Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties

doi:10.1007/s11465-020-0620-4

Front. Mech. Eng.

2021, Vol. 16

Issue (2) : 353-362 https://doi.org/10.1007/s11465-020-0620-4

RESEARCH ARTICLE

Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties

Hui LI^1,², Ruiqin LI¹(

), Jianwei ZHANG³

¹. School of Mechanical Engineering, North University of China, Taiyuan 030051, China
². Department of Mining Engineering, Lvliang University, Lvliang 033001, China
³. Department of Informatics, University of Hamburg, Hamburg 22527, Germany

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Abstract

This study proposes a gained switching-based discrete-time sliding mode control method to address the chattering issue in disturbed discrete-time systems, which suffer from various unknown uncertainties. Through the new structure of the designed reaching law, the proposed method can effectively increase the convergence speed while guaranteeing chattering-free control. The performance of controlling underactuated robotic systems can be further improved by the adoption of fuzzy logic to perform adaptive online hyper-parameter tuning. In addition, an underactuated robotic system with uncertainties is studied to validate the effectiveness of the proposed reaching law. Results reveal the dynamic performance and robustness of the proposed reaching law in the studied system and prove the proposed method’s superiority over other state-of-the-art methods.

Keywords sliding-mode control robot control discrete-time uncertain systems fuzzy logic

Corresponding Author(s): Ruiqin LI

Just Accepted Date: 30 January 2021 Online First Date: 10 March 2021 Issue Date: 15 June 2021

Cite this article:

Hui LI,Ruiqin LI,Jianwei ZHANG. Gained switching-based fuzzy sliding mode control for a discrete-time underactuated robotic system with uncertainties[J]. Front. Mech. Eng., 2021, 16(2): 353-362.

URL:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-020-0620-4
https://academic.hep.com.cn/fme/EN/Y2021/V16/I2/353

$s (k)$	$α (k)$	$β (k)$
NB	PS	PB
NS	PS	PM
ZO	PZ	PZ
PS	PS	PM
PB	PS	PB

Tab.1 Employed fuzzy rules in the designed control method

Fig.1 Interfaces of the designed FLS for the designed control method. (a) Input and (b) output.

Fig.2 Comparison with state-of-the-art methods in terms of (a)

s (k)

, (b)

u (k)

, (c)

x (k)

, (d)

x ˙ (k)

, (e)

θ (k)

, and (f)

θ ˙ (k)

Methods	Chattering	Total translation of x/m	Settling time of θ/s	QSMB of $s (k)$
Gao et al. [23]	Severe	9.0634	3.6254	0.06667
Song et al. [28]	Free	33.7830	4.9913	<10⁻⁷
Yan et al. [29]	Free	37.9558	5.1859	<10⁻⁷
Proposed method	Free	29.3947	4.7810	<10⁻⁷
Methods	Max. $e ss$ of x/m	Max. $e ss$ of $x ˙$ /(m·s^–1)	Max. $e ss$ of θ/rad	Max. $e ss$ of $θ ˙$ /(rad·s^–1)
Gao et al. [23]	0.0432	0.0511	7.9166×10⁻⁴	0.1138
Song et al. [28]	0.0438	0.0064	0.0001	0.0013
Yan et al. [29]	0.0433	0.0050	7.1276×10⁻⁴	0.0011
Proposed method	0.0431	0.0049	7.0571×10⁻⁴	0.0017

Tab.2 Comparative analysis of state-of-the-art methods

Fig.3 Comparison results under different trajectories (Eq. (38)) and disturbances (Eq. (39)). (a)

x (k)

, (b)

x ˙ (k)

, (c)

θ (k)

, and (d)

θ ˙ (k)

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