This chapter deals with the time discretization of variable-structure differentiatorsVariable structure differentiator with discontinuous (i.e., set-valued) parts. The explicit and implicit time-discretization schemes are developed for a specific type of variable-structure differentiatorVariable structure differentiator, i.e., arbitrary-order super-twisting differentiatorSuper-twisting differentiator. The causal implementation and some properties of the implicit discretizationImplicit discretization are studied analytically, e.g., finite-time convergence, numerical chattering suppression, exactness, gain insensitivity, and accuracy. These properties are validated in the open-loop configuration using numerical simulations. Furthermore, a laboratory setup, namely, a rotary inverted pendulum available at the INRIA Centre at the University of Lille, has been considered as the benchmark to study the behavior of the discretization methods in closed-loop control systems in practice. The experimental results are in accordance with the ones obtained from the analytical calculations and numerical simulations.


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    Title :

    Effect of Euler Explicit and Implicit Time Discretizations on Variable-Structure Differentiators


    Additional title:

    Studies in Systems, Decision and Control




    Publication date :

    2023-11-01


    Size :

    16 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English





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