Design of Fractional Order Differentiator Using Feedback System

2012 ◽  
Author(s):  
Xiaoli Yang ◽  
R.C. Kavanagh
Keyword(s):  
Fractional Order ◽  
Feedback System ◽  
Fractional Order Differentiator

Photonic Fractional-Order Differentiator Using an SOI Microring Resonator With an MMI Coupler

2013 ◽  
Vol 25 (15) ◽  
pp. 1408-1411 ◽  
Author(s):  
Hiva Shahoei ◽  
Dan-Xia Xu ◽  
Jens H. Schmid ◽  
Jianping Yao
Keyword(s):  
Fractional Order ◽  
Microring Resonator ◽  
Mmi Coupler ◽  
Fractional Order Differentiator

scholarly journals Model-free fractional order differentiator based on fractional order Jacobi orthonormal functions

2017 ◽  
Vol 71 ◽  
pp. 69-82 ◽  
Author(s):  
Xiao-Lin Li ◽  
Yi-Ming Chen ◽  
Da-Yan Liu ◽  
Yan-Qiao Wei ◽  
Driss Boutat
Keyword(s):  
Fractional Order ◽  
Model Free ◽  
Fractional Order Differentiator

Algebraic fractional order differentiator based on the pseudo-state space representation

2019 ◽  
Vol 22 (5) ◽  
pp. 1395-1413
Author(s):  
Xing Wei ◽  
Da-Yan Liu ◽  
Driss Boutat ◽  
Yi-Ming Chen
Keyword(s):  
Integral Equation ◽  
State Space ◽  
Fractional Order ◽  
Initial Conditions ◽  
Algebraic Method ◽  
Space Representation ◽  
State Space Representation ◽  
Algebraic Formula ◽  
Fractional Order Differentiator ◽  
Fractional Order Integral

Abstract The aim of this paper is to design an algebraic fractional order differentiator for a class of commensurate fractional order linear systems modeled by the pseudo-state space representation. For this purpose, a new algebraic method is introduced by designing an operator which can transform the considered system into a fractional order integral equation by eliminating unknown initial conditions. Based on the obtained equation, the desired fractional derivative is exactly given by a new algebraic formula using a recursive way. Then, a digital fractional order differentiator is introduced in discrete noisy cases. Finally, numerical results are given to illustrate the accuracy and the robustness of the proposed method.

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