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Fractional‐order iterative learning control for fractional‐order linear systems
Asian Journal of Control, 2011AbstractIn this paper, we discuss in time domain the convergence of the iterative process for fractional‐order systems. Fractional order iterative learning updating schemes are considered. For the linear time invariant (LTI) system case, the convergence conditions of the fractional‐order and integer‐order iterative learning schemes are proved to be ...
Li, Yan, Chen, YangQuan, Ahn, Hyo-Sung
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Communications in Nonlinear Science and Numerical Simulation, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Fractional order solutions to fractional order partial differential equations
SeMA Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bhupendra Nath Tiwari +4 more
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Fractional Order Universal Adaptive Stabilizer for Fractional Order Systems
Volume 4: 7th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B and C, 2009In this paper, the fractional order universal adaptive stabilization of fractional order SISO system is discussed. The fractional universal adaptive stabilizer is u(t) = −k(t)sgn{CB}y(t), where 0Dtβk(t) = ‖y(t)‖p, which guarantees the asymptotic stability of the equilibrium point of fractional order state space system with finite control effort ...
Yan Li, YangQuan Chen
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Designing of Fractional Order PID Controller for Unstable Fractional Order System
2019 Joint International Conference on Digital Arts, Media and Technology with ECTI Northern Section Conference on Electrical, Electronics, Computer and Telecommunications Engineering (ECTI DAMT-NCON), 2019This paper proposes the fractional-order proportional-integral-derivative (FOPID or $\mathbf { P } \mathbf { I } ^ { \lambda } \mathbf { D } ^ { \mu }$) controller design optimization for a stable fractional order (FO) system by using the flower pollination algorithm (FPA), one of the most efficient metaheuristic optimization search techniques.
Boonruk Chipipop, Deacha Puangdownreong
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Canadian Journal of Mathematics, 1950
The body of this paper is a complete answer to the following question:Let E be any space whatever. g(x) is a function mapping E into E. When does there exist a function f(x), of the same type, such that(1)
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The body of this paper is a complete answer to the following question:Let E be any space whatever. g(x) is a function mapping E into E. When does there exist a function f(x), of the same type, such that(1)
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2012
Thinking of Laplace and frequency domains, it should not be hard for the feedback control community to understand that, by considering more general control actions of the form s α ,α∈ℝ, we could achieve more satisfactory compromises between the positive and negative effects of the basic control actions (proportional, derivative, and integral ones) on ...
Blas M. Vinagre, Concepción A. Monje
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Thinking of Laplace and frequency domains, it should not be hard for the feedback control community to understand that, by considering more general control actions of the form s α ,α∈ℝ, we could achieve more satisfactory compromises between the positive and negative effects of the basic control actions (proportional, derivative, and integral ones) on ...
Blas M. Vinagre, Concepción A. Monje
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2015
In a letter to L’Hospital in 1695, Leibniz raised the possibility of generalizing the operation of differentiation to non-integer orders and L’Hospital asked what would be the result of half-differentiating a variable. Leibniz in an open letter dated September 30, 1695 replied “It leads to a paradox, from which 1 day useful consequences will be drawn”.
J. Sabatier, C. Farges, A. Oustaloup
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In a letter to L’Hospital in 1695, Leibniz raised the possibility of generalizing the operation of differentiation to non-integer orders and L’Hospital asked what would be the result of half-differentiating a variable. Leibniz in an open letter dated September 30, 1695 replied “It leads to a paradox, from which 1 day useful consequences will be drawn”.
J. Sabatier, C. Farges, A. Oustaloup
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2017
This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new
Biswas K. +5 more
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This book focuses on two specific areas related to fractional order systems – the realization of physical devices characterized by non-integer order impedance, usually called fractional-order elements (FOEs); and the characterization of vegetable tissues via electrical impedance spectroscopy (EIS) – and provides readers with new tools for designing new
Biswas K. +5 more
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Tuning fractional order proportional integral controllers for fractional order systems
Journal of Process Control, 2010Abstract In this paper, two fractional order proportional integral controllers are proposed and designed for a class of fractional order systems. For fair comparison, the proposed fractional order proportional integral (FOPI), fractional order [proportional integral] (FO[PI]) and the traditional integer order PID (IOPID) controllers are all designed ...
Ying Luo +3 more
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