Design of fractional order proportional-integral-derivative controller based on moment matching and characteristic ratio assignment method

Proceedings of the Institution of Mechanical Engineers. Part I: Journal of Systems and Control Engineering

Volumn 225, Issue 8, 2011, Pages 1040-1053

  Tabatabaei, M ^a   Haeri, M ^b  

^a ISLAMIC AZAD UNIVERSITY   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

Characteristic ratio assignment; Fractional order PID controller; Fractional order systems; Moment matching

Indexed keywords

ANALYTICAL METHOD; CHARACTERISTIC RATIO; CLOSED LOOP STABILITY; CLOSED LOOP TRANSFER FUNCTION; CONTROL PARAMETERS; CROSS-OVER FREQUENCIES; FRACTIONAL ORDER; FRACTIONAL-ORDER SYSTEMS; ILLUSTRATIVE EXAMPLES; MOMENT-MATCHING; PID CONTROLLERS; PROPORTIONAL INTEGRAL DERIVATIVE CONTROLLERS; CHARACTERISTIC RATIO ASSIGNMENTS; FRACTIONAL-ORDER PID CONTROLLERS;

CONTROLLERS; THREE TERM CONTROL SYSTEMS; TRANSFER FUNCTIONS; TWO TERM CONTROL SYSTEMS; CLOSED LOOP CONTROL SYSTEMS; CLOSED LOOP SYSTEMS;

PROPORTIONAL CONTROL SYSTEMS;

EID: 84856405421     PISSN: 09596518     EISSN: 20413041     Source Type: Journal    
DOI: 10.1177/0959651811409489     Document Type: Conference Paper

References (31)

1. Cafagna, D. Past and present-fractional calculus: a mathematical tool from the past for present engi-neers. IEEE Ind. Electron. Mag., 2007, 1(2), 35-40. (Pubitemid 350141726)
2. Podlubny, I. Fractional differential equations, 1999 (Academic Press, San Diego, California).
3. Oldham, K. B. and Spanier, J. The fractional calcu-lus: theory and application of differentiation and integration to arbitrary order, 1974, p. 1074 (Aca-demic Press, New York).
4. Chen, Y. Q., Petras, I., and Xue, D. Fractional order control- a tutorial. In Proceedings of the American control conference, St. Louis, Missouri, 10-12 June 2009, pp. 1397-1411.
5. Isabel, S. J. and Machado, J. A. T. Fractional con-trol of heat diffusion systems. Nonlinear Dyn., 2008, 54, 263-282.
6. Benchella, A., Poinot, T., and Trigeassou, J. C. Approximation and identification of diffusive inter-faces by fractional models. Signal Process., 2006, 86(10), 2712-2727.
7. Meral, F. C., Royston, T. J., and Magin, R. Frac-tional calculus in viscoelasticity: an experimental study. Commun. Nonlinear Sci. Numer. Simul., 2010, 15(4), 939-945.
8. Jesus, I. S., Machado, J. A. T., and Barbosa, R. S. Control of a heat diffusion system through a frac-tional order nonlinear algorithm. Comput. Math. Appl., 2010, 59(5), 1687-1694.
9. Naslin, P. Essentials of optimal control, 1969 (Bos-ton Technical Publishers Inc., Cambridge, Massachussetts).
10. Manabe, S. Coefficient diagram method. In Pro-ceedings of the 14th IFAC Symposium on Auto-matic control in aerospace, Seoul, Republic of Korea, 24-28 August 1998, pp. 199-210.
11. Kim, Y. C., Keel, L. H., and Bhattacharyya, S. P. Transient response control via characteristic ratio assignment. IEEE Trans. Autom. Control, 2003, 48, 2238-2244.
12. Tabatabaei, M. and Haeri, M. Characteristic ratio assignment in fractional order systems. ISA Trans., 2010, 49(4), 470-478.
13. Emre, E. and Silverman, L. H. Partial model matching of linear systems. IEEE Trans. Autom. Control, 1980, 25(2), 280-281.
14. Jin, L. and Kim, Y. C. Fixed, low-order controller design with time response specifications using non-convex optimization. ISA Trans., 2008, 47(4), 429-438.
15. Grimme, E. J. Krylov projection methods for model reduction. PhD Thesis, Electrical Engineering Department, University of Illinois at Urbana-Champaign, 1997.
16. Bultheel, A. and van Barel, M. Pade techniques for model reduction in linear system theory: a survey. J. Comput. Appl. Math., 1986, 14(3), 401-438. (Pubitemid 16493546)
17. Gibarilo, L. G. and Lees, F. P. The reduction of transfer function models to simple models using the method of moments. Chem. Engng Sci., 1969, 24(1), 85-93.
18. Nagata, M., Inagaki, D., Inoue, T., Mizumoto, I., and Iwai, Z. The application of a PID parameter tuning method based on model matching on fre-quency domain for printer ink-head speed control. In Proceedings of the IEEE/ASME Conference on Advanced intelligent mechatronics, Singapore, 14-17 July 2009, pp. 256-262.
19. Ramasamy, M. and Sundaramoorthy, S. PID con-troller tuning for desired closed-loop responses for SISO systems using impulse response. Comput. Chem. Engng, 2008, 32(8), 1773-1778.
20. Valerio, D. and Costa, J. Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Process., 2006, 86(10), 2771-2784.
21. Luo, Y. and Chen, Y. Q. Fractional order propor-tional derivative controller for a class of fractional order systems. Automatica, 2009, 45(10), 2446-2450.
22. Zhao, C., Xue, D., and Chen, Y. Q. A fractional PID tuning algorithm for a class of fractional order plants. In Proceedings of IEEE International Con-ference on Mechatronics and automation, Niagara, Canada, 29 July-1 August 2005, pp. 216-221. (Pubitemid 41585407)
23. Monje, C. A., Vinagre, B. M., Feliu, V., and Chen, Y. Q. Tuning and auto tuning of fractional order controllers for industry applications. Control Engng Pract., 2008, 16, 798-812. (Pubitemid 351470859)
24. Battle, V. F., Rivas Perez, R., and Rodriguez, L. S. Fractional robust control of main irrigation canals with variable dynamic parameters. Control Engng Pract., 2007, 15(6), 673-686. (Pubitemid 46357262)
25. μ control-ler design for integer and fractional plants using piecewise orthogonal functions. Commun. Non-linear Sci. Numer. Simul., 2010, 15(5), 1267-1278.
26. Merrikh-Bayat, F. and Karimi-Ghartemani, M. Method for designing PID stabilizers for minimum phase fractional-order systems. IET Control Theory Appl., 2010, 4(1), 61-70.
27. Hammaci, S. E. Stabilization using fractional-order PI and PID controllers. Nonlinear Dyn., 2008, 51(1-2), 329-343.
28. μ control-lers with an improved differential evolution. Engng Appl. Artif. Intell., 2009, 22(2), 343-350.
29. Cois, O., Oustaloup, A., Battaglia, E., and Battaglia, J. L. Non-integer model from modal decomposition for time domain system identifica-tion. In Proceedings of the IFAC Symposium on System identification, Santa Barbara, California, 21-23 July 2000, vol. 3, pp. 989-994 (IFAC, Santa Bar-bara, California)
30. Petras, I., Dorcak, L., and Kostial, I. A comparison of the integer and the fractional order controllers on the laboratory object. In Proceedings of the13th Interna-tional Conference on Automatic mining, High Tatros, Slovak Republic, 8-12 September 1998, pp. 451-454.
31. i-controllers. In Proceedings of the 36th IEEE Conference on Decision and control, 10-12 December 1999, San Diego, California, pp. 4985-4990 (IEEE Press, Piscataway, New Jersey).