SYNTHESIS OF FRACTIONAL ORDER FUZZY OBSERVER FOR A FRACTIONAL ORDER TAKAGI-SUGENO MODEL WITH UNMEASURABLE PREMISE VARIABLES

ABDELGHANI DJEDDI; TOUFIK AMIEUR; FAREH HANNACHI; SAMIR METATLA; ABDELAZIZ AOUICHE

doi:10.59277/RRST-EE.2024.1.8

Auteurs

ABDELGHANI DJEDDI Department of Electrical Engineering, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria Author
TOUFIK AMIEUR Department of Electrical Engineering, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria Author https://orcid.org/0000-0003-0870-5446
FAREH HANNACHI Department of Management Sciences, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria Author https://orcid.org/0000-0002-8213-2757
SAMIR METATLA Department of Electrical Engineering, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria Author https://orcid.org/0000-0002-6944-7586
ABDELAZIZ AOUICHE Department of Management Sciences, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria Author https://orcid.org/0000-0003-1378-7941

DOI :

https://doi.org/10.59277/RRST-EE.2024.1.8

Mots-clés :

Système Takagi-Sugeno d'ordre fractionnaire, Variables de prémisse non mesurables, Observateur Thau-Luenberger, Stabilité asymptotique, Inégalités matricielles linéaires

Résumé

Dans cet article, nous présentons une nouvelle approche : un observateur flou d'ordre fractionnaire, une extension de l'observateur de Thau-Luenberger, spécifiquement conçu pour les systèmes non linéaires caractérisés par des modèles Takagi-Sugeno proportionnés d'ordre non entier. Ce travail apporte des contributions significatives dans deux domaines clés. Premièrement, les fonctions d'activation du modèle et de l'observateur flou d'ordre fractionnaire Lipschitz dépendent de variables non mesurables, en particulier de l'état du système. Deuxièmement, notre observateur flou proposé intègre explicitement les conditions initiales du système. Les conditions de stabilité de l'observateur flou d'ordre fractionnaire sont exprimées par des inégalités matricielles bilinéaires, qui sont ensuite converties en inégalités matricielles linéaires (IML). Par la suite, des simulations numériques sont effectuées pour démontrer l'efficacité de notre estimateur proposé.

Biographie de l'auteur

TOUFIK AMIEUR, Department of Electrical Engineering, Echahid Cheikh Larbi Tebessi University, Tebessa, Algeria

Toufik Amieur In 2009, he graduated (as Magister) in Automatic, at Biskra University, Algeria. In 2017, he received the Doctorate Degree in Electrical Engineering from University of Guelma, Algeria and, in 2019, he received the Habilitation Degree from Ouargla University, Algeria. He is currently an Associate Professor at Tebessa University, Algeria. His main research area includes Nonlinear Control, Robust and Fractional Order Control, Renewable Energy.

Références

(1) I. N'Doye, M. Darouach, M. Zasadzinski, Design of unknown input fractional-order observers for fractional–order systems, International Journal of Applied Mathematics and Computer Sciences, 23, 3, pp. 491–500 (2013).

(2) E.A. Boroujeni, M. Pourgholi, H.R. Momeni, Reduced Order Linear Fractional Order Observer, International Conference on Control Communication and Computing (ICCC) (2013)

(3) Y. Boukal, N.E. Radhy, M. Darouach, M. Zasadzinski, Design of full and reduced orders observers for linear fractional-order systems in the time and frequency domains, Proceedings of the 3rd International Conference on Systems and Control, Algiers, Algeria, October 29-31 (2013).

(4) A. Jmal, O. Naifar, N. Derbel, Unknown input observer design for fractional-order one-sided Lipschitz systems, 14th International Multi-Conference on Systems, Signals & Devices (SSD) (2017).

(5) E. Hildebrandt, J. Kersten, A. Rauh, H. Aschemann, robust interval observer design for fractional-order models with applications to state estimation of batteries, Preprints of the 21st IFAC World Congress (Virtual) Berlin, Germany, July 12-17 (2020).

(6) T. Yang, Multi-observer approach for estimation and control under adversarial attacks, Doctoral thesis, Department of Electrical and Electronic Engineering, The University of Melbourne (2019).

(7) K. Tanaka, T. Ikeda, H.O. Wang, Fuzzy regulators and fuzzy observers: relaxed stability conditions and LMI-based designs, IEEE Transactions on Fuzzy Systems, 6, 2, pp. 250-265 (1998).

(8) A. Akhenak, Design of nonlinear observers by multi-model approach: application to diagnosis. Doctoral Thesis, National Polytechnic Institute of Lorraine, December 16 (2004).

(9) A. Ahriche, I. Abdelhakim, M.Z. Doghmane, M. Kidouche, S. Mekhilef, Stability and accuracy improvement of motor current estimator in low-speed operating based on sliding mode Takagi-Sugeno algorithm, Rev. Roum. Sci. Techn.–Électrotechn. et Énerg., 67, 2, pp. 99–104, Bucarest (2022).

(10) R. Caponetto, G. Dongola, L. Fortuna, I. Petráš, Fractional order systems modeling and control applications, World Scientific Series on Nonlinear Science, Series A, 72 (2010).

(11) C. Weise, Applications of equivalent representations of fractional- and integer-order linear time-invariant systems, Dissertation, Geboren am 11. in Freiberg (1989).

(12) S.J. Ohrem, C. Holden, Controller and observer design for first order LTI systems with unknown dynamics, ICCMA, 12–14, Tokyo, Japan (2018).

(13) M. Azimi, H.T. Shandiz, Simultaneous fault detection and control design for robots with linear fractional-order model, Proceedings of the 6th RSI International Conference on Robotics and Mechatronics (IcRoM) October 23-25, Tehran, Iran (2018).

(14) N. Vafamanda, S. Khorshidi, A. Khayatiana, Secure communication for non-ideal channel via robust TS fuzzy observer-based hyperchaotic synchronization, Solitons, and Fractals, 112, pp. 116–124 (2018).

(15) S. Medjmadj, D. Diallo, A. Arias, Mechanical sensor fault-tolerant controller in PMSM drive: experimental evaluation of observers and signal injection for position estimation, Rev. Roum. Sci. Techn.– Électrotechn. et Énerg., 66, 2, pp.77–83, Bucarest (2021).

(16) T. Ma, B. Wang, Disturbance observer-based Takagi-Sugeno fuzzy control of a delay fractional-order hydraulic turbine governing system with elastic water hammer via frequency distributed model, Information Sciences, 569, pp. 766–785 (2021).

(17) A Djeddi, Y Soufi, S Chenikher, A Aouiche, Synthesis of unknown inputs PI and PMI observers for Takagi-Sugeno augmented models applied on a manipulator arm, Electrotehnica, Electronica, Automatica, 68, 1, pp. 89-97 (2020).

(18) L. Yu, Y. Bar-Shalom, X. Rong Li, Advanced State Estimation Techniques: Theory and Applications, Wiley-IEEE (2023).

(19) A.M.N. Kiss, Analyse et synthèse de multimodèles pour le diagnostic. Application à une station d’épuration, Thèse de Doctorat de l’Institut National Polytechnique de Lorraine, CRAN Nancy (2010).

(20) Q. Gong, V. I. Utkin, Nonlinear Observer Design: An Introduction, CRC (2022).

(21) G. Tao, J. Gräf, A. Bartoszewicz, Nonlinear Observers and Applications, Springer (2023).

(22) N.K. M'Sirdi, A. D. Cristea, Nonlinear Observer Design via Sliding Mode and High-Gain Techniques, Springer (2022).

(23) X. Rong Li, Y. Wang, Adaptive State Estimation for Nonlinear Systems: From Theory to Application, Wiley-IEEE (2023).

(24) J. Gräf, A. Bartoszewicz, G. Tao, Advanced Techniques for Nonlinear Observer Design: A Unified Framework, Springer (2023).

(25) N. K. M'Sirdi, A.D. Cristea, Nonlinear Sliding Mode Observers: From Theory to Applications, Springer (2022).

(26) G. Tao, L. Yu, Optimal Nonlinear Observers: From Theory to Application, CRC (2023).

(27) A. Djeddi, D. Dib, A.T. Azar, S. Abdelmalek, Fractional order unknown inputs fuzzy observer for Takagi–Sugeno systems with unmeasurable premise variables, Mathematics, 7, 984 (2019).

(28) Z. Gao, X. Liao, Observer-based fuzzy control for nonlinear fractional-order systems via fuzzy T-S models: The 1< <2 case, Proceedings of the 19th World Congress, The International Federation of Automatic Control Cape Town, South Africa. 24-29 (2014).

(29) D. Matignon, Generalized fractional differential and difference equations: stability properties and modelling issues, Proc. of the Math. Theory of Networks and Systems Symposium, Padova, Italy (1998).

(30) M. Caputo, Linear model of dissipation whose Q is almost frequency independent. Geophysical Journal International, 13, 5, pp. 529-539 (1967).

(31) I. Podlubny, Fractional Differential Equations, Mathematics in Science and Engineering. Academic Press, New York, NY, USA, p. 198, (1999).

(32) K. B. Oldham, J. Spanier, The Fractional Calculus, Academic Press, New York (1974).

(33) I. Petras, Fractional-order nonlinear systems: modeling, analysis and simulation, Series Nonlinear Physical Science, Springer, Heidelberg (2011).

(34) I. Chihi, L. Sidhom, E.N. Kamavuako, Hammerstein–Wiener multimodel approach for fast and efficient muscle force estimation from EMG signals, Biosensors (Basel), 12, 2, pp. 117 (2022).

(35) A. Djeddi, Diagnostic de Systèmes Non Linéaires par Observateurs, Thèse de doctorat en Automatique, Université Badji Mokhtar Annaba (2017).

SYNTHÈSE D'UN OBSERVATEUR FUZZY D'ORDRE FRACTIONNEL POUR UN MODÈLE DE TAKAGI-SUGENO D'ORDRE FRACTIONNEL AVEC DES VARIABLES DE PRÉMISE NON MESURABLES

Auteurs

DOI :

Mots-clés :

Résumé

Biographie de l'auteur

Références

Téléchargements

Publiée

Numéro

Rubrique

Licence

Comment citer

Langue

Informations