Abstract

The control problem of underactuated systems with external perturbations is investigating in this paper. Using the super-twisting-based global sliding mode control (GSMC) method, an original control law is proposed to guarantee removal of the reaching mode and obtain the robustness and exponential stability of the underactuated systems. Via the offered scheme, a robust control law is designed so that the state trajectories of the underactuated systems are convergent to the global sliding surface in an exponential manner. Moreover, this article develops an adaptive super-twisting algorithm for these systems. The adaptive-tuning controller eliminates the need of the knowledge about upper bound of the exterior disturbance. The discontinuous sign function appears in the controller derivative; as a result, the actual control signal reached after integration is continuous and free of chattering. Demonstrative simulations on a cart–inverted pendulum system as well as an experimental study are presented to show the effectiveness and applicability of the proposed technique.