Second-order sliding-mode differentiators: an experimental comparative analysis using Van der Pol oscillator

Ahmed, Hafiz; Ríos, Héctor; Ayalew, Beshah; Wang, Yongqiang

doi:10.1080/00207179.2018.1442023

Cited by 15 publications

(8 citation statements)

References 74 publications

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“…Remark 2. In most of the existing SMOs and differentiator designs such as in previous studies [9][10][11][12][13][14][15][16][17], the discontinuous function such as sign(.) has been employed.…”

Section: Problem Statementmentioning

confidence: 99%

“…Then, Basin et al [14] have provided the results of nonrecursive fixed time HOSMD by introducing the discontinuous term with more than one degree in every differential equation of estimator. Stimulated by a new power rate reaching exponential law [15], a faster nonhomogeneous exponential sliding mode differentiator has been proposed in Deepika et al [16] An experimental application of all the aforementioned differentiators has been well presented in Ahmed et al [17] for reconstruction of states of Van der Pol oscillator.…”

Section: Introductionmentioning

confidence: 99%

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Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Deepika

2020

Asian Journal of Control

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This paper puts forward contemporary designs of sliding mode differentiator and state observer for evaluation of unknown nonlinear signal derivatives and unknown internal system states, respectively, by the virtue of tangential and inverse sinusoidal hyperbolic functions. The utility of the proposed frameworks is that it bestows smooth and robust estimation without inciting unacceptable oscillations (chattering), unlike high gain discontinuous function-based preliminary observers/differentiators. Moreover, the employed double hyperbolic functions would drive the various deviations in estimations of signals or states to a very close neighborhood of origin in finite time which is substantiated via Lyapunov's energy function. To demonstrate the efficiency of the introduced techniques, two examples for estimating the derivatives of a nonlinear signal and internal states of motor are also illustrated with time varying uncertainties. At last, the attained simulation outcomes of the proposed differentiator are further compared with formerly formulated designs such as higher-order sliding mode differentiator (HOSMD) and uniformly convergent differentiator (UCD).

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Section: Problem Statementmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Deepika

2020

Asian Journal of Control

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“…In [27], the outputs of the oscillators were forced to track the reference by NN-based feedback linearizing control algorithms. Experimentally, a sliding-mode observer was used to estimate the states of the oscillators [28]. In optimal control, the oscillators were presented by the strict-feedback nonlinear systems [1,Ch.…”

Section: Introductionmentioning

confidence: 99%

H∞ Control for Oscillator Systems With Event-Triggering Signal Transmission of Internet of Things

2023

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This article proposes to design a distributed H ∞ optimal control algorithm for Van der Pol oscillators with unknown internal dynamics, input constraints and external disturbances, via event-triggering signal transmission of the Internet of Things (IoT). First, the graph theory for the IoT is introduced. Second, the dynamics of Van der Pol oscillators are transformed into the tracking dynamics which cooperate via the IoT network. Third, unlike the existing online optimal control algorithms using adaptive dynamic programming, we design an H ∞ optimal control algorithm employing an event-triggering signal transmission mechanism to reduce the burden of communication resource and computation bandwidth of the IoT network. As the triggering condition and approximation parameter update policies are appropriately designed, the algorithm guarantees that the Zeno phenomenon is free, the consensus errors are uniformly ultimately bounded, and the external disturbance is compensated. Finally, numerical simulation results with comparison to the time-triggering algorithms confirm the effectiveness of the proposed algorithm.

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“…However, explicit discretization is considered as an inappropriate scheme especially, when dealing with the set‐valued functions, which causes problems such as numerical chattering and sensitivity to the gains 22‐26 . As a result, without addressing the discretization issue, any comparison between the SMB differentiators and other types of differentiators may potentially lead to unfair conclusions 7,27,28 …”

Section: Introductionmentioning

confidence: 99%

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

Mojallizadeh

Brogliato

Acary

2021

Intl J Robust & Nonlinear

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A complete review of the known differentiators and their time‐discretizations have been addressed in this study. To resolve the drawbacks of the explicit (forward Euler) discretization, which is commonly utilized in sliding‐mode‐based differentiators, implicit time discretization methods are proposed to handle the set‐valued functions. The proposed schemes are supported by some analytical results to show their crucial properties, for example, finite‐time convergence, exactness, invariant sliding‐surface, chattering elimination, insensitivity to the gains during the sliding‐phase, and the well‐posedness. The causal implementation of the proposed implicit schemes has been addressed clearly and supported by flowcharts. Semi‐implicit schemes are also presented to provide a compromise between the performance and the ease of implementation. Finally, an exhaustive comparison is made using numerical experiments among 25 different state‐of‐the‐art differentiators to evaluate the behaviors of the differentiators facing the noise and initial error. Realistic conditions are considered in the simulations to provide useful information based on practical conditions. General conclusions are that implicit discretizations can supersede explicit and semi‐implicit ones.

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Second-order sliding-mode differentiators: an experimental comparative analysis using Van der Pol oscillator

Abstract: This document is the author's post-print version, incorporating any revisions agreed during the peer-review process. Some differences between the published version and this version may remain and you are advised to consult the published version if you wish to cite from it.

Cited by 15 publications

References 74 publications

Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

Frameworks for double hyperbolic function‐based robust sliding mode differentiator and observer for nonlinear dynamics

H∞ Control for Oscillator Systems With Event-Triggering Signal Transmission of Internet of Things

Time‐discretizations of differentiators: Design of implicit algorithms and comparative analysis

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