Design of a Fractional Order CRONE and PID Controllers for Nonlinear Systems using Multimodel Approach
Abstract
This paper deals with the output regulation of nonlinear control systems in order to guarantee desired performances in the presence of plant parameters variations. The proposed control law structures are based on the fractional order PI (FOPI) and the CRONE control schemes. By introducing the multimodel approach in the closed-loop system, the presented design methodology of fractional PID control and the CRONE control guarantees desired transients. Then, the multimodel approach is used to analyze the closed-loop system properties and to get explicit expressions for evaluation of the controller parameters. The tuning of the controller parameters is based on a constrained optimization algorithm. Simulation examples are presented to show the effectiveness of the proposed method.References
K. J. Åström and T. Hägglund, “Advanced pid control,” in The Instrumentation, Systems, and Automation Society, Citeseer, 2006.
J. G. Ziegler and N. B. Nichols, “Optimum settings for automatic controllers,” trans. ASME, vol. 64, no. 11, 1942.
A. Oustaloup, La commande CRONE: commande robuste d’ordre non entier. Hermes, 1991.
M. Sugeno, “An introductory survey of fuzzy control,” Information sciences, vol. 36, no. 1-2, pp. 59–83, 1985.
R.Murray-Smith and T. Johansen,Multiple model approaches to nonlinearmodelling and control. CRC press, 1997.
P. McNamara and F. Milano, “Model predictive control-based agc for multi-terminal hvdc-connected ac grids,” IEEE Transactions on Power Systems, vol. 33, no. 1, pp. 1036–1048, 2018.
J. M. Böling, D. E. Seborg, and J. P. Hespanha, “Multi-model adaptive control of a simulated ph neutralization process,” Control Engineering Practice, vol. 15, no. 6, pp. 663–672, 2007.
N. Li, S.-Y. Li, and Y.-G. Xi, “Multi-model predictive control based on the takagi– sugeno fuzzy models: a case study,” Information Sciences, vol. 165, no. 3-4, pp. 247– 263, 2004.
D. Ichalal, B. Marx, J. Ragot, and D.Maquin, “Diagnostic des systemes non linéaires par approche multimodele,” in Workshop Surveillance, Sûreté et Sécurité des Grands Systèmes, 3SGS’08, p. CDROM, 2008.
N. Elfelly, J.-Y. Dieulot,M. Benrejeb, and P. Borne, “A new approach for multimodel identification of complex systems based on both neural and fuzzy clustering algorithms,” Engineering Applications of Artificial Intelligence, vol. 23, no. 7, pp. 1064–1071, 2010.
S. Oukacine, T. Djamah, S. Djennoune, R. Mansouri, and M. Bettayeb, “Multi-model identification of a fractional non linear system,” IFAC Proceedings Volumes, vol. 46, no. 1, pp. 48–53, 2013.
E. Ouhibi, M. B. Hariz, and F. Bouani, “Synthesis of a non-integer controller for fractional order systems,”
S. B. Atia, A. Messaoud, and R. B. Abdennour, “Internal multimodel control for discrete nonlinear systems with time-delay,” in Control and Automation (MED), 2016 24th Mediterranean Conference on, pp. 94–99, IEEE, 2016.
J. Osusk`y, M. Hypiusová, and T. Puleva, “Robust multimodel control applied on hydraulic turbine model,” in Cybernetics & Informatics (K&I), 2016, pp. 1–6, IEEE, 2016.
A. Tahar and M. N. Abdelkrim, “Multimodel H∞ loop shaping control of a DC motor under variable loads,” in 8th InternationalMulti-Conference on Systems, Signals and Devices (SSD), pp. 1–6, IEEE, 2011.
M. L.Wardi, R. Abdelkrim, A. Rhouma, M. Amairi, andM.N. Abdelkrim, “Fractional design for nonlinear systems based on multimodel approach,” in 16th International Multi-Conference on Systems, Signals and Devices (SSD), 2019.
M. L. Wardi, M. Amairi, and M. N. Abdelkrim, “Fractional PID controller design for nonlinear systems based on singular perturbation technique,” International Journal of Digital Signals and Smart Systems, 2017.
I. Podlubny, “Fractional-order systems and PIλDμ-controllers,” Automatic Control, IEEE Transactions on, vol. 44, no. 1, pp. 208–214, 1999.
Delmotte, F. (1997). Analyse multi-modèle. Thèse de doctorat, Lille1.
Simon, D., Marzocchi, A., Flecker, R., Lunt, D., Hilgen, F. et Meijer, P. (2016). Multi-model approach to reconstruct the mediterranean freshwater evolution. In EGU General Assembly Conference Abstracts, volume 18, page 14277.
M. L. Wardi, M. Amairi, and M. N. Abdelkrim, “Robust fractional control of a two time scale system,” in 17th international conference onSciences and Techniques of Automatic control and computer engineering (STA), 2015.
M. L. Wardi, M. Amairi, and M. N. Abdelkrim, “Output regulation of nonlinear systems with FOPI controller based on singular perturbation technique,” in 2017 18th International Conference on Sciences and Techniques of Automatic Control and Computer Engineering (STA), pp. 18–23, IEEE, 2017.
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