Improved adaptive dynamic non-singular terminal sliding mode controller with fractional disturbance observer

While terminal sliding mode control provides faster responses and reduces steady-state errors, it has the disadvantage of having singularity and chattering issues. This study addresses these issues. To address the first issue, a novel non-singular terminal sliding surface is proposed, and to address the second, a new adaptive reaching law that may accelerate system response without resulting in chattering is developed. In addition, this article proposes a novel fractional disturbance observer for rejecting severe and time-varying disturbances. Several simulated industrial case studies and a real-time application based on a cart pendulum setup are used to show the practical benefits of the proposed controller. The suggested approach outperforms the published methods for regulatory and servo responses, according to simulation results and the integral of squared error values used to evaluate the performance of the proposed and reported methods. The proposed method successfully handles time-varying disturbances, in contrast to other reported methods, which lose stability for the mentioned types of disturbances despite the inclusion of an additional mechanism for rejecting disturbances. The superiority of the method proposed is further assured by real-time results.