Fractional Order Digital Differentiator Design Based on Power Function and Least squares

A bad initialization of output-error (OE) technique can lead to an inappropriate identification results. In this paper, we introduce a solution to this problem; the basic idea is to estimate the parameters and the fractional order of the noninteger system by a new approach of least-squares (LS) method based on repeated fractional integration to initialize OE technique. It will be shown that LS method offers a good initialization to OE algorithm and leads to acceptable identification results. The performance of the proposed method is shown through numerical simulation examples.

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Efficient Design of Zero-Phase Riesz Fractional Order Digital Differentiator Using Manta-Ray Foraging Optimisation for Precise Electrocardiogram QRS Detection

IEEE Open Journal of Circuits and Systems ◽

10.1109/ojcas.2020.3035771 ◽

2020 ◽

Vol 1 ◽

pp. 280-292

Author(s):

Chandan Nayak ◽

Suman Kumar Saha ◽

Rajib Kar ◽

Durbadal Mandal

Keyword(s):

Fractional Order ◽

Efficient Design ◽

Qrs Detection ◽

Digital Differentiator ◽

Manta Ray ◽

Zero Phase

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A comparison between the direct and the indirect fractional order closed-loop bias eliminated least squares method

2016 17th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA) ◽

10.1109/sta.2016.7951978 ◽

2016 ◽

Author(s):

Z. Yakoub ◽

M. Chetoui ◽

M. Amairi ◽

M. Aoun

Keyword(s):

Least Squares ◽

Fractional Order ◽

Closed Loop ◽

Least Squares Method

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A Simplified Fractional Order Equivalent Circuit Model and Adaptive Online Parameter Identification Method for Lithium-Ion Batteries

Mathematical Problems in Engineering ◽

10.1155/2019/6019236 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Jianlin Wang ◽

Le Zhang ◽

Dan Xu ◽

Peng Zhang ◽

Gairu Zhang

Keyword(s):

Parameter Identification ◽

Least Squares ◽

Equivalent Circuit ◽

Fractional Order ◽

Equivalent Circuit Model ◽

Lithium Ion ◽

Circuit Model ◽

Stability And Convergence ◽

Battery Management System ◽

Identification Method

In order to improve the battery management system performance and enhance the adaptability of the system, a fractional order equivalent circuit model of lithium-ion battery based on electrochemical test was established. The parameters of the fractional order equivalent circuit model are identified by the least squares parameter identification method. The least squares parameter identification method needs to rely on the harsh test conditions of the laboratory, and the parameter identification result is static; it cannot adapt to the characteristics of the lithium battery under dynamic conditions. Taking into account the dynamic changes of lithium batteries, a parameter adaptive online estimation algorithm for fractional equivalent circuit model is proposed. Based on the theory of fractional order calculus and indirect Lyapunov method, the stability and convergence of the estimator are analyzed. Finally, simulation experiments show that this method can continuously estimate the parameters of the fractional order equivalent circuit under UDDS conditions.

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Design of Fractional Order Digital Differentiator Using Radial Basis Function

IEEE Transactions on Circuits and Systems I Regular Papers ◽

10.1109/tcsi.2009.2034808 ◽

2010 ◽

Vol 57 (7) ◽

pp. 1708-1718 ◽

Cited By ~ 46

Author(s):

Chien-Cheng Tseng ◽

Su-Ling Lee

Keyword(s):

Radial Basis Function ◽

Fractional Order ◽

Basis Function ◽

Digital Differentiator ◽

Radial Basis

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Optimal Design of Fractional-Order Digital Differentiator Using Flower Pollination Algorithm

Journal of Circuits System and Computers ◽

10.1142/s0218126618501293 ◽

2018 ◽

Vol 27 (08) ◽

pp. 1850129 ◽

Cited By ~ 5

Author(s):

Shibendu Mahata ◽

Suman Kumar Saha ◽

Rajib Kar ◽

Durbadal Mandal

Keyword(s):

Fractional Order ◽

Optimization Technique ◽

Phase Response ◽

Computational Time ◽

Infinite Impulse Response ◽

Flower Pollination Algorithm ◽

Solution Quality ◽

Digital Differentiator ◽

Flower Pollination ◽

Real Coded Genetic Algorithm

This paper presents an efficient approach to design wideband, accurate, stable, and minimum-phase fractional-order digital differentiators (FODDs) in terms of the infinite impulse response (IIR) filters using an evolutionary optimization technique called flower pollination algorithm (FPA). The efficiency comparisons of FPA with real-coded genetic algorithm (RGA), particle swarm optimization (PSO), and differential evolution (DE)-based designs are conducted with respect to different magnitude and phase response error metrics, parametric and nonparametric statistical hypotheses tests, computational time, and fitness convergence. Exhaustive simulation results clearly demonstrate that FPA significantly outperforms RGA, PSO, and DE in attaining the best solution quality consistently. Extensive analysis is also conducted in order to determine the role of control parameters of FPA on the performance of the designed FODDs. The proposed FPA-based FODDs outperform all the designs published in the recent literature with respect to the magnitude responses and also achieve a competitive performance in terms of the phase response.

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