Dead-beat gain correction: a promising chattering treatment method in sliding-mode algorithms
Mohammad Rasool Mojallizadeh, Mohamed Assaad Hamida, F. Plestan · HAL (Le Centre pour la Communication Scientifique Directe) · 2025
A new method is introduced in this paper to treat the numerical chattering, i.e., high-frequency oscillations that appear in the sliding-mode algorithms which degrades the sliding-mode controllers' performances. In this method, the original sliding-mode algorithm is modified by multiplying the existing discontinuous term by the dead-beat gain correction terms, in the discrete-time setting. These terms are calculated based on the deadbeat theorem such that the modified discrete-time algorithm presents a time-optimal convergence, with the same properties of the original continuous-time algorithm (same level of control effort, same stability features, etc.), leading to a chattering-free implementation. Compared to the trending discretization methods, i.e., implicit discretization, the proposed method is made fully explicitly leading to a straightforward implementation without appearing the generalized equations, enabling the method to be used systematically for a majority of sliding-mode algorithms. Moreover, the proposed method does not require extra parameters and cumbersome tuning procedures commonly exist in most adaptive sliding-mode algorithms. It will be shown, through a set of analytical and numerical studies, that the sliding-mode controller under the proposed implementation presents several important properties such as chattering reduction, finite-time convergence, and gain insensitivity, without exceeding the control effort compared to the originally designed continuous-time counterparts.