Introduction to single-input, single-output fractional control

IET Control Theory and Applications

Volumn 5, Issue 8, 2011, Pages 1033-1057

  Valerio D ^a   Sa Da Costa J ^a  

^a Instituto Superior Tecnico Institute for Mechanical Engineering   (Portugal)

Author keywords

[No Author keywords available]

Indexed keywords

CRONE CONTROL; CRONE CONTROLLERS; EXPERIMENTAL DATA; FRACTIONAL CONTROLLERS; GAIN VARIATIONS; IN-CONTROL; PLANT UNCERTAINTY; PROPORTIONAL INTEGRAL DERIVATIVE CONTROL; ROBUST PERFORMANCE; SINGLE INPUT , SINGLE OUTPUTS; THIRD GENERATION; TRANSFER FUNCTION MODEL;

PROPORTIONAL CONTROL SYSTEMS; TRANSFER FUNCTIONS;

CONTROLLERS;

EID: 79960615237     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta.2010.0332     Document Type: Article

References (69)

1. Oustaloup, A., Mathieu, B., and Lanusse, P.: ' The CRONE control of resonant plants: application to a flexible transmission ', Eur. J. Control, 1995, 1, p. 113-121 0947-3580
2. Altet, O., Moreau, X., Moze, M., Lanusse, P., and Oustaloup, A.: ' Principles and synthesis of hydractive CRONE suspension ', Nonlinear Dyn., 2004, 38, (1-2), p. 435-459 10.1007/s11071-004-3771-7 0924-090X (Pubitemid 40400631)
3. Moreau, X., Altet, O., and Oustaloup, A.: ' The CRONE suspension: management of the dilemma comfort-road holding ', Nonlinear Dyn., 2004, 38, (1-2), p. 461-484 10.1007/s11071-004-3772-6 0924-090X (Pubitemid 40400632)
4. Oustaloup, A., Cois, O., and Lanusse, P.: ' A survey on the CRONE approach' ', et al., Méhauté, A.L., Tenreiro Machado, J.A., Trigeassou, J.C., Sabatier, J., Fractional differentiation and its applications, (LAPS, Bordeaux, 2005), p. 735-780
5. Feliu-Batlle, V., Pérez, R., and Rodríguez, L.: ' Fractional robust control of main irrigation canals with variable dynamic parameters ', Control Eng. Pract., 2007, 15, p. 673-686 10.1016/j.conengprac. 2006.11.018 0967-0661 (Pubitemid 46357262)
6. Domingues, J., Valério, D., and da Costa, J.S.: ' Rule-based fractional control of an irrigation canal ', ASME J. Comput. Nonlinear Dyn., 2011, 6, (2), p. 024503 10.1115/1.4002509
7. Vinagre, B.: ' Modelado y control de sistemas dinámicos caracterizados por ecuaciones íntegrodiferenciales de orden fraccional' ', 2001, PhD, Universidad Nacional de Educación a Distancia, Madrid
8. Valério, D., and da Costa, J.S.: ' Fractional control of a flexible robot' ', Méhauté, A.L., Tenreiro Machado, J.A., Trigeassou, J.C., Sabatier, J., Fractional differentiation and its applications, (LAPS, Bordeaux, 2005), p. 649-660
9. Oldham, K.B., and Spanier, J.: ' The fractional calculus ', (Academic press, New York, 1974)
10. Samko, S.G., Kilbas, A.A., and Marichev, O.I.: ' Fractional integrals and derivatives ', (Gordon and Breach, Yverdon, 1993)
11. Miller, K.S., and Ross, B.: ' An introduction to the fractional calculus and fractional differential equations ', (John Wiley and Sons, New York, 1993)
12. Podlubny, I.: ' Fractional differential equations: an introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications ', (Academic Press, San Diego, 1999)
13. Kilbas, A.A., Srivastava, H.M., and Trujillo, J.J.: ' Theory and applications of fractional differential equations ', (Elsevier, Amsterdam, 2006)
14. Wheeler, N.: ' Construction & physical application of the fractional calculus' ', February, 1997
15. Lavoie, J.L., Osler, T.J., and Tremblay, R.: ' Fractional derivatives and special functions ', SIAM Rev., 1976, 18, (2), p. 240-268 10.1137/1018042 0036-1445
16. Davis, P.J.: ' Gamma function and related functions' ', Abramowitz, M., Stegun, I.A., Handbook of mathematical functions with formulas, graphs and mathematical tables, (Tenho de descobrir qual, Ignoro, 1970), p. 253-293
17. Chen, Y.Q., Petras, I., and Vinagre, B.: ' A list of Laplace and inverse Laplace transforms related to fractional order calculus' ', Available at http://ivopetras.tripod.com/foc-laplace.pdf, accessed November 2001
18. Bonneta, C., and Partington, J.R.: ' Coprime factorizations and stability of fractional differential systems ', Syst. Control Lett., 2000, 41, p. 167-174 10.1016/S0167-6911(00)00050-5 0167-6911
19. Matignon, D.: ' Stability properties for generalized fractional differential systems ', ESAIM Proc., 1998, 5, p. 145-158 10.1051/proc:1998004
20. Malti, R., Moreau, X., and Khemane, F.: ' Resonance of fractional transfer functions of the second kind' ', Fractional Differentiation and its Applications, (, IFAC, Ankara, 2008)
21. Oustaloup, A.: ' La commande CRONE: Commande Robuste d'Ordre Non Entier ', (Hermès, Paris, 1991)
22. Oustaloup, A., Levron, F., Matthieu, B., and Nanot, F.M.: ' Frequency-band complex noninteger differentiator: characterization and synthesis ', IEEE Trans. Circuits Syst. I, Fundam. Theory Appl., 2000, 47, (1), p. 25-39 10.1109/81.817385 1057-7122 (Pubitemid 30549106)
23. 1/n by a regular Newton process ', IEEE Trans. Circuit Theory, 1964, 7, p. 210-213 0018-9324
24. Wall, H.S.: ' Analytic theory of continued fractions ', (D. Van Nostrand Company, Princeton, 1948)
25. Press, W.H., Teukolsky, S.A., and Vetterling, W.T.: ' Numerical recipes in C - the art of scientific computing ', (Cambridge University Press, Cambridge, 1992)
26. ∞ optimized wave-absorbing control: analytical and experimental results ', J. Guid. Control Dyn., 1993, 16, (6), p. 1146-1153 10.2514/3.21139 0731-5090
27. Lubich, Ch.: ' Discretized fractional calculus ', SIAM J. Math. Anal., 1986, 17, (3), p. 704-719 10.1137/0517050 0036-1410
28. Tenreiro Machado, J.A.: ' Analysis and design of fractional-order digital control systems ', J. Syst. Anal. Model. Simul., 1997, 27, p. 107-122
29. Tenreiro Machado, J.A.: ' On the implementation of fractional-order control systems through discrete-time algorithms ', Proc. Jubilee Int. Conf. Bánki Donát Polytechnic Müszaki Föiskola, Bánki Donát, 1999, p. 39-44
30. Vinagre, B.M., Podlubny, I., Hernández, A., and Feliu, V.: ' Some approximations of fractional order operators used in control theory and applications ', Fract. Calc. Appl. Anal., 2000, 3, p. 231-248
31. Tenreiro Machado, J.A.: ' Discrete-time fractional-order controllers ', Fract. Calc. Appl. Anal., 2001, 4, (1), p. 47-66
32. Chen, Y.Q., and Vinagre, B.: ' A new IIR-type digital fractional order differentiator ', Signal Process., 2003, 83, p. 2359-2365 10.1016/S0165-1684(03) 00188-9 0165-1684
33. Valério, D., and da Costa, J.S.: ' Time-domain implementation of fractional order controllers ', IEE Proc. Control Theory Appl., 2005, 152, (5), p. 539-552 10.1049/ip-cta:20045063 1350-2379 (Pubitemid 41353586)
34. Tseng, C.-C.: ' Design of fractional order digital FIR differentiators ', IEEE Signal Process. Lett., 2001, 8, (3), p. 77-79 10.1109/97.905945 1070-9908 (Pubitemid 32255387)
35. Malti, R., Victor, S., and Oustaloup, A.: ' Advances in system identification using fractional models ', ASME J. Comput. Nonlinear Dyn., 2008, 3, p. 021401 10.1115/1.2833910
36. Levy, E.: ' Complex curve fitting ', IRE Trans. Autom. Control, 1959, 4, p. 37-44 10.1109/TAC.1959.1104874
37. Valério, D., Ortigueira, M.D., and da Costa, J.S.: ' Identifying a transfer function from a frequency response ', ASME J. Comput. Nonlinear Dyn., 2008, 3, (2), p. 021207 10.1115/1.2833906
38. Oustaloup, A., Lanusse, P., and Levron, F.: ' Frequency-domain synthesis of a filter using Viéte root functions ', IEEE Trans. Autom. Control, 2002, 47, (5), p. 837-841 10.1109/TAC.2002.1000283 0018-9286 (Pubitemid 34692271)
39. Caponetto, R., Fortuna, L., and Porto, D.: ' A new tuning strategy for a non integer order PID controller ', Fractional Differentiation and its Applications, Bordeaux, 2004
40. Zhao, C., Xue, D., and Chen, Y.Q.: ' A fractional order PID tuning algorithm for a class of fractional order plants ', Int. Conf. on Mechatronics & Automation, Niagara Falls, 2005
41. α controllers ', Nonlinear Dyn., 2007, 49, p. 251-257 10.1007/s11071-006-9125-x 0924-090X (Pubitemid 46739713)
42. Chen, Y.Q., Dou, H., Vinagre, B.M., and Monje, C.A.: ' A robust tuning method for fractional order pi controllers ', Fractional Differentiation and its Applications, Porto, 2006
43. μ controllers ', Fractional Differentiation and its Applications, Porto, 2006
44. Valério, D., and da Costa, J.S.: ' Tuning of fractional PID controllers with Ziegler-Nichols type rules ', Signal Process., 2006, 86, (10), p. 2771-2784 10.1016/j.sigpro.2006.02.020 0165-1684
45. Chen, Y.Q., Bhaskaran, T., and Xue, D.: ' Practical tuning rule development for fractional order proportional and integral controllers ', J. Comput. Nonlinear Dyn., 2008, 3, p. 021403 10.1115/1.2833934
46. μ tuning ', Fractional Differentiation and its Applications, Bordeaux, 2004
47. Monje, C.A., Vinagre, B.M., Feliu, V., and Chen, Y.Q.: ' Tuning and auto-tuning of fractional order controllers for industry applications ', Control Eng. Pract., 2008, 16, (7), p. 798-812 10.1016/j.conengprac.2007.08.006 0967-0661 (Pubitemid 351470859)
48. μ controllers using the integral time absolute error criterion ', Information and Automation for Sustainability, Colombo, 2008
49. Maiti, D., Biswas, S., and Konar, A.: ' Design of a fractional order PID controller using particle swarm optimization technique ', Second National Conf. on Recent Trends in Information Systems, 2008
50. Valério, D., and da Costa, J.S.: ' Tuning rules for fractional PIDs ', Tenreiro Machado, J.A., Sabatier, J., Agrawal, O., Fractional calculus: theoretical developments and applications in physics and engineering, (Springer, Dordrecht, 2007), p. 463-476
51. Padula, F., and Visioli, A.: ' Set-point weighting for fractional PID controllers ', Fractional Differentiation and its Applications, Badajoz, 2010
52. Bhambhani, V., Chen, Y.Q., and Xue, D.: ' Optimal fractional order proportional integral controller for varying time-delay systems ', IFAC World Congress, 2008, p. 4910-4915
53. Horowitz, I.M.: ' A synthesis theory for linear time-varying feedback systems with plant uncertainty ', IEEE Trans. Autom. Control, 1975, 20, (4), p. 454-464 10.1109/TAC.1975.1101007 0018-9286
54. Trigeassou, J.-C., and Maamri, N.: ' State space modeling of fractional differential equations and the initial condition problem ', Int. Multi-Conf. on Systems, Signals and Devices, Djerba, 2009
55. 2 norm of fractional differential systems ', ASME 2003 Design Engineering Technical Conf. Computers and Information in Engineering Science, Chicago, 2003
56. ∞ norm minimisation ', Sel. Top. Model. Control, 2002, 3, p. 50-54
57. ∞ norms ', Acta Polytech. Hung., 2006, 3, (4), p. 55-70
58. Calderón, A.J., Vinagre, B.M., and Feliú, V.: ' Fractional sliding mode control of a DC-DC buck converter with application to DC motor drives ', Int. Conf. on Advanced Robotics, Coimbra, 2003, p. 252-257
59. Efe, M.Ö.: ' Fractional order sliding mode controller design for fractional order dynamic systems' ', Baleanu, D., Güvenç, Z.B., Tenreiro Machado, J.A., New trends in nanotechnology and fractional calculus applications, (Springer, Dordrecht, 2010), p. 463-470
60. Efe, M.Ö.: ' A fractional order adaptation law for integer order sliding mode control of a 2DOF robot' ', Baleanu, D., Güvenç, Z.B., Tenreiro Machado, J.A., New trends in nanotechnology and fractional calculus applications, (Springer, Dordrecht, 2010), p. 471-478
61. Nataraj, P.S.V., and Tharewal, S.: ' On fractional-order QFT controllers ', J. Dyn. Syst. Meas. Control, 2007, 129, p. 212-218 10.1115/1.2432361 (Pubitemid 46715213)
62. Oustaloup, A., and Mathieu, B.: ' La commande CRONE du scalaire au multivariable ', (Hermès, Paris, 1999)
63. Lorenzo, C.F., and Hartley, T.T.: ' Variable order and distributed order fractional operators ', Nonlinear Dyn., 2002, 29, p. 57-98 10.1023/A: 1016586905654 0924-090X (Pubitemid 34945393)
64. Valério, D., and da Costa, J.S.: ' Variable-order fractional derivatives and their numerical approximations ', Signal Process., 2011, 91, (3), p. 470-483 10.1016/j.sigpro.2010.04.006 0165-1684
65. Valério, D., and da Costa, J.S.: ' Variable order fractional controllers ', Fractional Differentiation and its Applications, 2010
66. Metoui, B., Melchior, P., Najar, S., Abdelkrim, M.N., and Oustaloup, A.: ' Robust path planning for dynamic environment based on fractional attractive force ', Int. Multi-Conf. on Systems, Signals and Devices, 2009
67. Oustaloup, A., Orsoni, B., Melchior, P., and Linarès, H.: ' Path planning by fractional differentiation ', Robotica, 2003, 21, p. 59-69 10.1017/S0263574702004319 0263-5747
68. Melchior, P., Orsoni, B., Lavialle, O., Poty, A., and Oustaloup, A.: ' Consideration of obstacle danger level in path planning using a* and fast-marching optimisation: comparative study ', Signal Process., 2003, 83, p. 2387-2396 10.1016/S0165-1684(03)00191-9 0165-1684
69. Lorenzo, C.F., and Hartley, T.T.: ' Initialization of fractional-order operators and fractional differential equations ', J. Comput. Nonlinear Dyn., 2008, 3, p. 021101 10.1115/1.2833585