Computing and Estimating the Reaching Time of the Super-Twisting Algorithm

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Abstract

The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are Hölder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.
Original languageEnglish
Title of host publicationVariable-Structure Systems and Sliding-Mode Control
Subtitle of host publicationFrom Theory to Practice
PublisherSpringer International
Chapter3
Pages73-123
ISBN (Electronic)978-3-030-36621-6
ISBN (Print)978-3-030-36620-9
DOIs
Publication statusPublished - 2020

Publication series

NameStudies in Systems, Decision and Control
PublisherSpringer
Volume271
ISSN (Print)2198-4182

Fingerprint

Computing
Perturbation
Perturbation Bound
Convergence Time
Numerical Comparisons
Sliding Mode
Quadratic Function
Stability Criteria
Estimate
Lyapunov Function
Asymptotic Properties
Lipschitz
Sufficient
Upper bound
Converge
Controller
Necessary
Range of data
Family
Observation

Cite this

Seeber, R. (2020). Computing and Estimating the Reaching Time of the Super-Twisting Algorithm. In Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice (pp. 73-123). (Studies in Systems, Decision and Control; Vol. 271). Springer International. https://doi.org/10.1007/978-3-030-36621-6_3

Computing and Estimating the Reaching Time of the Super-Twisting Algorithm. / Seeber, Richard.

Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice. Springer International, 2020. p. 73-123 (Studies in Systems, Decision and Control; Vol. 271).

Research output: Chapter in Book/Report/Conference proceedingChapterResearchpeer-review

Seeber, R 2020, Computing and Estimating the Reaching Time of the Super-Twisting Algorithm. in Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice. Studies in Systems, Decision and Control, vol. 271, Springer International, pp. 73-123. https://doi.org/10.1007/978-3-030-36621-6_3
Seeber R. Computing and Estimating the Reaching Time of the Super-Twisting Algorithm. In Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice. Springer International. 2020. p. 73-123. (Studies in Systems, Decision and Control). https://doi.org/10.1007/978-3-030-36621-6_3
Seeber, Richard. / Computing and Estimating the Reaching Time of the Super-Twisting Algorithm. Variable-Structure Systems and Sliding-Mode Control: From Theory to Practice. Springer International, 2020. pp. 73-123 (Studies in Systems, Decision and Control).
@inbook{9ff4a7b037814eea83879fbfd1c054e1,
title = "Computing and Estimating the Reaching Time of the Super-Twisting Algorithm",
abstract = "The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are H{\"o}lder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.",
author = "Richard Seeber",
year = "2020",
doi = "10.1007/978-3-030-36621-6_3",
language = "English",
isbn = "978-3-030-36620-9",
series = "Studies in Systems, Decision and Control",
publisher = "Springer International",
pages = "73--123",
booktitle = "Variable-Structure Systems and Sliding-Mode Control",

}

TY - CHAP

T1 - Computing and Estimating the Reaching Time of the Super-Twisting Algorithm

AU - Seeber, Richard

PY - 2020

Y1 - 2020

N2 - The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are Hölder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.

AB - The super-twisting algorithm is a second order sliding mode algorithm that may be used either for control or for observation purposes. An important performance characteristic of this algorithm is the so-called reaching or convergence time, the time it takes for the controller to reach the sliding surface or for the estimates to converge. In this chapter, three techniques are discussed to estimate, i.e., upper-bound, and in some cases even compute this reaching time in the presence of additive perturbations, which are Hölder continuous in the state or Lipschitz continuous in the time. The first is obtained from an analytic computation of the unperturbed reaching time; the second is based on a family of quadratic Lyapunov functions; and the third is derived from a necessary and sufficient stability criterion. For each approach the range of permissible perturbations, its asymptotic properties with respect to parameters and perturbation bounds, and, when applicable, the selection of parameters is discussed. Numerical comparisons illustrate the results obtained with each approach.

U2 - 10.1007/978-3-030-36621-6_3

DO - 10.1007/978-3-030-36621-6_3

M3 - Chapter

SN - 978-3-030-36620-9

T3 - Studies in Systems, Decision and Control

SP - 73

EP - 123

BT - Variable-Structure Systems and Sliding-Mode Control

PB - Springer International

ER -