Fractional integral sliding modes for robust tracking of nonlinear systems

Muñoz‐Vázquez, Aldo Jonathan; Parra-Vega, Vicente; Sánchez‐Orta, Anand

doi:10.1007/s11071-016-3086-5

Cited by 17 publications

(14 citation statements)

References 22 publications

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“…Then, it is plausible to argue that a fractional calculus based disturbance observer can be synthesised to exactly estimate fractal non-differentiable disturbances. The proposed fractional-order nonlinear observer (FNDOB) is based on a fractional sliding mode scheme recently proposed in [23,24], inspired in the pioneer work of [25,26], as well as successfully implemented in [15,27], by designing continuous controllers that compensate for Hölder disturbances in finite-time, however, the exact observation of Hölder disturbances and its application to the velocity control of wind turbines, to reduce the effect of the turbulent component of the wind flow, remains as an open problem.…”

Section: On Disturbance Observer Based Controlmentioning

confidence: 99%

Robust control of wind turbines based on fractional nonlinear disturbance observer

Muñoz‐Vázquez

Parra-Vega²,

Sánchez‐Orta³

et al. 2019

Asian Journal of Control

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In order to assure maximum energy conversion, the angular velocity of the wind turbine rotor tracks a nominal profile depending on the wind speed. However, conventionally, wind flows present non‐differentiable components due to turbulence and gust winds, which affect the wind energy management. Thus, a fast and robust controller is required to induce such nominal regime for maximum energy transfer. A fractional‐order nonlinear disturbance‐observer (FNDOB) is proposed in this paper to cancel the non‐differentiable components of the wind speed, as well as dynamic uncertainties and other aerodynamic disturbances. The proposed FNDOB is based on continuous fractional sliding modes, assuring that disturbances and uncertainties are exactly compensated in finite‐time. A representative simulation study for a variable‐speed wind turbine is presented to show the reliability of the proposed scheme, and a comparative analysis with respect to a conventional linear disturbance observer based control is presented.

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Section: On Disturbance Observer Based Controlmentioning

confidence: 99%

Robust control of wind turbines based on fractional nonlinear disturbance observer

Muñoz‐Vázquez

Parra-Vega²,

Sánchez‐Orta³

et al. 2019

Asian Journal of Control

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“…Secondly, recent results in [26][27][28] are adopted to design a fractional-order sliding mode control that rejects exactly (not just equivalently) the matched Hölder disturbances in finite-time, by invoking the topological properties of differintegral operators [17]. Finally, a nominal controller is designed to enforce finite-time convergence of the whole (pseudo)state [10].…”

Section: Proposed Solution and Contributionmentioning

confidence: 99%

“…The interested reader is referred to [14,17,18,[26][27][28], and for completeness, in this section, the differintegral operators and some properties of Hölder functions are introduced. Consider ∈ (0, 1] and the following differintegral operators:…”

Section: Fractional Differintegral Operators Fractional Calculus Is mentioning

confidence: 99%

“…, }, with Ω the timeinterval at which the system is studied, output = 1 stands for the measured variable, is the control input, and : Ω → R represents matched disturbances and uncertainties. Examples of Hölder effects in physical systems modeled throughout , are given in [27][28][29][30][31].…”

Section: System Description and Control Statementmentioning

confidence: 99%

“…where the continuous nominal control 0 stabilizes the ideal system without disturbance [10], and the differintegral sliding mode control compensates the matched Hölder disturbance [26][27][28]. Let be a penalization variable that measures the deviation from the ideal system (without disturbances) to the real system defined by (7).…”

Section: Disturbance Observer Based On Fractional Differintegralmentioning

confidence: 99%

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Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

Muñoz‐Vázquez

Parra-Vega²,

Sánchez‐Orta³

et al. 2017

Mathematical Problems in Engineering

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The problem of designing a continuous control to guarantee finite-time tracking based on output feedback for a system subject to a Hölder disturbance has remained elusive. The main difficulty stems from the fact that such disturbance stands for a function that is continuous but not necessarily differentiable in any integer-order sense, yet it is fractional-order differentiable. This problem imposes a formidable challenge of practical interest in engineering because (i) it is common that only partial access to the state is available and, then, output feedback is needed; (ii) such disturbances are present in more realistic applications, suggesting a fractional-order controller; and (iii) continuous robust control is a must in several control applications. Consequently, these stringent requirements demand a sound mathematical framework for designing a solution to this control problem. To estimate the full state in finite-time, a high-order sliding mode-based differentiator is considered. Then, a continuous fractional differintegral sliding mode is proposed to reject Hölder disturbances, as well as for uncertainties and unmodeled dynamics. Finally, a homogeneous closed-loop system is enforced by means of a continuous nominal control, assuring finite-time convergence. Numerical simulations are presented to show the reliability of the proposed method.

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On dynamic sliding mode control of nonlinear fractional-order systems using sliding observer

2018

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Fractional integral sliding modes for robust tracking of nonlinear systems

Cited by 17 publications

References 22 publications

Robust control of wind turbines based on fractional nonlinear disturbance observer

Robust control of wind turbines based on fractional nonlinear disturbance observer

Output Feedback Finite‐Time Stabilization of Systems Subject to Hölder Disturbances via Continuous Fractional Sliding Modes

On dynamic sliding mode control of nonlinear fractional-order systems using sliding observer

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