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International Journal of Robust and Nonlinear Control
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Chattering analysis for Lipschitz continuous sliding‐mode controllers

Chattering analysis for Lipschitz continuous sliding-mode controllers
Authors: Carlos Arturo Martínez‐Fuentes; Ulises Pérez‐Ventura; Leonid Fridman;

Chattering analysis for Lipschitz continuous sliding‐mode controllers

Abstract

SummaryIn this article, an analysis of chattering in systems driven by Lipschitz continuous sliding‐mode controllers (LCSMC) is performed using the describing function approach. Two kinds of LCSMC are considered: the first one is based on a linear sliding variable (LSV) and the second one on a terminal sliding variable (TSV). Predictions of amplitude, frequency, and average power of self‐excited oscillations, are used to compare such LCSMC respect to the supertwisting controller (STC) in systems with fast‐actuators. Theoretical predictions and simulations allow the following conclusions: (i) LCSMC still may induce fast‐oscillations (chattering) of smaller amplitude and average power, than ones caused by the STC in the absence of the measurement noises. (ii) The level of chattering with LSV‐LCSMC could be smaller than one produced by TSV‐LCSMC. (iii) The zero (sliding) dynamics of the LSV‐LCSMC cannot be arbitrarily fast or the closed‐loop system may lose even practical stability, unlike the TSV‐LCSMC whose trajectories are finally bounded.

Keywords

sliding-mode, FOS: Electrical engineering, electronic engineering, information engineering, chattering, Variable structure systems, Systems and Control (eess.SY), frequency domain analysis, Electrical Engineering and Systems Science - Systems and Control, Frequency-response methods in control theory

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
22
Top 10%
Top 10%
Top 10%
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bronze