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.
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