Structural conditions for chattering avoidance in implicitly discretized sliding mode differentiators

Richard Seeber; Stefan Koch

doi:10.1109/LCSYS.2023.3282886

Structural conditions for chattering avoidance in implicitly discretized sliding mode differentiators

Richard Seeber^*, Stefan Koch

^*Corresponding author for this work

Institute of Automation and Control (4430)

Research output: Contribution to journal › Article › peer-review

Abstract

The present paper considers the implicit discretization of Levant’s arbitrary order robust exact differentiator. It is shown that an improper implicit discretization may lead to an undesired bias in the differentiation error and, surprisingly, to discretization chattering despite the implicit discretization. Necessary and sufficient structural conditions for avoiding both of these problems are presented, which define a family of chattering-free discrete-time differentiators. A guideline for selecting a representative from this family is given. Numerical simulations illustrate the results.

Original language	English
Pages (from-to)	2065-2070
Number of pages	6
Journal	IEEE Control Systems Letters
Volume	7
Early online date	2023
DOIs	https://doi.org/10.1109/LCSYS.2023.3282886
Publication status	Published - 5 Jun 2023

Keywords

robust exact differentiator
implicit Euler discretization
sampled measurements
Estimation error
Transforms
Observers
Time measurement
Doppler effect
Task analysis
Standards
Robust exact differentiator

ASJC Scopus subject areas

Control and Optimization
Control and Systems Engineering

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abstract = "The present paper considers the implicit discretization of Levant{\textquoteright}s arbitrary order robust exact differentiator. It is shown that an improper implicit discretization may lead to an undesired bias in the differentiation error and, surprisingly, to discretization chattering despite the implicit discretization. Necessary and sufficient structural conditions for avoiding both of these problems are presented, which define a family of chattering-free discrete-time differentiators. A guideline for selecting a representative from this family is given. Numerical simulations illustrate the results.",

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AB - The present paper considers the implicit discretization of Levant’s arbitrary order robust exact differentiator. It is shown that an improper implicit discretization may lead to an undesired bias in the differentiation error and, surprisingly, to discretization chattering despite the implicit discretization. Necessary and sufficient structural conditions for avoiding both of these problems are presented, which define a family of chattering-free discrete-time differentiators. A guideline for selecting a representative from this family is given. Numerical simulations illustrate the results.

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KW - implicit Euler discretization

KW - sampled measurements

KW - Estimation error

KW - Transforms

KW - Observers

KW - Time measurement

KW - Doppler effect

KW - Task analysis

KW - Standards

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JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

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Structural conditions for chattering avoidance in implicitly discretized sliding mode differentiators

Abstract

Keywords

ASJC Scopus subject areas

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