Discretization of complex-order algorithms for control applications

JVC/Journal of Vibration and Control

Volumn 14, Issue 9-10, 2008, Pages 1349-1361

  Barbosa, Ramiro S ^a   Tenreiro MacHado, J A ^a   Silva, Manuel F ^a  

^a INSTITUTO SUPERIOR DE ENGENHARIA DO PORTO   (Portugal)

Author keywords

Complex order differintegrals; Conjugated order differintegrals; Discretization; Fractional calculus; Fractional order control

Indexed keywords

CHLORINE COMPOUNDS;

COMPLEX-ORDER DIFFERINTEGRALS; CONJUGATED-ORDER DIFFERINTEGRALS; CONTROL APPLICATIONS; DISCRETIZATION; FRACTIONAL CALCULUS; FRACTIONAL-ORDER CONTROL; FREQUENCY DOMAINS; IN-CONTROL; TIME RESPONSES;

TRANSFER FUNCTIONS;

EID: 52349119862     PISSN: 10775463     EISSN: 17412986     Source Type: Journal    
DOI: 10.1177/1077546307087445     Document Type: Conference Paper

References (18)

1. Al-Alaoui, M.A., 1993, " Novel digital integrator and differentiator, " Electronics Letters 29 (4). 376-378.
2. Barbosa, R.S., Tenreiro Machado, J.A., and Ferreira, I.M., 2005, " Pole-zero approximations of digital fractional-order integrators and differentiators using signal modeling techniques, " in Proceedings of the l6th World IFAC Congress, Prague, Czech Republic, July 4-8, on CD-ROM.
3. Barbosa, R.S., Tenreiro Machado, J.A., and Silva, M.F., 2006 a, " Time domain design of fractional differintegrators using least-squares, " Signal Processing 86 (10). 2567-2581.
4. Barbosa, R.S., Tenreiro Machado, J.A., and Silva, M.F., 2006 b, " Discretization of complex-order differintegrals, " in Proceedings of the Second IEAC Workshop on Fractional Differentiation and its Applications, Instituto Superior de Engenharia do Porto (ISEP), Porto, Portugal, July 19-21, pp. 340-345.
5. Chen, Y.Q., Vinagre, B.M., and Podlubny, I., 2004, " Continued fraction expansion approaches to discretizing fractional order derivatives-an expository review, " Nonlinear Dynamics 38 (1-4). 115-170.
6. Hartley, T.T., Adams, J.L. and Lorenzo, C.F., 2005 a, " Complex-order distributions, " in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, DETC2005-84952, on CD-ROM.
7. Hartley, T.T., Lorenzo, C.F., and Adams, J.L., 2005 b, " Conjugated-order differintegrals, " in Proceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, DETC2005-84951, on CD-ROM.
8. Lanusse, P., Oustaloup, A., and Sabatier, J., 2005, " Step-by-step presentation of a 3rd generation CRONE controller design with an anti-windup system, " in Proceedings of the Fifth EUROMECH Nonlinear Conference, Eindhoven, The Netherlands, August 7-12, pp. 1338-1347.
9. Love, E.R., 1971, " Fractional derivative of imaginary order, " Journal of the London Mathematical Society 3 (2). 241-259.
10. Nigmatullin, R.R., 2005, " Theory of dielectric relaxation in non-crystalline solids: From a set of micromotions to the averaged collective motion in the mesoscale region, " Physica B: Physics of the Condensed Matter 358, 201-215.
11. Nigmatullin, R.R. and Le Mehaute, A., 2005, " Is there a geometric/physical meaning of the fractional integral with complex exponent?, " Journal of Non-Crystalline Solids 351, 2888-2899.
12. Nigmatullin, R.R. and Trujillo, J.J., 2005, " The mesoscopic 'fractional' kinetic equations and a generalized Riemann-Liouville integral, " in Proceedings of the Fifth EUROMECH Nonlinear Conference, Eindhoven, The Netherlands, August 7-12, pp. 1402-1408.
13. Oldham, K.B. and Spanier, J., 1974, The Fractional Calculus, Academic Press, New York.
14. Oustaloup, A., Levron, F., Mathieu, B., and Nanot, F.M., 2000, " Frequency-band complex noninteger differentiator: Characterization and synthesis, " IEEE Transactions on Circuits and Systems-I: Fundamental Theory and Applications 47 (1). 25-39.
15. Podlubny, I., 1999, Fractional Differential Equations, Academic Press, San Diego, CA
16. Samko, S.G., Kilbas, A.A., and Marichev, O.I., 1993, Fractional Integrals and Derivatives: Theory and Applications, Gordon and Breach Science, Amsterdam, The Netherlands.
17. Silva, M.F., Tenreiro Machado, J.A., and Barbosa, R.S., 2006, " Complex-order dynamics in hexapod locomotion, " Signal Processing 86 (10). 2785-2793.
18. Tenreiro Machado, J.A., 2001, " Discrete-time fractional-order controllers, " Journal of Fractional Calculus & Applied Analysis 4 (1). 47-66.