Continuous sliding-mode control for underactuated systems: Relative degree one and two

This paper deals with the design of sliding-mode controllers for the stabilization of some types of underactuated systems. The proposed method takes advantage of the mechanical properties of three different types of underactuated systems instead of using nonlinear transformations. In order to design the controller, some sliding variables with relative degree one and two are introduced. The theoretical differences between these approaches are discussed and some simulation results show the practical differences. Experimental results on a cart–pole system are presented to validate the proposed control strategy.