Note on fractional-order proportional-integral-differential controller design

IET Control Theory and Applications

Volumn 5, Issue 17, 2011, Pages 1978-1989

  Yeroglu, C ^a   Tan, N ^a  

^a INONU UNIVERSITY   (Turkey)

Author keywords

[No Author keywords available]

Indexed keywords

BODE ENVELOPE; CONTROLLER PARAMETER; DESIGN PROCEDURE; DESIGN TECHNIQUE; FRACTIONAL ORDER; INTEGRAL TERMS; OPTIMISATIONS; PARAMETRIC UNCERTAINTIES; PID CONTROLLERS; PROPORTIONAL INTEGRAL DIFFERENTIAL CONTROLLERS; PROPORTIONAL-INTEGRAL; SIMULATION EXAMPLE;

CONTROLLERS; DESIGN; ELECTRIC CONTROL EQUIPMENT; LINEAR EQUATIONS; THREE TERM CONTROL SYSTEMS; TWO TERM CONTROL SYSTEMS;

PROPORTIONAL CONTROL SYSTEMS;

EID: 80755169324     PISSN: 17518644     EISSN: 17518652     Source Type: Journal    
DOI: 10.1049/iet-cta.2010.0746     Document Type: Article

References (43)

1. m controllers ', IEEE Trans. Autom. Control, 1999, 44, (1), p. 208-214 10.1109/9.739144 0018-9286
2. Sabatier, J., Poullain, S., Latteux, P., Thomas, J.L., and Oustaloup, A.: ' Robust speed control of a low damped electromechanical system based on CRONE control: application to a four mass experimental test bench ', Nonlinear Dyn., 2004, 38, p. 383-400 10.1007/s11071-004-3768-2 0924-090X (Pubitemid 40400628)
3. Chen, Y.Q., Ahn, H.S., and Podlubny, I.: ' Robust stability check of fractional order linear time invariant systems with interval uncertainties ', Signal Process., 2006, 86, p. 2611-2618 10.1016/j.sigpro.2006.02.011 0165-1684 (Pubitemid 44026624)
4. Tan, N., Özgüven, Ö.F., and Özyetkin, M.M.: ' Robust stability analysis of fractional order interval polynomials ', ISA Trans., 2009, 48, p. 166-172 10.1016/j.isatra.2009.01.002
5. Nataraj, P.S.V.: ' Computation of spectral sets for uncertain linear fractional-order systems using interval constraints propagation ', Third IFAC Workshop on Fractional Differentiation and its Application, Ankara, 2008
6. Xue, D., Chen, Y.Q., and Atherton, D.P.: ' Linear feedback control analysis and design with MATLAB ', (SIAM Press, 2007)
7. Nakagava, N., and Sorimachi, K.: ' Basic characteristics of a fractance device ', IEICE Trans. Fundam., 1992, 12, p. 1814-1818, E75-A
8. Hwang, C., and Cheng, Y.C.: ' A numerical algorithm for stability testing of fractional delay systems ', Automatica, 2006, 42, p. 825-831 10.1016/j.automatica.2006.01.008 0005-1098
9. Petras, I.: ' The fractional order controllers: methods for their synthesis and application ', J. Electr. Eng., 1999, 50, p. 284-288
10. Manabe, S.: ' Early development of fractional order control ', Proc. ASME 2003 Design Engineering Technical Conf., Chicago, Illinois, 2003
11. Valério, D., and Da Costa, J.S.: ' Time domain implementation of fractional order controllers ', IEE Proc. Control Theory Appl., 2005, 5, p. 539-552 10.1049/ip-cta:20045063 1350-2379 (Pubitemid 41353586)
12. Machado, J.: ' Discrete-time fractional-order controllers ', Fract. Calc. Appl. Anal., 2001, 4, (1), p. 47-66
13. Monje, C.A., Vinagre, B.M., and Feliu, V.: et al. ' Tuning and auto-tuning of fractional order controllers for industry applications ', Control Eng. Pract., 2008, 16, p. 798-812 10.1016/j.conengprac.2007.08.006 0967-0661 (Pubitemid 351470859)
14. Chen, Y.Q., and Moore, K.L.: ' Discretization schemes for fractional order differentiators and integrators ', IEEE Trans. Circuits Syst. I: Fundam. Theory Appl., 2002, 49, (3), p. 363-367 10.1109/81.989172 1057-7122 (Pubitemid 34466606)
15. Ogata, K.: ' Modern control engineering ', (Prentice-Hall, New Jersey, 2002)
16. Åström, K., and Hägglund, T.: ' PID controllers: theory, design and tuning ', (Instrument Society of America, North Carolina, 1995)
17. Oustaloup, A.: ' LaDerivation Non Entiere ', (HERMES, Paris, 1995)
18. Oustaloup, A., Levron, F., Mathieu, 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)
19. Podlubny, I.: ' Fractional differential equations ', (Academic Press, San Diego, California, 1999)
20. μ controller ', IJ-STA, 2008, 2, p. 414-429
21. Vinagre, B.M., Monje, C.A., Calderon, A.J., and Suarez, J.I.: ' Fractional PID controllers for industry application ', J. Vibr. Control, 2007, 13, (9-10), p. 1419-1429 10.1177/1077546307077498 (Pubitemid 47482826)
22. Vinagre, B.M., Podlubny, I., Dorcak, L., and Feliu, V.: ' On fractional PID controllers: a frequency domain approach ', IFAC Workshop on Digital Control. Past, Present and Future of PID Control, Terrasa, Spain, 2000, p. 53-58
23. ∞ norm minimization ', Sel. Top. Model. Control, 2002, 3, p. 50-54
24. Xue, D., and Chen, Y.Q.: ' A comparative introduction of four fractional order controllers ', Proc. Fourth World Congress, Intelligent Control and Auto, 2002, p. 3228-3235, vol. 4
25. Hamamci, S.E.: ' An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers ', IEEE Trans. Autom. Control, 2007, 52, p. 1964-1969 10.1109/TAC.2007.906243 0018-9286 (Pubitemid 350130541)
26. Barbosa, R.S., Machado, J.A.T., and Ferreira, I.M.: ' Tuning of PID controllers based Bode's ideal transfer function ', Nonlinear Dyn., 2004, 38, p. 305-321 10.1007/s11071-004-3763-7 0924-090X (Pubitemid 40400623)
27. a controllers ', Nonlinear Dyn., 2007, 49, (1-2), p. 251-257 10.1007/s11071-006-9125-x 0924-090X (Pubitemid 46739713)
28. λ controllers: some tuning rules for robustness to plant uncertainties ', Nonlinear Dyn., 2004, 38, p. 369-381 10.1007/s11071-004-3767-3 0924-090X (Pubitemid 40400627)
29. Bhattacharyya, S.P., Chapellat, H., and Keel, L.H.: ' Robust control: the parametric approach ', (Prentice-Hall, 1995)
30. Kharitonov, V.L.: ' Asymptotic stability of an equilibrium position of a family of systems of linear differential equations ', Diff. Eqns., 1979, 14, p. 1483-1485
31. Bartlett, A.C., Hollot, C.V., and Lin, H.: ' Root location of an entire polytope of polynomials: it suffices to check the edges ', Math. Controls, Signals Syst., 1988, 1, p. 61-71 10.1007/BF02551236 (Pubitemid 18608943)
32. Hollot, C.V., and Tempo, R.: ' On the Nyquist envelope of an interval plant family ', IEEE Trans. Autom. Control, 1994, 39, p. 391-396 10.1109/9.272342 0018-9286
33. Tan, N., and Atherton, D.P.: ' Frequency response of uncertain systems: a 2q-convex parpolygonal approach ', IEE Proc. Control Theory Appl., 2000, 147, (5), p. 547-555 10.1049/ip-cta:20000636 1350-2379
34. Yeroglu, C., Tan, N., and Özyetkin, M.M.: ' Frequency response computation of fractional order interval transfer functions ', Int. J. Control Autom. Syst., 2010, 8, (5), p. 1009-1017 10.1007/s12555-010-0510-3 1598-6446
35. Caponetto, R., Dongola, G., Fortuna, L., and Petráš, I.: ' Fractional order systems, modeling and control applications, world scientific series on nonlinear science, series A ', (World Scientific Publishing Co. Pvt. Ltd., 2010), 72
36. Dorcak, L.: ' Numerical models for simulation the fractional-order control systems, UEF-04-94 ', (The Academy of Sciences, Institute of Experimental Physics, Kosice, Slovakia, 1994)
37. Oldham, K.B., and Spanier, J.: ' The fractional calculus: theory and applications of differentiation and integration to arbitrary order ', (Dover Books on Mathematics, 2006)
38. μ controller ', ELECO 2009 Sixth Int. Conf. Electrical and Electronics Engineering, Bursa, Turkey, 2009
39. Valério, D.: ' Ninteger v. 2.3 fractional control toolbox for MatLab ', http://web.ist.utl.pt/~duarte.valerio, 2005
40. Roy, A., and Iqbal, K.: ' PID controller tuning for the first-order-plus-dead-time process model via Hermite-Biehler theorem ', ISA Trans., 2004, 44, p. 363-378 10.1016/S0019-0578(07)60210-9
41. μ controller for FOPDT systems ', Fourth IFAC Workshop on Fractional Differentiation and its Applications, Badajoz, Spain, 2010
42. Chen, Y.Q., Hu, C.H., and Moore, K.L.: ' Relay feedback tuning of robust PID controllers with iso-damping property ', Proc. 42nd IEEE Conf. on Decision and Control, Maui, Hawaii, USA, 2003
43. Yeroglu, C., and Tan, N.: ' Development of a toolbox for frequency response analysis of fractional order control systems ', 19th, European Conf. on Circuit Theory and Design, Antalya, August, 2009