Fractional-order Modeling and Control of Dynamic Systems

Tepljakov, Aleksei

doi:10.1007/978-3-319-52950-9

Cited by 154 publications

(106 citation statements)

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“…In the past two decades, there has been tremendous interest in studying fractional differential equations (FDEs for short) due to their extensive applications in various fields of engineering and scientific disciplines (see [1][2][3][4][5][6][7][8]). For example, in [8], Laskin proposed the following fractional stochastic dynamic model for the considered market:…”

Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

2018

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Section: Introductionmentioning

confidence: 99%

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

2018

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“…The fractional‐order nature of the integration operator, s −δ , makes it digitally nonimplementable. Hence, the fractional integral operator is approximated using a fifth‐order Oustaloup's recursive filter in order to practically implement it using an embedded computers . The lower and upper bounds of the translational frequencies of the filter are empirically selected as ω L = 10 −3 rad/s and ω H = 10 3 rad/s, respectively .…”

Section: Fractional‐order Proportional‐integral Controllermentioning

confidence: 99%

Time‐optimal control of DC‐DC buck converter using single‐input fuzzy augmented fractional‐order PI controller

Saleem

Shami

Mahmood-ul-Hasan

2019

Int Trans Electr Energ Syst

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Summary This paper presents a robust and optimal output‐voltage tracking controller for a DC‐DC buck converter. A fractional‐order proportional‐integral (FPI) controller is primarily used to eliminate the steady‐state error and damp the oscillations. In order to improve the error convergence rate of the response, the FPI controller is augmented with a single‐input fuzzy‐logic based precompensator stage. The fuzzy precompensator aggregates the information regarding the error and error derivative using the signed‐distance method. The derived aggregated signal is used to infer logical control decisions based on a predefined one‐dimensional rule base. The simplification yields shorter computation time and a piecewise linear control surface that improves the system's immunity against exogenous disturbances and unprecedented nonlinearities. The error derivative is indirectly computed by measuring the capacitor current in real time. This modification further enhances the computational efficiency, offers minimum‐time transient recovery, and compensates the hysteresis effect rendered by parasitic impedances. The controller gains are optimally selected using the particle swarm optimization algorithm. Credible hardware‐in‐the‐loop experiments are conducted to validate the time optimality and robustness of the proposed controller. The experimental results clearly demonstrate the significant improvement rendered by the proposed controller in the system's reference tracking performance, disturbance‐rejection capability, and transient recovery time.

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“…For continuous implementation, pole-zero pairs should be in the negative real axis of -plane and for discrete implementation, pole-zero pairs should lie within the unit circle of -plane. More number of pole-zero pairs exhibit better and close approximation, but increases the memory requirements and complexity; however, the advent of modern powerful software can easily deal with additional complexity [106].…”

Section: Implementation Challenges and Softwarementioning

confidence: 99%

Fractional-Order System Modeling and its Applications

Kothari¹,

Mehta²,

Prasad³

2019

JESTR

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In order to control or operate any system in a closed-loop, it is important to know its behavior in the form of mathematical models. In the last two decades, a fractional-order model has received more attention in system identification instead of classical integer-order model transfer function. Literature shows recently that some techniques on fractional calculus and fractional-order models have been presenting valuable contributions to real-world processes and achieved better results. Such new developments have impelled research into extensions of the classical identification techniques to advanced fields of science and engineering. This article surveys the recent methods in the field and other related challenges to implement the fractional-order derivatives and miss-matching with conventional science. The comprehensive discussion on available literature would help the readers to grasp the concept of fractional-order modeling and can facilitate future investigations. One can anticipate manifesting recent advances in fractional-order modeling in this paper and unlocking more opportunities for research.

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Fractional-order Modeling and Control of Dynamic Systems

Cited by 154 publications

References 0 publications

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

Existence and uniqueness results for the coupled systems of implicit fractional differential equations with periodic boundary conditions

Time‐optimal control of DC‐DC buck converter using single‐input fuzzy augmented fractional‐order PI controller

Fractional-Order System Modeling and its Applications

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