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Fractional-order Systems and Controls

About: The article was published on 2010-01-01. It has received 1696 citations till now. The article focuses on the topics: Order (business).
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TL;DR: This review article aims to present some short summaries written by distinguished researchers in the field of fractional calculus that will guide young researchers and help newcomers to see some of the main real-world applications and gain an understanding of this powerful mathematical tool.

922 citations

Journal ArticleDOI
TL;DR: This review investigates its progress since the first reported use of control systems, covering the fractional PID proposed by Podlubny in 1994, and is presenting a state-of-the-art fractionalpid controller, incorporating the latest contributions in this field.

447 citations

Journal ArticleDOI
TL;DR: The authors presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering, and presents a discussion of the relationship between fractional derivatives and integral derivatives.
Abstract: This paper presents a review of definitions of fractional order derivatives and integrals that appear in mathematics, physics, and engineering.

387 citations

Journal ArticleDOI
TL;DR: A new tuning method for fractional order proportional and derivative (PD ¿) or FO-PD controller is proposed for a class of typical second-order plants and shows that the closed-loop system can achieve favorable dynamic performance and robustness.
Abstract: In recent years, it is remarkable to see the increasing number of studies related to the theory and application of fractional order controller (FOC), specially PI ? D ? controller, in many areas of science and engineering. Research activities are focused on developing new analysis and design methods for fractional order controllers as an extension of classical control theory. In this paper, a new tuning method for fractional order proportional and derivative (PD ?) or FO-PD controller is proposed for a class of typical second-order plants. The tuned FO-PD controller can ensure that the given gain crossover frequency and phase margin are fulfilled, and furthermore, the phase derivative w. r. t. the frequency is zero, i.e., the phase Bode plot is flat at the given gain crossover frequency. Consequently, the closed-loop system is robust to gain variations. The FOC design method proposed in the paper is practical and simple to apply. Simulation and experimental results show that the closed-loop system can achieve favorable dynamic performance and robustness.

378 citations

Journal ArticleDOI
TL;DR: The existence and uniqueness of global solutions in the space of weighted continuous functions are proved and the stability of the solution for a weighted Cauchy-type problem is analyzed.
Abstract: We consider an initial value problem for a class of nonlinear fractional differential equations involving Hilfer fractional derivative. We prove existence and uniqueness of global solutions in the space of weighted continuous functions. The stability of the solution for a weighted Cauchy-type problem is also analyzed.

348 citations