Sampled Describing Function Analysis of Second Order Sliding Modes

Stefan Koch; Markus Reichhartinger; Martin Horn; Leonid Fridman

doi:10.1109/CDC.2016.7799399

Sampled Describing Function Analysis of Second Order Sliding Modes

Stefan Koch, Markus Reichhartinger, Martin Horn, Leonid Fridman

Institute of Automation and Control (4430)

Research output: Chapter in Book/Report/Conference proceeding › Conference paper › peer-review

Abstract

The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.

Original language	English
Title of host publication	Decision and Control (CDC), 2016 IEEE 55th Conference on
Pages	7318-7324
Number of pages	7
ISBN (Electronic)	978-1-5090-1837-6
DOIs	https://doi.org/10.1109/CDC.2016.7799399
Publication status	Published - 29 Dec 2016
Event	55th IEEE Conference on Decision and Control - ARIA Resort & Casino, Las Vegas, United States Duration: 12 Dec 2016 → 14 Dec 2016 http://cdc2016.ieeecss.org/

Conference

Conference	55th IEEE Conference on Decision and Control
Country/Territory	United States
City	Las Vegas
Period	12/12/16 → 14/12/16
Internet address	http://cdc2016.ieeecss.org/

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10.1109/CDC.2016.7799399

Cite this

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title = "Sampled Describing Function Analysis of Second Order Sliding Modes",

abstract = "The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.",

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doi = "10.1109/CDC.2016.7799399",

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AU - Horn, Martin

AU - Fridman, Leonid

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Y1 - 2016/12/29

N2 - The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.

AB - The describing function method is applied to characterize the steady state behavior of the linear sampled data systems stabilized by a second-order sliding mode algorithm. A describing function of the nonlinearity including a sample and hold element is derived. The proposed method allows to predict the amplitude, frequency and phase of occurring limit cycles caused by the discrete time implementation of discontinuous control algorithms. It is shown that the derived describing function is closely related to its classical continuous time counterpart. The proposed approach is demonstrated using a numerical simulation example as well as a real world experiment.

U2 - 10.1109/CDC.2016.7799399

DO - 10.1109/CDC.2016.7799399

M3 - Conference paper

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EP - 7324

BT - Decision and Control (CDC), 2016 IEEE 55th Conference on

T2 - 55th IEEE Conference on Decision and Control

Y2 - 12 December 2016 through 14 December 2016

ER -

Sampled Describing Function Analysis of Second Order Sliding Modes

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