Experimental study of fractional order proportional derivative controller synthesis for fractional order systems

Luo, Ying; Chen, YangQuan; Pi, Yiming

doi:10.1016/j.mechatronics.2010.10.004

Cited by 105 publications

(70 citation statements)

References 14 publications

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“…It has been found that in many practical cases, systems can be more adequately described using fractional-order differential equations [1][2][3][4][5][6][7][8][9][10][11]. Furthermore, fractional-order derivatives are excellent instruments for the description of memory and hereditary properties of various materials and processes [12].…”

Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

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Abstract. The problem of finite-time synchronization of fractional-order simplest two-component chaotic oscillators operating at high frequency and application to digital cryptography is addressed. After the investigation of numerical chaotic behavior in the system, an adaptive feedback controller is designed to achieve the finite-time synchronization of two oscillators, based on the Lyapunov function. This controller could find application in many other fractional-order chaotic circuits. Applying synchronized fractionalorder systems in digital cryptography, a well secured key system is obtained. Numerical simulations are given to illustrate and verify the analytic results.

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Section: Introductionmentioning

confidence: 99%

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

et al. 2017

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“…Now, define the chaos synchronization problem as follows: design an appropriate controller for system (4) such that the state trajectories of the above response system can track the state trajectories of the following drive chaotic system:…”

Section: Problem Statementmentioning

confidence: 99%

“…Although fractional calculus is a more than 300-year-old mathematical tool, its application in physics and engineering, especially in modeling and control, began only recently; for example, microelectromechanical systems [4] and systems consisting of viscoelastic materials [5] can be described more accurately using fractional calculus. Applications of fractional-order control techniques in chaotic systems have also been presented.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Song

Tejado

et al. 2017

Journal of Control Science and Engineering

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The synchronization of two fractional-order complex chaotic systems is discussed in this paper. The parameter uncertainty and external disturbance are included in the system model, and the synchronization of the considered chaotic systems is implemented based on the finite-time concept. First, a novel fractional-order nonsingular terminal sliding surface which is suitable for the considered fractional-order systems is proposed. It is proven that once the state trajectories of the system reach the proposed sliding surface they will converge to the origin within a given finite time. Second, in terms of the established nonsingular terminal sliding surface, combining the fuzzy control and the sliding mode control schemes, a novel robust single fuzzy sliding mode control law is introduced, which can force the closed-loop dynamic error system trajectories to reach the sliding surface over a finite time. Finally, using the fractional Lyapunov stability theorem, the stability of the proposed method is proven. The proposed method is implemented for synchronization of two fractional-order Genesio-Tesi chaotic systems with uncertain parameters and external disturbances to verify the effectiveness of the proposed fractional-order nonsingular terminal fuzzy sliding mode controller.

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“…We note the rapid growth of the development of algorithms using fractional differentiation, specifically in the field of artificial intelligence. These include, for example, image-processing algorithms [5], the identification of image features [6][7][8], and computer [9][10][11] and experimental [12,13] implementation of fractal proportional-integral-derivative (PID) controllers for industrial control systems.…”

Section: Introductionmentioning

confidence: 99%

Best Approximation of the Fractional Semi-Derivative Operator by Exponential Series

Zakharchenko

Kovalenko

2018

Mathematics

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A significant reduction in the time required to obtain an estimate of the mean frequency of the spectrum of Doppler signals when seeking to measure the instantaneous velocity of dangerous near-Earth cosmic objects (NEO) is an important task being developed to counter the threat from asteroids. Spectral analysis methods have shown that the coordinate of the centroid of the Doppler signal spectrum can be found by using operations in the time domain without spectral processing. At the same time, an increase in the speed of resolving the algorithm for estimating the mean frequency of the spectrum is achieved by using fractional differentiation without spectral processing. Thus, an accurate estimate of location of the centroid for the spectrum of Doppler signals can be obtained in the time domain as the signal arrives. This paper considers the implementation of a fractional-differentiating filter of the order of 1 ⁄2 by a set of automation astatic transfer elements, which greatly simplifies practical implementation. Real technical devices have the ultimate time delay, albeit small in comparison with the duration of the signal. As a result, the real filter will process the signal with some error. In accordance with this, this paper introduces and uses the concept of a "pre-derivative" of 1 ⁄2 of magnitude. An optimal algorithm for realizing the structure of the filter is proposed based on the criterion of minimum mean square error. Relations are obtained for the quadrature coefficients that determine the structure of the filter.

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Experimental study of fractional order proportional derivative controller synthesis for fractional order systems

Cited by 105 publications

References 14 publications

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Finite-time synchronization of fractional-order simplest two-component chaotic oscillators

Synchronization of Two Fractional-Order Chaotic Systems via Nonsingular Terminal Fuzzy Sliding Mode Control

Best Approximation of the Fractional Semi-Derivative Operator by Exponential Series

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