Comment on “Fractional-order fixed-time nonsingular terminal sliding mode synchronization and control of fractional-order chaotic systems”

Khanzadeh, Alireza; Mohammadzaman, Iman

doi:10.1007/s11071-018-4525-2

Cited by 12 publications

(4 citation statements)

References 2 publications

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“…In contrast to some previous works (see previous studies [24][25][26]), the second-order predefined-time stability concept has been considered to enforce a second-order predefined-time sliding mode for a class of fractionalorder systems. Besides, the controller is continuous even in the case of unknown disturbances, where the initial condition is not explicitly taken into account in the control design.…”

Section: Simulation Resultsmentioning

confidence: 99%

“…However, to guarantee the existence of a fixed-time sliding mode in the case of a Caputo derivative-based system, the initial condition is assumed available to be compensated by the controller, which in turn becomes very large at the initial condition. In contrast to previous studies, [24][25][26][27] and inspired in Pisano et al, [15] this paper proposes an auxiliary controller by means of a well-suited dynamic extension. This formulation allows inducing an integer-order reaching phase, such that the controller is well-defined for any time.…”

Section: Introductionmentioning

confidence: 98%

“…In these works, a sliding mode is enforced in a time that is uniformly bounded with respect to the initial condition. The fixed-time stability concept has been considered to design suitable controllers for fractional-order systems of order in (0, 1) [24][25][26][27]. However, to guarantee the existence of a fixed-time sliding mode in the case of a Caputo derivative-based system, the initial condition is assumed available to be compensated by the controller, which in turn becomes very large at the initial condition.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Second‐order predefined‐time sliding‐mode control of fractional‐order systems

Muñoz‐Vázquez

Sánchez‐Torres

Defoort

2020

Asian Journal of Control

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This paper presents a predefined-time control of fractional-order linear system subject to a large class of continuous but not necessarily integer-order differentiable disturbances. The dynamical system is based on the Caputo derivative and has an order that lies in (1,2). The proposed controller, based on a dynamic extension, induces an integer-order reaching phase, such that an invariant second-order sliding mode is enforced in predefined-time, that is, the solution of the fractional-order system and its integer-order derivative converge to the origin within a time that is prescribed as a tunable control parameter. The controller is continuous and able to compensate for unknown continuous disturbances. A simulation study is carried out in order to show the effectiveness of the proposed scheme.

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Section: Simulation Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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Second‐order predefined‐time sliding‐mode control of fractional‐order systems

Muñoz‐Vázquez

Sánchez‐Torres

Defoort

2020

Asian Journal of Control

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“…Lemma 1. [38] If 0 < α < 1 , f (t) ∈ C , R-L and Caputo fractional derivatives can be associated with each other as follows:…”

Section: Dynamic Analysis Of the Fractional-order Ferroresonance Systemmentioning

confidence: 99%

Dynamic Analysis and Suppression Strategy Research on a Novel Fractional-Order Ferroresonance System

Yang,

Fan,

et al. 2023

Fractal Fract

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Ferroresonance is characterized by overvoltage and irregular operation in power systems, which can greatly endanger system equipment. Mechanism analysis of the ferroresonance phenomenon depends mainly on model accuracy. Due to the fractional-order characteristics of capacitance and inductance, fractional-order models are more universal and accurate than integer-order models. A typical 110 kV ferroresonance model is first established. The influence of the excitation amplitude on the dynamic behavior is analyzed. The fractional-order ferroresonance model is then introduced, and the effects of the fractional order and flux-chain order on the system’s motion state are studied via bifurcation diagrams and phase portraits. In order to suppress the nonlinear dynamic behavior of fractional-order ferroresonance systems, a novel fractional-order fast terminal sliding mode control method based on finite-time theory and the frequency distributed model is proposed. A new fractional-order sliding mode surface and control law using a saturation function are developed. A robust fractional-order sliding mode controller could achieve finite-time stabilization and tracking despite model uncertainties and external disturbances. Compared with conventional sliding mode methods, the simulation results highlight the effectiveness and superiority. The research provides a theoretical basis for ferroresonant analysis and suppression in large-scale interconnected power grids.

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