A New Varying-Gain-Exponent-Based Differentiator/Observer: An Efficient Balance Between Linear and Sliding-Mode Algorithms

Ghanes, Malek; Barbot, Jean–Pierre; Fridman, Leonid; Levant, Arie; Boisliveau, Robert

doi:10.1109/tac.2020.2973609

Cited by 46 publications

(29 citation statements)

References 33 publications

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“…In this context, two different adaptation techniques, namely adaptive coefficients and adaptive exponents , have been introduced. Some studies 18,60,61 dealt with the adaptive laws for the coefficients, while in other studies, 19‐21 the adaptation mechanisms are considered for the exponents. These schemes are introduced in Sections 2.7.1 and 2.7.2, respectively.…”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

“…The idea of variable gain exponent comes from the observation that by changing the exponent of an SMB differentiator, a trade‐off can be made between the exactness and robustness to noise. Comparisons, based on laboratory set‐ups, between the LF and the STD show that the SMB differentiators are more sensitive to measurement noise 19‐21 . Consequently, a modified SMB differentiator has been developed for noisy environments, where the exponent of the sliding variable (see

α (t)

in (11) can take a value between 0.5 (corresponding to the STD) and 1 (corresponding to a LF).…”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

“…The most recent study on the variable gain exponent differentiator (VGED) has been conducted in Reference 21. The continuous‐time VGED reads as: where, as before,

σ_{0} (t) = z_{0} (t) - f (t)

, and

f (t) = f_{0} (t) + n (t)

is the input signal which is polluted by an additive noise

n (t)

.…”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

“…The SMB differentiators mostly have a fixed structure such that a trade‐off usually has to be made between the exactness and the robustness to noise when dealing with the parameter tuning. Hence, SMB differentiators with adaptation mechanisms 18‐21 have also been proposed to achieve both robustness and the exactness. The adaptive SMB differentiators can be categorized into two groups, namely, adaptation for the coefficients 18 and adaptation for the exponents 19‐21 …”

Section: Introductionmentioning

confidence: 99%

“…Hence, SMB differentiators with adaptation mechanisms 18‐21 have also been proposed to achieve both robustness and the exactness. The adaptive SMB differentiators can be categorized into two groups, namely, adaptation for the coefficients 18 and adaptation for the exponents 19‐21 …”

Section: Introductionmentioning

confidence: 99%

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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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Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

α (t)

in (11) can take a value between 0.5 (corresponding to the STD) and 1 (corresponding to a LF).…”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

“…The most recent study on the variable gain exponent differentiator (VGED) has been conducted in Reference 21. The continuous‐time VGED reads as: where, as before,

σ_{0} (t) = z_{0} (t) - f (t)

, and

f (t) = f_{0} (t) + n (t)

is the input signal which is polluted by an additive noise

n (t)

.…”

Section: A Summary Of the Continuous‐time Differentiatorsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Mojallizadeh

Brogliato

Acary

2021

Intl J Robust & Nonlinear

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Dynamic Parameter Identification for Cable-Driven Parallel Robots

Rasheed,

Michel,

Caro

et al. 2023

Mechanisms and Machine Science

Self Cite

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This paper presents an initial work of identifying the dynamic parameters for cable-driven parallel robot (CDPR), CRAFT with a rigorous protocol. An orbital trajectory of the platform is designed in order to get a pure translation movement of the platform. This trajectory evolves in a plane and allows the identification of four dynamic parameters, the mass of the platform and the first three moments along the three main axes. The identification results obtained respectively from the data from the experimental measurements of the moving platform, and from the experimental measurements treated with the application of a semi-implicit homogeneous differentiator, show that in spite of the complexity of CRAFT an identification of all its essential dynamic parameters is possible. Moreover, in the long term, an online identification of CRAFT during handling tasks is envisaged.

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Effect of Euler Explicit and Implicit Time Discretizations on Variable-Structure Differentiators

Mojallizadeh,

Brogliato

2023

Studies in Systems, Decision and Control

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A New Varying-Gain-Exponent-Based Differentiator/Observer: An Efficient Balance Between Linear and Sliding-Mode Algorithms

Cited by 46 publications

References 33 publications

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

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

Dynamic Parameter Identification for Cable-Driven Parallel Robots

Effect of Euler Explicit and Implicit Time Discretizations on Variable-Structure Differentiators

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