Transient oscillations in super twisting sliding mode control systems with actuator dynamics

Yikai Zhang; Kemao Ma

doi:10.1016/j.jfranklin.2025.108077

Transient oscillations in super twisting sliding mode control systems with actuator dynamics

Yikai Zhang
, Kemao Ma^*

^*Corresponding author for this work

School of Astronautics, Harbin Institute of Technology
National Key Laboratory of Complex System Control and Intelligent Agent Cooperation

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

1 Scopus citations

Abstract

This paper investigates the transient oscillatory behavior in a super-twisting sliding mode control system, considering actuator dynamics with first-order and constant-delay models. By extending the dynamic harmonic balance (DHB) approach, the “small-decay DHB” method based on the describing function (DF) method is proposed for a more general system including process memory nonlinearities, neglecting higher-order decay terms for efficiency. This method enables the derivation of analytical expressions for the instantaneous parameters (amplitude, decay rate, and frequency) of transient oscillations. A definition of the settling time is proposed to account for transient properties, and its analytical expression is derived with respect to the gains of the super-twisting algorithm. The effectiveness of the theoretical analysis is confirmed through numerical simulations.

Original language	English
Article number	108077
Journal	Journal of the Franklin Institute
Volume	362
Issue number	16
DOIs	https://doi.org/10.1016/j.jfranklin.2025.108077
State	Published - 15 Oct 2025
Externally published	Yes

Keywords

Describing function
Settling time
Small-decay dynamic harmonic balance
Super-twisting algorithm
Transient oscillations

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10.1016/j.jfranklin.2025.108077

Cite this

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title = "Transient oscillations in super twisting sliding mode control systems with actuator dynamics",

abstract = "This paper investigates the transient oscillatory behavior in a super-twisting sliding mode control system, considering actuator dynamics with first-order and constant-delay models. By extending the dynamic harmonic balance (DHB) approach, the “small-decay DHB” method based on the describing function (DF) method is proposed for a more general system including process memory nonlinearities, neglecting higher-order decay terms for efficiency. This method enables the derivation of analytical expressions for the instantaneous parameters (amplitude, decay rate, and frequency) of transient oscillations. A definition of the settling time is proposed to account for transient properties, and its analytical expression is derived with respect to the gains of the super-twisting algorithm. The effectiveness of the theoretical analysis is confirmed through numerical simulations.",

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AU - Zhang, Yikai

AU - Ma, Kemao

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N2 - This paper investigates the transient oscillatory behavior in a super-twisting sliding mode control system, considering actuator dynamics with first-order and constant-delay models. By extending the dynamic harmonic balance (DHB) approach, the “small-decay DHB” method based on the describing function (DF) method is proposed for a more general system including process memory nonlinearities, neglecting higher-order decay terms for efficiency. This method enables the derivation of analytical expressions for the instantaneous parameters (amplitude, decay rate, and frequency) of transient oscillations. A definition of the settling time is proposed to account for transient properties, and its analytical expression is derived with respect to the gains of the super-twisting algorithm. The effectiveness of the theoretical analysis is confirmed through numerical simulations.

AB - This paper investigates the transient oscillatory behavior in a super-twisting sliding mode control system, considering actuator dynamics with first-order and constant-delay models. By extending the dynamic harmonic balance (DHB) approach, the “small-decay DHB” method based on the describing function (DF) method is proposed for a more general system including process memory nonlinearities, neglecting higher-order decay terms for efficiency. This method enables the derivation of analytical expressions for the instantaneous parameters (amplitude, decay rate, and frequency) of transient oscillations. A definition of the settling time is proposed to account for transient properties, and its analytical expression is derived with respect to the gains of the super-twisting algorithm. The effectiveness of the theoretical analysis is confirmed through numerical simulations.

KW - Describing function

KW - Settling time

KW - Small-decay dynamic harmonic balance

KW - Super-twisting algorithm

KW - Transient oscillations

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DO - 10.1016/j.jfranklin.2025.108077

M3 - 文章

AN - SCOPUS:105018092872

SN - 0016-0032

VL - 362

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 16

M1 - 108077

ER -

Transient oscillations in super twisting sliding mode control systems with actuator dynamics

Abstract

Keywords

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