Modeling of discrete-time fractional-order state space systems using the balanced truncation method

Lecture Notes in Electrical Engineering

Volumn 357, Issue , 2016, Pages 119-127

  Rydel, Marek ^a   Stanisławski, Rafał ^a   Bialic, Grzegorz ^a   Latawiec, Krzysztof J ^a  

^a OPOLE UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

CALCULATIONS; CONTROL THEORY;

APPROXIMATION RESULTS; BALANCED TRUNCATION METHOD; DISCRETE TIME; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; LINEAR TIME INVARIANT; REDUCTION METHOD; STATE EQUATIONS;

EQUATIONS OF STATE;

EID: 84950237236     PISSN: 18761100     EISSN: 18761119     Source Type: Book Series    
DOI: 10.1007/978-3-319-23039-9_10     Document Type: Conference Paper

References (23)

1. Antoulas, A.: Approximation of large-scale dynamical system. Society for Industrial and Applied Mathematics, Philadelphia (2005)
2. Bania, P., Baranowski, J.: Laguerre polynomial approximation of fractional order linear systems. In: Advances in the Theory and Applications of Non-integer Order Systems, Lecture Notes in Electrical Engineering. vol. 257, pp. 171-182. Springer, Dordrecht, Netherlands (2013)
3. Barbosa, R., Machado, J.: Implementation of discrete-time fractional-order controllers based on LS approximations. Acta Polytech. Hung. 3(4), 5-22 (2006)
4. Chen, Y., Vinagre, B., Podlubny, I.: A new discretization method for fractional order differentiators via continued fraction expansion. In: Proceedings of DETC’2003, ASME Design Engineering Technical Conferences, Vol. 340, pp. 349-362. Chicago, IL (2003)
5. Gao, Z.: Improved oustaloup approximation of fractional-order operators using adaptive chaotic particle swarm optimization. J. Syst. Eng. Electron. 23(1), 145-153 (2012)
6. Jiang, C.X., Carletta, J.E., Hartley, T.T.: Implementation of fractional-order operators on field programmable gate arrays. In: Sabatier, J. (ed.) Advances in fractional calculus: theoretical developments and applications in physics and engineering, pp. 333-346. Springer, Dordrecht (2007)
7. Kootsookos, O.J., Williamson, R.C.: FIR approximation of fractional sample delay systems. IEEE Trans. Circ. Syst. II 43(3), 269-271 (1996)
8. Latawiec, K.J., Stanisławski, R., Gałek, M., Łukaniszyn, M.: Modeling and identification of a fractional-order discrete-time SISO Laguerre-Wiener system. In: Proceedings of the 19th International Conference on Methods and Models in Automation and Robotics, pp. 165-168. Miedzyzdroje, Poland (2014)
9. Maione, G.: A digital, noninteger order differentiator using Laguerre orthogonal sequences. Int. J. Intell. Control Syst. 11(2), 77-81 (2006)
10. Moore, B.: Principal component analysis in linear systems: Controllability, observability and model reduction. IEEE Trans. Autom. Control AC-26(1), 17-32 (1981)
11. Obinata, G., Anderson, B.: Model reduction for control system design. Springer, London (2001)
12. Poinot, T., Trigeassou, J.C.: Identification of fractional systems using an output-error technique. Nonlinear Dyn. 38(1), 133-154 (2004)
13. Rachid, M., Maamar, B., Said, D.: Comparison between two approximation methods of state space fractional systems. Signal Process. 91(3), 461-469 (2011)
14. Rydel, M., Stanisławski, W.: Selection of reduction parameters of rational krylov methods for complex mimo lti models using evolutionary algorithm. In: 19th International Conference on Methods and Models in Automation and Robotics, pp. 720-725 (2014)
15. Stanisławski, R.: New Laguerre filter approximators to the Grünwald-Letnikov fractional difference. Math. Probl. Eng. 2012, Article ID: 732917, (2012)
16. Stanisławski, R., Gałek, M., Latawiec, K.J., Łukaniszyn, M.: Modeling and identification of a fractional-order discrete-time Laguerre-Hammerstein system. In: Progress in Systems Engineering-Proceedings of Twenty Third International Conference on Systems Engineering, Advances in Intelligent Systems and Computing Series. Springer, Dordrecht, Netherlands (2014)
17. Stanisławski, R., Latawiec, K.J.: Normalized finite fractional differences—the computational and accuracy breakthroughs. Int. J. Appl. Math. Comput. Sci. 22(4), 907-919 (2012)
18. Stanisławski, R., Latawiec, K.J., Gałek, M., Łukaniszyn, M.: Modeling and identification of fractional-order discrete-time Laguerre-based feedback-nonlinear systems. In Latawiec, K. et al. (ed.) Advances in Modelling and Control of Non-integer Order Systems, Lecture Notes in Electrical Engineering, pp. 101-112. Springer, Dordrecht, Netherlands (2014)
19. Stanisławski, R., Latawiec, K.J., Łukaniszyn, M.: A comparative analysis of Laguerre-based approximators to the Grünwald-Letnikov fractional-order difference. Math. Probl. Eng. 2015, 1-10, Article ID: 512104 (2015)
20. Stanisławski, W., Rydel, M.: Hierarchical models of complex plants on basis of power boiler example. Arch. Control Sci. 20(LVI)(4), 381-416 (2010)
21. Tseng, C., Pei, S., Hsia, S.: Computation of fractional derivatives using Fourier transform and digital FIR diferentiator. Signal Process. 80(1), 151-159 (2000)
22. Varga, A.: Efficient minimal realization procedure based on balancing. In: IMACS/IFAC Symposium on Modeling and Control of Technological Systems, vol. 2, pp. 42-47 (1991)
23. Vinagre, B.M., Podlubny, I., Hernandez, A., Feliu, V.: Some approximations of fractional order operators used in control theory and applications. Fract. Calculus Appl. Anal. 3(3), 945-950 (2000)