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Digital implementation of sliding-mode control via the implicit method: A tutorial

Bernard Brogliato 1 Andrey Polyakov 2
1 TRIPOP - Modélisation, simulation et commande des systèmes dynamiques non lisses
Inria Grenoble - Rhône-Alpes, LJK - Laboratoire Jean Kuntzmann
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
Abstract : The objective of this article, is to provide a clear presentation of the discretization of continuous-time sliding-mode controllers, also known in the Automatic Control literature as the emulation method, when the implicit (backward) Euler scheme is used. First-order, second-order and homogeneous controllers are considered. The main theoretical results are recalled in each case, and the focus is put on the discrete-time implementation structure and on the algorithms which allow the designer to solve, at each time-step, the one-step generalized equations which are needed to compute the controllers. The article ends with some open issues.
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Submitted on : Tuesday, August 11, 2020 - 3:01:20 PM
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Bernard Brogliato, Andrey Polyakov. Digital implementation of sliding-mode control via the implicit method: A tutorial. International Journal of Robust and Nonlinear Control, Wiley, 2021, Special Issue: Homogeneous Sliding‐Mode Control and Observation, 31 (9), pp.3528-3586. ⟨10.1002/rnc.5121⟩. ⟨hal-02523011v2⟩

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