Revisiting four approximation methods for fractional order transfer function implementations: Stability preservation, time and frequency response matching analyses

2020 ◽  
Vol 49 ◽  
pp. 239-257
Author(s):  
Furkan Nur Deniz ◽  
Baris Baykant Alagoz ◽  
Nusret Tan ◽  
Murat Koseoglu
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Fractional Order ◽  
Approximation Methods ◽  
Frequency Response Matching

Algebraic bound for the phase–frequency response of the commande robuste d'ordre non-entier approximation of fractional differentiators and its applications in control systems analysis

2021 ◽  
pp. 107754632098776
Author(s):  
Khashayar Neshat ◽  
Mohammad Saleh Tavazoei
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Control Systems ◽  
Fractional Order ◽  
Upper Bound ◽  
Systems Analysis ◽  
Sufficient Conditions ◽  
Approximation Process ◽  
Positive Realness

This article deals with analyzing the phase–frequency response of commande robuste d'ordre non-entier approximations of fractional-order differentiators. More precisely, an algebraic tight upper bound is derived for the phase of the approximations obtained from the commande robuste d'ordre non-entier method. Then, some applications for this achievement are discussed in the viewpoint of control systems analysis. These applications include usefulness of the obtained upper bound in stability preservation analysis during the commande robuste d'ordre non-entier–based approximation process and applicability of such a bound in finding necessary or sufficient conditions for test of positive realness/negative imaginariness of a fractional-order transfer function.

scholarly journals A PID and PIDA Controller Design for an AVR System using Frequency Response Matching

2019 ◽  
Vol 8 (10) ◽  
pp. 1675-1681
Keyword(s):  
Transfer Function ◽  
Frequency Response ◽  
Closed Loop ◽  
Reference Model ◽  
Voltage Regulation ◽  
System Model ◽  
Proportional Integral Derivative ◽  
Proportional Integral ◽  
Avr System ◽  
Frequency Response Matching

A proportional integral derivative (PID) and proportional integral derivative acceleration (PIDA) controller have been designed for voltage regulation in power system. The controller (i.e. PID and PIDA) has been proposed via frequency response matching of desired reference model with that of system model transfer function. The proposed PID controller has been designed using one point frequency response matching as well as pole placement technique, while PIDA controller has been designed using two point frequency response matching by equating desired set-point closed loop reference model with that of closed loop transfer function of system model. The response of the proposed PIDA controller shows improved performance for automatic voltage regulator (AVR) system in comparison with recently available literature. The proposed PID and PIDA controllers provide fast and smooth response for an AVR system. The advantages associated with the PIDA controller for an AVR system is to reduce rise time, percentage overshoot and improved robustness, stability margin.

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.

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