Higher Order Sliding Mode stabilization of an inverted cart-pendulum system

Abstract

: Stabilization of a cart-pendulum system through Higher Order Sliding Mode design is presented. From Singular LQ method, a relationship between order of singularity of a given performance index and the order of sliding mode controller is established. Thus, several arbitrary relative degree optimal sliding surfaces and its corresponding Higher Order Sliding Mode Controller can be specified for a given system. Continuous Higher Order Sliding Mode Controllers are obtained through a robustification method for arbitrary relative degree controllers based on Integral Sliding Modes and Super-Twisting Algorithm. An agreement between the accuracy/complexity of the Continuous Higher Order Sliding Mode Controller and the limited accuracy offered by the system’s sensors and actuators is obtained experimentally.