Robust output‐feedback control for the cart–pole system: a coupled super‐twisting sliding‐mode approach

This study presents an output‐feedback controller for a cart–pole system via coupled sliding‐mode algorithms. Due to the fact that this system is underactuated, a special type of sliding surface is employed instead of using a transformation to the regular form. Then, a continuous sliding‐mode controller is designed using the super‐twisting algorithm so that robustness of the control scheme is guaranteed. Since the proposed controller requires the knowledge of the velocities, a homogeneous sliding‐mode observer is introduced to estimate such velocities. Then, in order to improve the control effort, a variable gain super‐twisting algorithm is also proposed. The closed‐loop stability is also guaranteed by means of input‐to‐state stability properties and Lyapunov function approaches. All the results are validated by means of real‐time experiments, providing also a comparison between the proposed controllers and a chattering attenuation approach.