removal are main features.•The proposed controller ensures asymptotic stability.•Control energy spent is minimal.

In this paper an integral backstepping sliding mode controller is proposed for controlling underactuated systems. A feedback control law is designed based on backstepping algorithm and a sliding surface is introduced in the final stage of the algorithm. The backstepping algorithm makes the controller immune to matched and mismatched uncertainties and the sliding mode control provides robustness. The proposed controller ensures asymptotic stability. The effectiveness of the proposed controller is compared against a coupled sliding mode controller for swing-up and stabilization of the Cart-Pendulum System. Simulation results show that the proposed integral backstepping sliding mode controller is able to reject both matched and mismatched uncertainties with a chattering free control law, while utilizing less control effort than the sliding mode controller.