Laguerre-based modeling of fractional-order LTI SISO systems

2013 18th International Conference on Methods and Models in Automation and Robotics, MMAR 2013

Volumn , Issue , 2013, Pages 610-615

  Stanislawski, Rafal ^a   Latawiec, Krzysztof J ^a   Hunek, Wojciech P ^a   Zukaniszyn, Marian ^a  

^a OPOLE UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

ROBOTICS;

COMPUTATIONAL RESULTS; DISCRETE TIME; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LAGUERRE; LAGUERRE FILTER; SIMULATION EXAMPLE; SISO SYSTEMS;

ALGEBRA;

EID: 84893505454     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/mmar.2013.6669980     Document Type: Conference Paper

References (30)

1. H. Akçay, "Synthesis of complete orthonormal fractional basis functions with prescrived poles," IEEE transactions on signal processing, vol. 56, pp. 4716-4728, 2008.
2. M. Aoun, R. Malti, F. Levron, and A. Oustaloup, "Synthesis of fractional Laguerre basis for system approximation," Automatica, vol. 43, no. 9, pp. 1640-1648, 2007.
3. R. Barbosa and J. Machado, "Implementation of discrete-time fractional-order controllers based on LS approximations," Acta Polytechnica Hungarica, vol. 3, no. 4, pp. 5-22, 2006.
4. M. Busówicz and T. Kaczorek, "Simple conditions for practical stability of positive fractional discrete-time linear systems," International Journal of Applied Mathematics and Computer Science, vol. 19, no. 2, pp. 263-269, 2009.
5. Y. Chen, B. Vinagre, and I. Podlubny, "A new discretization method for fractional order differentiators via continued fraction expansion," in Proceedings of DETC'2003, ASME Design Engineering Technical Conferences, vol. 340, Chicago, IL, 2003, pp. 349-362.
6. A. Dzielínski and D. Sierociuk, "Stability of discrete fractional order state-space systems," Journal of Vibration and Control, vol. 14, no. 9-10, pp. 1543-1556, 2008.
7. P. S. C. Heuberger, P. M. J. Van den Hof, and B. Wahlberg, Modeling and identification with rational orthogonal basis functions. Springer-Verlag, London, UK, 2005.
8. C. X. Jiang, J. E. Carletta, and T. T. Hartley, "Implementation of fractional-order operators on field programmable gate arrays," in Advances in Fractional Calculus: Theoretical Developments and Applications in Physics and Engineering, J. Sabatier and et al., Eds. Springer, Dordrecht, Netherlands, 2007, pp. 333-346.
9. T. Kaczorek, "Practical stability of positive fractional discrete-time linear systems," Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 56, no. 4, pp. 313-317, 2008.
10. O. J. Kootsookos and R. C. Williamson, "FIR approximation of fractional sample delay systems," IEEE Transactions on Circus and Systems-II, vol. 43, no. 3, pp. 269-271, 1996.
11. K. Latawiec, C. Marciak, W. Hunek, and R. Stanisáwski, "A new analytical design methodology for adaptive control of nonlinear blockoriented systems," in Proceedings the 7th World Multi-Conference on Systemics, Cybernetics and Informatics, vol. 11, Orlando, Florida, 2003, pp. 215-220.
12. K. Latawiec, R. Rojek, C. Marciak, and G. Oliveira, "Adaptive estimation of Laguerre models with time-varying delay," in Procedings 2nd IFAC Workshop on Linear Time Delay Systems, Ancona, Italy, 2000, pp. 163-167.
13. C. Monje, Y. Chen, B. Vinagre, D. Xue, and V. Feliu, Fractional-order Systems and Controls. Springer-Verlag, London, UK, 2010.
14. H. Peng, T. Ozaki, V. Haggan-Ozaki, and Y. Toyota, "A nonlinear exponential ARX model based multivariable generalized predictive control strategy for thermal power plants," IEEE transactions on Control Systems Technology, vol. 10, no. 2, pp. 256-262, 2002.
15. I. Podlubny, Fractional differential equations. Academic Press, Orlando, FL, 1999.
16. R. Stanisáwski, "Hammerstein system identification by means of orthonormal basis functions and radial basis functions," in Emerging Technologies, Robotics and Control Systems, S. Pennacchio, Ed. Internationalsar, Palermo, Italy, 2007, pp. 69-73.
17. -, "Identification of open-loop stable linear systems using fractional orthonormal basis functions," in Proceedings of the 14th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 2009, pp. 935-985.
18. -, "New Laguerre filter approximators to the Gr̈unwald-Letnikov fractional difference," Mathematical Problems in Engineering, vol. 2012, 2012, Paper ID: 732917.
19. -, Advances in modeling of fractional difference systems-new accuracy, stability and computational results. Opole University of Technology Press, Opole, Poland, 2013.
20. R. Stanisáwski, W. P. Hunek, and K. J. Latawiec, "Modeling of nonlinear block-oriented systems using orthonormal basis and radial basis functions," Systems Science, vol. 35, no. 2, pp. 11-18, 2009.
21. -, "Normalized finite fractional discrete-time derivative a new concept and its application to obf modeling," Measurements, Automation and Monitoring, vol. 57, no. 3, pp. 241-243, 2011.
22. R. Stanisáwski and K. J. Latawiec, "Regular vs. inverse orthonormal basis functions concepts in identification of feedback-nonlinear systens by means of radial basis functions," International Journal of Factory Automation, Robotics and Soft Computing, vol. 2007, no. 4, pp. 64-68, 2007.
23. -, "Modeling of open-loop stable linear systems using a combination of a finite fractional derivative and orthonormal basis functions," in Proceedings of the 15th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 2010, pp. 411-414.
24. -, "Normalized finite fractional differences: the computational and accuracy breakthroughs," International Journal of Applied Mathematics and Computer Science, vol. 22, no. 4, pp. 907-919, 2012.
25. -, "Stability analysis for discrete-time fractional-order LTI statespace systems. Part I: New necessary and sufficient conditions for asymptotic stability." Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 61, no. 2, 2013, (in press).
26. -, "Stability analysis for discrete-time fractional-order LTI statespace systems. Part II: New stability criterion for FD-based systems," Bulletin of the Polish Academy of Sciences, Technical Sciences, vol. 61, no. 2, 2013, (in press).
27. R. Stanisáwski, K. J. Latawiec, and W. Stanisáwski, "Modeling of a boiler proper using acomplex structure model by means of multivariable orthonormal basis functions," in Proceedings of the 12th International Conference on Methods and Models in Automation and Robotics, Miedzyzdroje, Poland, 2006, pp. 935-985.
28. C. Tseng, S. Pei, and S. Hsia, "Computation of fractional derivatives using Fourier transform and digital FIR diferentiator," Signal Processing, vol. 80, no. 1, pp. 151-159, 2000.
29. P. Van den Hof, P. Heuberger, and J. Bokor, "System identification with generalized orthonormal basis functions," Automatica, vol. 31, no. 12, pp. 1821-1834, 1995.
30. B. M. Vinagre, I. Podlubny, A. Hernandez, and V. Feliu, "Some approximations of fractional order operators used in control theory and applications," Fractional Calculus &Applied Analysis, vol. 3, no. 3, pp. 945-950, 2000.