Adaptive Stabilization for a Class of Fractional-Order Systems with Nonlinear Uncertainty

Jmal, Assaad; Naifar, Omar; Makhlouf, Abdellatif Ben; Derbel, Nabil; Hammami, Mohamed Ali

doi:10.1007/s13369-019-04148-3

Cited by 5 publications

(2 citation statements)

References 27 publications

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“…Fractional order controllers, like CRONE control and expanded fractional control theories based on adaptive control and sliding mode control, have produced improved results in both theory and practice [28,29]. The fractional order control has been investigated in robotic and engineering systems and used to obtain reliable performances in industrial systems, despite its inherent complexity [30][31][32][33].…”

Section: Introductionmentioning

confidence: 99%

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

2023

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Rehabilitation Exoskeleton is becoming more and more important in physiotherapists’ routine work. To improve the treatment performance, such as reducing the recovery period and/or monitoring and reacting to unpredictable situations, the rehabilitation manipulators need to help the patients in various physical trainings. A special case of the active disturbance rejection control (ADRC) is applied to govern a proper realisation of basic limb rehabilitation trainings. The experimental study is performed on a model of a flexible joint manipulator, whose behaviour resembles a real exoskeleton rehabilitation device (a one-degree-of-freedom, rigid-link, flexible-joint manipulator). The fractional (FADRC) is an unconventional model-independent approach, acknowledged as an effective controller in the existence of total plant uncertainties, and these uncertainties are inclusive of the total disturbances and unknown dynamics of the plant. In this work, three FADRC schemes are used, the first one using a fractional state observer (FSO), or FADRC1, second one using a fractional proportional-derivative controller (FPD), or FADRC2, and the third one a Multi-loop fractional in PD-loop controller and the observer-loop (Feedforward and Feedback), or FADRC3. The simulated Exoskeleton system is subjected to a noise disturbance and the FADRC3 shows the effectiveness to compensate all these effects and satisfies the desired position when compared with FADRC1 and FADRC2. The design and simulation were carried out in MATLAB/Simulink.

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Section: Introductionmentioning

confidence: 99%

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

2023

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“…In the literature, different definitions of the fractional derivative can be found. In the last years, various works within the control theory area have been published using different fractional derivative concepts, such as the Caputo derivative [13] and the Caputo–Katugampola derivative [14]. Recently, in Khalil et al [15], some researchers have defined a new simple and effective derivative known as the “conformable fractional derivative.” It is important to mention that the conformable derivative tool allows to overcome some technical problems in investigating FO systems.…”

Section: Introductionmentioning

confidence: 99%

Non‐fragile H_∞ observer for Lipschitz conformable fractional‐order systems

Naifar

Jmal

Makhlouf

2021

Asian Journal of Control

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The issue of designing simultaneously robust and non‐fragile observers for the classical integer‐order systems has been widely investigated in the literature. Yet, there are just some few works that have tackled the same problem for non‐integer‐order systems. Moreover, the conformable derivative is an interesting concept that has been introduced by some researchers in the last decade. This new derivative presents some advantageous mathematical properties, compared with older concepts. In this paper, and motivated by these facts, the authors suggest a first scheme to design observers, which are simultaneously robust and non‐fragile, for Lipschitz nonlinear conformable fractional‐order systems. The H∞ performance theory is used for that purpose. The efficiency of the developed approach is confirmed through simulations for a numerical example.

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Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

Peng

Wang

Zuo

2022

Applied Mathematics and Computation

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Adaptive Stabilization for a Class of Fractional-Order Systems with Nonlinear Uncertainty

Cited by 5 publications

References 27 publications

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Non‐fragile H_∞ observer for Lipschitz conformable fractional‐order systems

Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

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Adaptive Stabilization for a Class of Fractional-Order Systems with Nonlinear Uncertainty

Cited by 5 publications

References 27 publications

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Fractional multi-loop active disturbance rejection control for a lower knee exoskeleton system

Non‐fragile H∞ observer for Lipschitz conformable fractional‐order systems

Co-design of state-dependent switching law and control scheme for variable-order fractional nonlinear switched systems

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Non‐fragile H_∞ observer for Lipschitz conformable fractional‐order systems