On fractional PI λ controllers: Some tuning rules for robustness to plant uncertainties

Nonlinear Dynamics

Volumn 38, Issue 1-4, 2004, Pages 369-381

  Monje, Concepción A ^a   Calderon, Antonio J ^a   Vinagre, Blas M ^a   Chen, Yangquan ^b   Feliu, Vicente ^c  

^a UNIVERSITY OF EXTREMADURA   (Spain)

^b Utah State University   (United States)

^c UNIVERSITY OF CASTILLA LA MANCHA   (Spain)

Author keywords

Controller tuning; Fractional differentiator; Fractional order dynamic systems; PID; Proportional and integral (PI) controller

Indexed keywords

CONTROL SYSTEM ANALYSIS; ITERATIVE METHODS; NONLINEAR SYSTEMS; OPTIMIZATION; PROPORTIONAL CONTROL SYSTEMS; THREE TERM CONTROL SYSTEMS; TUNING; TWO TERM CONTROL SYSTEMS; UNCERTAIN SYSTEMS;

CONTROLLER TUNING; FRACTIONAL DIFFERENTIATORS; FRACTIONAL-ORDER DYNAMIC SYSTEMS; PID CONTROLLERS; PROPORTIONAL AND INTEGRAL (PI) CONTROLLERS;

ROBUSTNESS (CONTROL SYSTEMS);

EID: 15544379983     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-004-3767-3     Document Type: Conference Paper

References (22)

1. Aström, K. J. and Hägglund T., 'The future of PID control', in IFAC Workshop on Digital Control. Past, Present and Future of PID Control, Terrassa, Spain, 2000, pp. 19-30.
2. Axtel, M. and Bise, E. M., 'Fractional calculus applications in control systems', in Proceedings of the IEEE National Aerospace and Electronics Conference, New York, 1990, pp. 563-566.
3. Barbosa, R. S., Machado, J. A. T., and Ferreira, I. M., 'A fractional calculus perspective of PID tuning', in Proceedings of the DETC'03, Chicago, Illinois, 2003.
4. Calderón, A. J., Vinagre, B. M., and Feliu, V., 'Fractional sliding mode control of a DC-DC buck converter with application to DC motor drives', in ICAR 2003: The 11th International Conference on Advanced Robotics, Coimbra, Portugal, 2003, pp. 252-257.
5. Calderón, A. J., Vinagre, B. M., and Feliu, V., 'Linear fractional order control of a DC-DC buck converter', in ECC 03: European Control Conference 2003, Cambridge, UK, 2003.
6. Caponetto, R., Fortuna, L., and Porto, D., 'Parameter tuning of a non-integer order PID controller', in Proceedings of the Fifteenth International Symposium on Mathematical Theory of Networks and Systems, Notre Dame, Indiana, 2002 ( http://www.nd.edu/mtns/papers/7434.pdf ).
7. Chen, Y. Q., Hu, C. H., and Moore, K. L., 'Relay feedback tuning of robust PID controllers with iso-damping property', in 42nd IEEE Conference on Decision and Control, Maui, Hawaii, 2003.
8. Feliu, V., Gorostiaga L., Vinagre, B., and Monje, C., 'Robust Smith predictor for first order processes with dead time based on a fractional controller', Internal Report, 2002.
9. Feliu, V., Rivas, R., Gorostiaga, L., and Sánchez, L., 'Fractional control for an open irrigation canal', in Proceedings of the 6th Inter-Regional Conference on Environment-Water', Albacete, Spain, 2003.
10. Franklin, G., Powell, J., and Naeini, A., Feedback Control of Dynamic Systems, Addison-Wesley, Reading, Massachusetts, 1986.
11. Leu, J. F., Tsay, S. Y., and Hwang, C., 'Design of optimal fractional-order PID controllers', Journal of the Chinese Institute of Chemical Engineers 33(2), 2002, 193-202.
12. Manabe, S., 'The non-integer integral and its application to control Systems', Electrotechnical Journal of Japan 6(3/4), 1961, 83-87.
13. Monje, C. A., Calderón, A. J., and Vinagre, B. M., 'PI vs fractional DI control: First results', in CONTROLO 2002: 5th Portuguese Conference on Automatic Control, Aveiro, Portugal, 2002, pp. 359-364.
14. Monje, C. A., Vinagre, B. M., Chen, Y. Q., and Feliu, V., 'Une Proposition pour la Synthèse de Correcteurs PI d'Ordre Non Entier', in Action Thématique SDNE, Bordeaux ( http://www.lap.u-bordeaux.fr/AT-sdne/ ).
15. Oldham, K. and Spanier, J., The Fractional Calculus, Academic Press, New York, 1974.
16. Oustaloup, A., La Commande CRONE: Commande Robuste d'Ordre Non Entier, Hermes, Paris, 1991.
17. Oustaloup, A., La Dérivation non Entière, Hermes, Paris, 1995.
18. Podlubny, I., 'Fractional-order Systems and PID-controllers', IEEE Transaction on Automatic Control 44(1), 1999, 208-214.
19. Sánchez, Y., 'Fractional-PID control for active reduction of vertical tail buffeting', Technical Report, Saint Louis University, St. Louis, Missouri, 1999.
20. Vinagre, B. M., 'Modelado y Control de Sistemas Dinámicos Caracterizados por Ecuaciones Ïntegro-Diferenciales de Orden Fraccional', Ph.D. thesis, Escuela de Ingenierías Industriales, Universidad de Extremadura, Badajoz, Spain, 2001.
21. Vinagre, B. M., Podlubny, I., Dorcak, L., and Feliu, V., 'On fractional PID controllers: A frequency domain approach', in IFAC Workshop on Digital Control. Past, Present and Future of PID Control, Terrasa, Spain, 2000, pp. 53-58.
22. Ziegler, J. G. and Nichols, N. B., 'Optimum settings for automatic controllers', Transactions of the ASME 64, 1942, 759-768.