An Algorithm for Fractional Order System Identification

In this paper, a new algorithm for fractional order system identification is set up. We study the structure of vector fitting and give a decomposition through the computational instance. In the vector fitting method, we use the complex least-square method to instead least-square method when calculating the residues and dealing with the errors based on vector fitting. And the rational fractional function has been extended from integer field to fractional domain. For validity, a comparison between the original and the present method is conducted.

[1]  Cao Hongxing,et al.  Problems in wavelet analysis of hydrologic series and some suggestions on improvement , 2007 .

[2]  Yangquan Chen,et al.  Computers and Mathematics with Applications Stability of Fractional-order Nonlinear Dynamic Systems: Lyapunov Direct Method and Generalized Mittag–leffler Stability , 2022 .

[3]  Rik Pintelon,et al.  System Identification: A Frequency Domain Approach , 2012 .

[4]  Rachid Mansouri,et al.  Vector Fitting fractional system identification using particle swarm optimization , 2008, Appl. Math. Comput..

[5]  Jan Abraham Ferreira,et al.  Improved analytical modeling of conductive losses in magnetic components , 1994 .

[6]  Mathieu Moze,et al.  LMI stability conditions for fractional order systems , 2010, Comput. Math. Appl..

[7]  B. Vahidi,et al.  Duality-Synthesized Circuit for Eddy Current Effects in Transformer Windings , 2013, IEEE Transactions on Power Delivery.

[8]  Piotr J. Chrzan,et al.  Half-Order Modeling of Saturated Synchronous Machine , 2014, IEEE Transactions on Industrial Electronics.

[9]  S. Das,et al.  Functional Fractional Calculus for System Identification and Controls , 2007 .

[10]  Franklin Fa-Kun Kuo,et al.  Network analysis and synthesis , 1962 .

[11]  P. L. Dowell,et al.  Effects of eddy currents in transformer windings , 1966 .

[12]  片山 徹.  Subspace methods for system identification , 2005 .

[13]  D. Inman.  Nonlinearity in Structural Dynamics: Detection, Identification and Modelling , 2002 .

[14]  Yangquan Chen,et al.  Necessary and sufficient stability condition of fractional-order interval linear systems , 2008, Autom..

[15]  A. Semlyen,et al.  Rational approximation of frequency domain responses by vector fitting , 1999 .