Sub-optimum H2 rational approximations to fractional order linear systems

Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference - DETC2005

Volumn 6 B, Issue , 2005, Pages 1527-1536

  Xue, Dingyü ^a   Chen, Yangquan ^b,c  

^a NORTHEASTERN UNIVERSITY   (China)

^b Utah State University   (United States)

^c UNIVERSITY OF UTAH   (United States)

Author keywords

Fractional order systems; Model reduction; Optimal model reduction

Indexed keywords

COMPUTER SOFTWARE; HYDROGEN; INTEGRAL EQUATIONS; LINEAR SYSTEMS;

FRACTIONAL ORDER SYSTEMS; MODEL REDUCTION; OPTIMAL MODEL REDUCTION; RATIONAL APPROXIMATION;

APPROXIMATION THEORY;

EID: 33244484599     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1115/detc2005-84743     Document Type: Conference Paper

References (42)

1. Oldham, K. B., and Spanier, J., 1974, The Fractional Calculus. Academic Press, New York.
2. Samko, S. G., Kilbas, A. A., and Marichev, O. I., 1987. Fractional integrals and derivatives and some of their applications. Nauka i technika, Minsk.
3. Miller, K. S., and Ross, B. 1993. An Introduction to the Fractional Calculus and Fractional Differential Equations. Wiley, New York.
4. Podlubny, I., 1994. Fractional-order systems and fractional-order controllers. Tech. Rep. UEF-03-94, Slovak Academy of Sciences. Institute of Experimental Physics, Department of Control Engineering. Faculty of Mining, University of Technology. Kosice, November.
5. Lurie, B. J., 1994. 'Three-parameter tunable tilt-integral-derivative (TID) controller". US Patent US5371670.
6. μ-controllers". IEEE Trans. Automatic Control, 44 (1) , pp. 208-214.
7. Oustaloup, A., Mathieu, B., and Lanusse, P., 1995. "The CRONE control of resonant plants: application to a flexible transmission". European Journal of Control, 1 (2).
8. Oustaloup, A., Moreau, X., and Nouillant, M., 1996. "The CRONE suspension". Control Engineering Practice, 4 (8), pp. 1101-1108.
9. Raynaud, H., and Zergaïnoh, A., 2000. "State-space representation for fractional order controllers". Automatica, 36 , pp. 1017-1021.
10. Manabe, S., 1960. "The non-integer integral and its application to control systems". JIEE (Japanese Institute of Electrical Engineers) Journal, 80 (860), pp. 589-597.
11. Manabe, S., 1961. "The non-integer integral and its application to control systems". ETJ of Japan, 6 (3-4), pp. 83-87.
12. Oustaloup, A., 1981. "Fractional order sinusoidal oscilators: Optimization and their use in highly linear FM modulators". IEEE Transactions on Circuits and Systems, 28 (10), pp. 1007-1009.
13. Axtell, M., and Bise, E. M., 1990. "Fractional calculus applications in control systems". In Proceedings of the IEEE 1990 Nat. Aerospace and Electronics Conf., pp. 563-566.
14. Vinagre, B. M., and Chen, Y., 2002. "Lecture notes on fractional calculus applications in automatic control and robotics". In The 41st IEEE CDC2002 Tutorial Workshop # 2, B. M. Vinagre and Y. Chen, Eds., pp. 1-310. [Online] http://mechatronics.ece.usu.edu /foc/cdc02-tw2-ln.pdf.
15. Editor), J. A. T. M. G., 2002. "Special issue on fractional calculus and applications". Nonlinear Dynamics, 29 March, pp. 1-385.
16. Ortigueira, M. D., and Editors), J. A. T. M. G., 2003. "Spe-cial issue on fractional signal processing and applications". Signal Processing, 83 (11) Nov., pp. 2285-2480.
17. Oustaloup, A., 1995. La Dérivation non Entiére. HERMES, Paris.
18. Oustaloup, A., Sabatier, J., and Lanusse, P., 1999. "From fractal robustness to CRONE control". Fractionnai Calculus and applied Analysis, 2(1), pp. 1-30.
19. Oustaloup, A., and Mathieu, B., 1999. La commande CRONE : du scalaire au multivariable. HERMES, Paris.
20. Petráš, I., 1999. "The fractional-order controllers: Methods for their synthesis and application". Journal of Electrical Engineering, 50 (9-10), pp. 284-288.
21. Oustaloup, A., Levron, F., Nanot, F., and Mathieu, B., 2000. "Frequency band complex non integer differentiator : characterization and synthesis". IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 47 (1) January, pp. 25-40.
22. Ichise, M., Nagayanagi, Y., and Kojima, T., 1971. "An analog simulation of non-integer order transfer functions for analysis of electrode processes". Journal of electroanalytical chemistry, 33, pp. 253-265.
23. Oldham, K. B., 1973. "Semiintegral electroanalysis: Analog implementation". Analytical Chemistry, 45 (1), pp. 39-47.
24. Sugi, M., Hirano, Y., Miura, Y. F., and Saito, K., 1999. "Simulation of fractal immittance by analog circuits: An approach to optimized circuits". IEICE Trans. Fundamentals (8), pp. 1627-1635.
25. Podlubny, I., Petrs, I., Vinagre, B. M., O'leary, P., and Dorck, L., 2002. "Analogue Realizations of Fractional-Order Controllers". Nonlinear Dynamics, 29 (1-4) July, pp. 281-296.
26. Machado, J. A. T., 1997. "Analysis and design of fractional-order digital control systems". J. of Systems Analysis-Modeling-Simulation, 27, pp. 107-122.
27. Vinagre, B. M., Petras, L., Merchan, P., and Dorcak, L., 2001. "Two digital realisation of fractional controllers: application to temperature control of a solid". In Proc. of the European Control Conference (ECC2001), pp. 1764-1767.
28. Vinagre, B. M., Podlubny, I., Hernandez, A., and Feliu, V., 2000. "On realization of fractional-order controllers". In Proc. of the Conference Internationale Francophone d'Automatique.
29. Vinagre, B. M., Podlubny, I., Hernandez, A., and Feliu, V., 2000. "Some approximations of fractional order operators used in control theory and applications". Fractional Calculus and Applied Analysis, 3 (3), pp. 231-248.
30. Chen, Y., and Moore, K. L., 2002. "Discretization Schemes for Fractional-Order Differentiators and Integrators". IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications, 49 (3) March, pp. 363-367.
31. Vinagre, B. M., Chen, Y. Q., and Petras, I., 2003. "Two direct Tustin discretization methods for fractional-order differentiator/ integrator". The Journal of Franklin Institute, 340 (5), pp. 349-362.
32. Chen, Y. Q., and Vinagre, B. M., 2003. "A new IIR-type digital fractional order differentiator". Signal Processing, 83 (11) Nov., pp. 2359-2365.
33. Al-Alaoui, M. A., 1993. "Novel digital integrator and differentiator". Electronics Letters, 29 (4), pp. 376-378.
34. Al-Alaoui, M. A., 1995. "A class of second-order integrators and low-pass differentiators". IEEE Trans. on Circuit and Systems I: Fundamental Theory and Applications, 42 (4), pp. 220-223.
35. Al-Alaoui, M. A., 1997. "Filling the gap between the bilinear and the backward difference transforms: an interactive design approach". Int. J. of Electrical Engineering Education, 34 (4), pp. 331-337.
36. Tseng, C., Pei, S., and Hsia, S., 2000. "Computation of Fractional Derivatives using Fourier Transform and Digital FIR Differentiator". Signal Processing, 80, pp. 151-159.
37. Tseng, C., 2001. "Design of fractional order digital FIR differentiator". IEEE Signal Processing Letters, 8 (3), pp. 77-79.
38. Chen, Y., Vinagre, B. M., and Podlubny, I., 2003. "A new discretization method for fractional order differentiators via continued fraction expansion". In Proc. of The First Symposium on Fractional Derivatives and Their Applications at The 19th Biennial Conference on Mechanical Vibration and Noise, the ASME International Design Engineering Technical Conferences & Computers and Information in Engineering Conference (ASME DETC2003), pp. 1-8, DETC2003/VIB - 48391.
39. Oustaloup, A., Melchoir, P., Lanusse, P., Cois, C., and Dancla, F., 2000. "The CRONE toolbox for Matlab". In Proceedings of the 11th IEEE International Symposium on Computer Aided Control System Design - CACSD.
40. Xue, D., and Atherton, D. P., 1994. "A suboptimal reduction algorithm for linear systems with a time delay". International Journal of Control, 60 (2), pp. 181-196.
41. Press, W. H., Flannery, B. P., and Teukolsky, S. A., 1986. Numerical recipes, the art of scientific computing. Cambridge University Press, Cambridge.
42. Wang, F. S., Juang, W. S., and Chan, C. T., 1995. "Optimal tuning of PID controllers for single and cascade control loops". Chemical Engineering Communications, 132, pp. 15-34.