Fractional-order Difference Basis Functions - a new modeling concept for dynamical systems

This paper presents a new concept for modeling of linear fractional-order dynamical systems. The proposed model is based on specific basis functions, the so called Fractional-order Difference Basis Functions, which are a generalization of the delayed filters used in the FIR model. In the paper, we show elementary properties of the model and present a method for model implementation. Simulation example shows that the model can be effective in modeling of a class of dynamical systems.

[1]  O. Nelles Nonlinear System Identification , 2001 .

[2]  Krzysztof J. Latawiec,et al.  Modeling and identification of a fractional-order discrete-time SISO Laguerre-Wiener system , 2014, 2014 19th International Conference on Methods and Models in Automation and Robotics (MMAR).

[3]  Preston R. Clement,et al.  Laguerre Functions in Signal Analysis and Parameter Identification , 1982 .

[4]  Myo-Taeg Lim,et al.  Switching Extensible FIR Filter Bank for Adaptive Horizon State Estimation With Application , 2016, IEEE Transactions on Control Systems Technology.

[5]  Krzysztof J. Latawiec,et al.  Modeling and Identification of Fractional-Order Discrete-Time Laguerre-Based Feedback-Nonlinear Systems , 2014, RRNR.

[6]  B. Wahlberg,et al.  Modelling and Identification with Rational Orthogonal Basis Functions , 2000 .

[7]  Amila Dubravi,et al.  USING ORTHONORMAL FUNCTIONS IN MODEL PREDICTIVE CONTROL , 2012 .

[8]  Wojciech P. Hunek,et al.  Finite approximations of a discrete-time fractional derivative , 2011, 2011 16th International Conference on Methods & Models in Automation & Robotics.

[9]  Lawrence R. Rabiner,et al.  Approximate design relationships for low-pass FIR digital filters , 1973 .

[10]  Peter J. Kootsookos,et al.  FIR approximation of fractional sample delay systems , 1996 .

[11]  Andrzej Tarczynski,et al.  Evaluation of several variable FIR fractional-sample delay filters , 1994, Proceedings of ICASSP '94. IEEE International Conference on Acoustics, Speech and Signal Processing.

[12]  Gerald D. Cain,et al.  Offset windowing for FIR fractional-sample delay , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[13]  Amila Dubravić,et al.  Korištenje ortonormalnih funkcija u prediktivnom upravljanju na osnovu modela , 2012 .

[14]  K. Latawiec,et al.  Fractional-Order Discrete-Time Laguerre Filters: A New Tool for Modeling and Stability Analysis of Fractional-Order LTI SISO Systems , 2016 .

[15]  Soo-Chang Pei,et al.  A generalized approach to the design of variable fractional-delay FIR digital filters , 2008, Signal Process..

[16]  Abdelfatah Charef,et al.  A new approach for the design of fractional delay by an FIR filter. , 2018, ISA transactions.

[17]  Truong Q. Nguyen,et al.  On M-channel linear phase FIR filter banks and application in image compression , 1997, IEEE Trans. Signal Process..

[18]  YangQuan Chen,et al.  Fractional-order Systems and Controls , 2010 .

[19]  Guido Maione,et al.  On the Laguerre Rational Approximation to Fractional Discrete Derivative and Integral Operators , 2013, IEEE Transactions on Automatic Control.

[20]  B. Wahlberg System identification using Laguerre models , 1991 .