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.
Effect of Euler Explicit and Implicit Time Discretizations on Variable-Structure Differentiators
Studies in Systems, Decision and Control
01.11.2023
16 pages
Aufsatz/Kapitel (Buch)
Elektronische Ressource
Englisch
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