Rational Approximation and Analog Realization of Fractional Order Transfer Function with Multiple Fractional Powered Terms

2012 ◽  
Vol 15 (3) ◽  
pp. 723-735 ◽  
Author(s):  
M. Khanra ◽  
J. Pal ◽  
K. Biswas
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Rational Approximation

Fractional order robust control based on Bode's ideal transfer function

2008 ◽  
Vol 42 (6-8) ◽  
pp. 999-1014 ◽  
Author(s):  
Abdelbaki Djouambi ◽  
Abdelfatah Charef ◽  
Alina Voda-Besancon
Keyword(s):  
Robust Control ◽  
Transfer Function ◽  
Fractional Order ◽  
Bode’S Ideal Transfer Function

The multi-model approach for fractional-order systems modelling

2016 ◽  
Vol 40 (1) ◽  
pp. 331-340 ◽  
Author(s):  
Samia Talmoudi ◽  
Moufida Lahmari
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Global Model ◽  
Fractional Order Systems ◽  
New Approach ◽  
Physical Systems ◽  
Integer Order ◽  
Systems Modelling ◽  
Model Approach

Currently, fractional-order systems are attracting the attention of many researchers because they present a better representation of many physical systems in several areas, compared with integer-order models. This article contains two main contributions. In the first one, we suggest a new approach to fractional-order systems modelling. This model is represented by an explicit transfer function based on the multi-model approach. In the second contribution, a new method of computation of the validity of library models, according to the frequency [Formula: see text], is exposed. Finally, a global model is obtained by fusion of library models weighted by their respective validities. Illustrative examples are presented to show the advantages and the quality of the proposed strategy.

On the approximate inverse Laplace transform of the transfer function with a single fractional order

2020 ◽  
pp. 014233122097766
Author(s):  
Ali Yüce ◽  
Nusret Tan
Keyword(s):  
Transfer Function ◽  
Laplace Transform ◽  
Fractional Order ◽  
Analytical Solutions ◽  
Transfer Functions ◽  
Inverse Laplace Transform ◽  
Fractional Order Systems ◽  
Approximate Inverse ◽  
Classical Mathematics ◽  
Curve Fitting Method

The history of fractional calculus dates back to 1600s and it is almost as old as classical mathematics. Although many studies have been published on fractional-order control systems in recent years, there is still a lack of analytical solutions. The focus of this study is to obtain analytical solutions for fractional order transfer functions with a single fractional element and unity coefficient. Approximate inverse Laplace transformation, that is, time response of the basic transfer function, is obtained analytically for the fractional order transfer functions with single-fractional-element by curve fitting method. Obtained analytical equations are tabulated for some fractional orders of [Formula: see text]. Moreover, a single function depending on fractional order alpha has been introduced for the first time using a table for [Formula: see text]. By using this table, approximate inverse Laplace transform function is obtained in terms of any fractional order of [Formula: see text] for [Formula: see text]. Obtained analytic equations offer accurate results in computing inverse Laplace transforms. The accuracy of the method is supported by numerical examples in this study. Also, the study sets the basis for the higher fractional-order systems that can be decomposed into a single (simpler) fractional order systems.

Fractional Order Pole Placement for a buck converter based on commensurable transfer function

2020 ◽  
Vol 107 ◽  
pp. 370-384
Author(s):  
Florindo A. de C. Ayres ◽  
Iury Bessa ◽  
Vinicius Matheus Batista Pereira ◽  
Nei Junior da Silva Farias ◽  
Alessandra Ribeiro de Menezes ◽  
...  
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Buck Converter ◽  
Pole Placement ◽  
Order Pole

scholarly journals The Study of Fractional Order Controller with SLAM in the Humanoid Robot

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Shuhuan Wen ◽  
Xiao Chen ◽  
Yongsheng Zhao ◽  
Ahmad B. Rad ◽  
Kamal Mohammed Othman ◽  
...  
Keyword(s):  
Transfer Function ◽  
Power Series ◽  
Fractional Order ◽  
Humanoid Robot ◽  
Power Series Expansion ◽  
Pi Controller ◽  
Fractional Order Pi Controller ◽  
Fractional Order Controller ◽  
Accumulated Error ◽  
Fopi Controller

We present a fractional order PI controller (FOPI) with SLAM method, and the proposed method is used in the simulation of navigation of NAO humanoid robot from Aldebaran. We can discretize the transfer function by the Al-Alaoui generating function and then get the FOPI controller by Power Series Expansion (PSE). FOPI can be used as a correction part to reduce the accumulated error of SLAM. In the FOPI controller, the parameters (Kp,Ki,  and  α) need to be tuned to obtain the best performance. Finally, we compare the results of position without controller and with PI controller, FOPI controller. The simulations show that the FOPI controller can reduce the error between the real position and estimated position. The proposed method is efficient and reliable for NAO navigation.

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