Adaptation of Levant's differentiator based on barrier function

Obeid, Hussein; Laghrouche, Salah; Harmouche, Mohamed; Golkani, Mohammad Ali

doi:10.1080/00207179.2017.1406149

Cited by 29 publications

(24 citation statements)

References 13 publications

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“…As soon as the state of the system reaches the domain Ω * at time T > t 1 , the size of real 2-SM can be estimated according with |s| < C 2 , | . s| < 2L + C + (L + ) 2 2 T which determines the practical accuracy for the algorithm (12).…”

Section: Boundness Of L(t)mentioning

confidence: 99%

“…Nevertheless, these control strategies require numerous gains/parameters, and the selection of their values lacks of a systematic method of tuning. In the work of Obeid et al, a methodology based on a barrier function for the adaptation gains has been developed; however, it depends on the upper bound of the second derivative of the sliding surface. In the work of Li et al, an adaptation law based on the fuzzy sliding mode algorithm has been proposed.…”

Section: Introductionmentioning

confidence: 99%

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A simplified version of adaptive super‐twisting control

Gutierrez

León-Morales

Plestan

et al. 2019

Intl J Robust & Nonlinear

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Summary In this paper, a simplified super‐twisting control with adaptive gain is proposed for a class of nonlinear uncertain systems. A strong Lyapunov function is constructed to design a sliding mode controller with adaptive gain. Furthermore, the analysis of the finite time convergence towards the equilibrium point of the closed‐loop system is detailed. Regarding previous works from literature, the main contribution of this approach is the simplification of the gain tuning process by maintaining a high level of performance. Finally, simulation results for tracking control of a quadrotor are given to show the performance of the proposed algorithm.

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Section: Boundness Of L(t)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A simplified version of adaptive super‐twisting control

Gutierrez

León-Morales

Plestan

et al. 2019

Intl J Robust & Nonlinear

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show abstract

“…Through the adaptation process, the BF can induce uncontrollably high gains, which can limit real-time implementation. The gain adaptation of BF is completely closed to the BF boundary [22,23]. Theoretically, the BF gains can converge to infinity.…”

Section: Introductionmentioning

confidence: 96%

“…The barrier function method (BFM) is employed for the adaptation mechanism of the STA coefficients. The barrier function (BF) adaptation method can be found in the recent scholars [22][23][24][25]. The original idea of the BF adaptation law is suppression of unknown bounded disturbances and uncertainty [24].…”

Section: Introductionmentioning

confidence: 99%

“…The original idea of the BF adaptation law is suppression of unknown bounded disturbances and uncertainty [24]. The adaptation principle of BF can be applied to FSCM and HSMC algorithms as a feedback controller, as well as state estimators and differentiators [23][24][25]. In theory, the BF adaptation technique doesn't have the capability to suppress the chattering phenomenon of FSCM or HSMC controllers.…”

Section: Introductionmentioning

confidence: 99%

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The Effective Chattering Suppression Technique with Adaptive Super-Twisted Sliding Mode Controller Based on the Quasi-Barrier Function; An Experimentation Setup

Svečko¹,

Gleich²,

Sarjaš³

2020

Applied Sciences

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The paper presents a modified adaptation algorithm for the super-twisted sliding mode controller structure, based on the barrier function method. The aim of the paper is to reduce the chattering phenomena of the controller, which limited the use of the controller in different applications. The chattering phenomena are mostly caused by the overestimated controller gain due to the assumed disturbance bound, which is mostly inaccurate. The chattering origins are also the unknown parasitic dynamic of the system and discrete implementation of the controller. The proposed method with the Barrier function is used to alleviate the chattering phenomena with the adaptation of the controller parameters. The novelty of the method is using an adaptation procedure only in prescribed regions of the sliding variable, otherwise, the adaptation is not used. The advantage of the method is the proper rejection of the chattering phenomena in the vicinity of the manifold of the sliding variable, regardless of the order of the system. With proper selection of the adaptation boundary, the effect of discrete implementation, especially for a longer sampling time of the algorithm, can be suppressed efficiently, as well as the effect of the overestimated controller parameters. The proposed method is verified and compared with a standard version of the algorithm in simulation and real-time environments.

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Dual layer barrier functions based adaptive higher order sliding mode control

Obeid

Laghrouche

2021

Intl J Robust & Nonlinear

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This article presents an adaptive discontinuous higher order sliding mode control (HOSMC) strategy for a disturbed chain of integrators of order n. This strategy employs a barrier function‐based dual layer adaptation and it ensures the convergence of the sliding variable and its (n − 1) first derivatives to zero without requiring any information on the bounds of the disturbances or their derivatives. It consists in applying a barrier function‐based adaptive super‐twisting methodology compensating Lipschitz disturbances with some error, and a growing gain‐based adaptive HOSMC which just needs to counteract this error. Real‐time simulation platform is used to test the efficacy of the proposed strategy to control a linear induction motor considering dynamic end effects.

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Adaptation of Levant's differentiator based on barrier function

Cited by 29 publications

References 13 publications

A simplified version of adaptive super‐twisting control

A simplified version of adaptive super‐twisting control

The Effective Chattering Suppression Technique with Adaptive Super-Twisted Sliding Mode Controller Based on the Quasi-Barrier Function; An Experimentation Setup

Dual layer barrier functions based adaptive higher order sliding mode control

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