scholarly journals An Effective Approach of Approximation of Fractional Order System using Real Interpolation Method

2017 ◽  
Vol 1 (1) ◽  
pp. 39
Author(s):  
Dung Quang Nguyen
Keyword(s):  
Transfer Function ◽  
Fractional Order ◽  
Transfer Functions ◽  
Interpolation Method ◽  
Fractional Order System ◽  
Real Interpolation ◽  
Order System ◽  
Frequency Method ◽  
Time Frequency ◽  
Real Interpolation Method

Fractional-order controllers are recognized to guarantee better closed-loop performance and robustness than conventional integer-order controllers. However, fractional-order transfer functions make time, frequency domain analysis and simulation significantly difficult. In practice, the popular way to overcome these difficulties is linearization of the fractional-order system. Here, a systematic approach is proposed for linearizing the transfer function of fractional-order systems. This approach is based on the real interpolation method (RIM) to approximate fractional-order transfer function (FOTF) by rational-order transfer function. The proposed method is implemented and compared to CFE high-frequency method; Carlson’s method; Matsuda’s method; Chare ’s method; Oustaloup’s method; least-squares, frequency interpolation method (FIM). The results of comparison show that, the method is simple, computationally efficient, flexible, and more accurate in time domain than the above considered methods.  This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

scholarly journals Determination of all stability region of unstable fractional order system in case of bearing system

2019 ◽  
Vol 10 (4) ◽  
pp. 1734
Author(s):  
Van-Duc Phan ◽  
Phu Tran Tin ◽  
Nguyen Quang Dung ◽  
Minh Tran ◽  
Tran Thanh Trang
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Decomposition Method ◽  
Interpolation Method ◽  
Fractional Order System ◽  
Stable Region ◽  
Order System ◽  
Real Interpolation Method ◽  
Bearing System

In this paper, we propose and investigate the optimal tuning PID controller of unstable fractional order system by desired transient characteristics using the real interpolation method (RIM). The research shows that the main advantages of this method are drawn as the followings: 1) Carrying out an investigation of the stable region of coefficients of a PID controller using D-decomposition method; 2) Applying the method to investigate an unstable fractional order system.

Stability and resonance analysis of a general non-commensurate elementary fractional-order system

2020 ◽  
Vol 23 (1) ◽  
pp. 183-210 ◽  
Author(s):  
Shuo Zhang ◽  
Lu Liu ◽  
Dingyu Xue ◽  
YangQuan Chen
Keyword(s):  
Fractional Order ◽  
Transfer Functions ◽  
Order Parameters ◽  
Fractional Order System ◽  
Order System ◽  
Stability Conditions ◽  
Order Restriction ◽  
Resonance Analysis ◽  
General Kind ◽  
The Stability

AbstractThe elementary fractional-order models are the extension of first and second order models which have been widely used in various engineering fields. Some important properties of commensurate or a few particular kinds of non-commensurate elementary fractional-order transfer functions have already been discussed in the existing studies. However, most of them are only available for one particular kind elementary fractional-order system. In this paper, the stability and resonance analysis of a general kind non-commensurate elementary fractional-order system is presented. The commensurate-order restriction is fully released. Firstly, based on Nyquist’s Theorem, the stability conditions are explored in details under different conditions, namely different combinations of pseudo-damping (ζ) factor values and order parameters. Then, resonance conditions are established in terms of frequency behaviors. At last, an example is given to show the stable and resonant regions of the studied systems.

Real Interpolation of Sobolev Spaces on Subdomains of Rn

1978 ◽  
Vol 30 (01) ◽  
pp. 190-214 ◽  
Author(s):  
R. A. Adams ◽  
J. J. F. Fournier
Keyword(s):  
Sobolev Space ◽  
Fractional Order ◽  
Sobolev Spaces ◽  
Besov Spaces ◽  
Interpolation Method ◽  
A Priori ◽  
Real Interpolation ◽  
Convenient Tool ◽  
Real Interpolation Method ◽  
Nikolskii Spaces

The real interpolation method is a very convenient tool in the study of imbedding relationships among Sobolev spaces and some of their fractional order generalizations, (Besov spaces, Nikolskii spaces etc.) Central to the application of these methods is the a priori determination that a given Sobolev space Wk'p(Ω) belongs to an appropriate class of spaces intermediate between two other “extreme” spaces.

scholarly journals Optimal tuning PID controller of unstable fractional order system by desired transient characteristics using RIM

2019 ◽  
Vol 14 (3) ◽  
pp. 1177
Author(s):  
Phu Tran Tin ◽  
Le Anh Vu ◽  
Minh Tran ◽  
Nguyen Quang Dung ◽  
Tran Thanh Trang
Keyword(s):  
Fractional Order ◽  
Pid Controller ◽  
Interpolation Method ◽  
Optimal Solution ◽  
Practical Method ◽  
Fractional Order System ◽  
Order System ◽  
The Novel ◽  
Transient Characteristics ◽  
Novel Method

<p>In this paper, we propose the method of tuning a conventional PID controller for unstable transient characteristics. The results show that: 1) This is the novel practical method based on the desired settling time and overshoot percentage; 2) The results are close to the desired parameters; 3) The novel method can tune an unstable fractional order system by real interpolation method (RIM); 4) The novel method is simplicity and computer efficiency; 5) The novel method can find an optimal solution for tuning task in both academic and industrial purposes.</p>

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