Robust stability check for fractional PID-based control systems

Transactions of the Institute of Measurement and Control

Volumn 35, Issue 2, 2013, Pages 236-246

  Akbari Moornani, Kamran ^a   Haeri, Mohammad ^b  

^a TARBIAT MODARES UNIVERSITY   (Iran)

^b SHARIF UNIVERSITY OF TECHNOLOGY   (Iran)

Author keywords

BIBO stability; fractional order system; fractional PID controller; non fragile controller; robustness; zero exclusion condition

Indexed keywords

CONTROLLERS; ELECTRIC CONTROL EQUIPMENT; PROPORTIONAL CONTROL SYSTEMS; ROBUSTNESS (CONTROL SYSTEMS); SYSTEM STABILITY; THREE TERM CONTROL SYSTEMS;

BIBO STABILITY; FRACTIONAL PID CONTROLLERS; FRACTIONAL-ORDER SYSTEMS; NONFRAGILE CONTROLLERS; ZERO EXCLUSION CONDITION;

CLOSED LOOP SYSTEMS;

EID: 84876066820     PISSN: 01423312     EISSN: None     Source Type: Journal    
DOI: 10.1177/0142331212440477     Document Type: Article

References (28)

1. Akbari Moornani K, Haeri M. Robustness in fractional proportional- integral-derivative-based closed-loop systems. IET Control Theory & Applications. 2010a ; 4 (10). 1933-1944
2. Akbari Moornani K, Haeri M. On robust stability of LTI fractional-order delay systems of retarded and neutral type. Automatica. 2010b ; 46 (2). 362-368
3. Akbari Moornani K, Haeri M. Robust stability testing function and Kharitonov-like theorem for fractional order interval systems. IET Control Theory & Applications. 2010c ; 4 (10). 2097-2108
4. Astrom KJ, Hagglund T Advanced PID Control. Research Triangle Park, NC: ISA ; 2005 :
5. Barmish BR New Tools for Robustness of Linear Systems. New York: Macmillan Publishing Company ; 1994 :
6. Bonnet C, Partington JR. Coprime factorizations and stability of fractional differential systems. System & Control Letter. 2000 ; 41: 167-174
7. Bonnet C, Partington JR. Analysis of fractional delay systems of retarded and neutral type. Automatica. 2002 ; 38: 1133-1138 (Pubitemid 34524669)
8. Caponetto R, Dongola G, Fortuna L, Gallo A. New results on the synthesis of FO-PID controllers. Communications in Nonlinear Science and Numerical Simulation. 2010 ; 15 (4). 997-1007
9. Caponetto R, Fortuna L, Porto D. Parameter tuning of a non integer order PID controller. Fifteenth International Symposium on Mathematical Theory of Networks and Systems ; 2002 Notre Dame, Indiana ; 2002..
10. Cois O, Oustaloup A, Battaglia E, Battaglia JL. Non integer model from modal decomposition for time domain system identification. Proceedings of the 12th IFAC SYSID2000 ; 2000 Santa Barbara, CA ; 2000. 989.
11. Das S Functional Fractional Calculus for System Identification and Controls. Berlin: Springer-Verlag ; 2008 :
12. Hamamci SE. An algorithm for stabilization of fractional-order time delay systems using fractional-order PID controllers. IEEE Transactions on Automatic Control. 2007 ; 52 (10). 1964-1969 (Pubitemid 350130541)
13. Hamamci SE. Stabilization using fractional-order PI and PID controllers. Nonlinear Dynamics. 2008 ; 51: 329-343 (Pubitemid 47632368)
14. Applications of Fractional Calculus in Physics. Hilfer R, ed. Singapore: World Scientific ; 2000 :
15. Ho MT, Datta A, Bhattacharyya SP. Robust and non-fragile PID controller design. International Journal of Robust Nonlinear Control. 2001 ; (11). 681-708 (Pubitemid 32610084)
16. Keel LH, Bhattacharyya SP. Robust, fragile, or optimal?. IEEE Transactions on Automatic Control. 1997 ; 42 (8). 1098-1105 (Pubitemid 127760280)
17. Kilbas AA, Srivastava HM, Trujillo JJ Theory and Applications of Fractional Differential Equations. Amsterdam: Elsevier B.V. ; 2006 :
18. Marden M Geometry of Polynomials. Providence, RI: American Mathematical Society ; 1966 :
19. Matignon D. Stability result for fractional differential equations with applications to control processing. IMACS-SMC Proceedings ; 1996 Lille ; 1996. 963.
20. Monje CA, Vinagre BM, Chen YQ, Feliu V, Lanusse P, Sabatier J Fractional Differentiation and its Application. Bordeaux: ; 2004 :
21. Monje CA, Vinagre BM, Feliu V, Chen YQ. Tuning and auto-tuning of fractional order controllers. Control Engineering Practice. 2008 ; 16 (7). 798-812 (Pubitemid 351470859)
22. Petras I, Vinagre BM. Practical application of digital fractional-order controller to temperature control. Acta Montanistica Slovaca. 2002 ; 7 (2). 131-137
23. Petras I, Vinagre BM, Dorcak L, Feliu V. Fractional digital control of a heat solid: experimental results. Proceedings of the International Carpathian Control Conference ; 2002 Malenovice ; 2002. 208.
24. Podlubny I. Fractional-order systems and PIλDμ -controllers. IEEE Transactions on Automatic Control. 1999 ; 44 (1). 208-214
25. Advances in Fractional Calculus. Sabatier J Agrawal OP Machado JAT, ed. Berlin: Springer ; 2007 :
26. Tabatabaei M, Haeri M. Design of fractional order PID controller based on moment matching and CRA method. Proceedings of the Institution of Mechanical Engineers, Part I, Journal of Systems and Control Engineering. 2011 ;:
27. Valerio D, Costa JS. Tuning of fractional PID controllers with Ziegler-Nichols-type rules. Signal Processing. 2006 ; 86 (10). 2771-2784
28. Vinagre BM, Podlubny I, Dorcak L, Feliu V. On fractional PID controllers: a frequency domain approach. Proceedings of the IFAC Workshop on Digital Control. Past, Present and Future of PID Control ; 2000 Terrasa ; 2000..