The development of fractional-order controllers is currently one of the most promising fields of research. However, most of the work in this area addresses the case of linear systems. This paper reports on the analysis of fractional-order control of nonlinear systems. The performance of discrete fractional-order PID controllers in the presence of several nonlinearities is discussed. Some results are provided that indicate the superior robustness of such algorithms.
Al-Alaoui, M.A., 1993, “Novel digital integrator and differentiator ,” Electronics Letters29(4), 376—378.
2.
Barbosa, R.S., Machado, J.A.T., and Ferreira, I.M., 2004, “Tuning of PID controllers based on Bode's ideal transfer function,” Nonlinear Dynamics38(1—4), 305—321.
3.
Barbosa, R.S., Machado, J.A.T., and Silva, M.F., 2006, “Time domain design of fractional differintegrators using least-squares,” Signal Processing86(10), 2567—2581.
4.
Lanusse, P., Oustaloup, A., and Sabatier, J., 2005, “Step-by-step presentation of a 3rd generation CRONE controller design with anti-windup system,” in Proceedings of the Fifth EURMECH Nonlinear Dynamics Conference (ENOC'05), Eindhoven, The Netherlands, August 7—12, CD-ROM.
Manabe, S., 1963, “The system design by the use of a model consisting of a saturation and non-integer integrals,” ETJ of Japan8(3/4), 147—150.
7.
Manabe, S., 2003, “Early development of fractional order control ,” in Proceedings of the 19th Biennial Conference on Mechanical Vibration and Noise (VIB'03), Chicago, IL , September 2—6, CD-ROM.
8.
Phillips, C. and Harbor, R., 1996, Feedback Control Systems, Prentice-Hall , Englewood Cliffs, NJ.
9.
Podlubny, I., 1999, Fractional Differential Equations, Academic Press, San Diego, CA.
10.
Slotine, J.E. and Li, W., 1991, Applied Nonlinear Control, Prentice-Hall , Englewood Cliffs, NJ.
11.
Smith, J.M., 1987, Mathematical Modeling and Digital Simulation for Engineers and Scientists, 2nd edn, Wiley , New York.
12.
Vinagre, B.M., Chen, Y.Q., and Petras, I., 2003, “Two direct Tustin discretizations methods for fractional-order differentiator/integrator,” Journal of the Franklin Institute340, 349—362.
