Discrete-time Takagi-Sugeno singular systems with unmeasurable decision variables: state and fault fuzzy observer design

• Autorzy: Aitdaraou Khaoula , Essabre Mohamed , El Assoudi Abdellatif , El Yaagoubi El Hassane

Identyfikatory

DOI

10.24425/acs.2023.146278

• Języki publikacji: EN

Abstrakty

EN

The studied problem in this paper, treat the issue of state and fault estimation using a fuzzy observer in the case of unmeasurable decision variable for Discrete-Time Takagi-Sugeno Singular Sytems (DTSSS). First, an augmented system is introduced to gather state and fault into a single vector, then on the basis of Singular Value Decomposition (SVD) approach, this observer is designed in explicit form to estimate both of state and fault of a nonlinear singular system. The exponential stability of this observer is studied using Lyapunov theory and the convergence conditions are solved with Linear Matrix Inequalities (LMIs). Finally a numerical example is simulated, and results are given to validate the offered approach.

Słowa kluczowe

EN

observer design; unmeasurable decision variable; SVD approach; Lyapunov function; LMIs

• Wydawca: Polish Academy of Sciences, Committee of Automatic Control and Robotics
• Czasopismo: Archives of Control Sciences
• Rocznik: 2023
• Tom: Vol. 33, No. 2
• Strony: 321--338
• Opis fizyczny: Bibliogr. 33 poz., rys., wzory

Twórcy

autor

Aitdaraou Khaoula

• Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
• ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco

autor

Essabre Mohamed

• Laboratory of Materials, Energy and Control Systems, Faculty of Sciences and Technologies Mohammedia, Hassan II University of Casablanca, Morocco

autor

El Assoudi Abdellatif

• Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
• ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco

autor

El Yaagoubi El Hassane

• Laboratory of High Energy Physics and Condensed Matter, Faculty of Science, Hassan II University of Casablanca, B.P 5366, Maarif Casablanca, Morocco
• ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis Casablanca, Morocco

Bibliografia

• [1] P.H. Wu and C.H. Kuo: The design and implementation of a remote automatic control laboratory: Using PID control as an example. Tamkang Journal of Science and Engineering, 11(2), (2008), 219-228. DOI: 10.6180/jase.2008.11.2.14.
• [2] Q. Zhang, Y. Hu, A. Wang and N. Jiang: Nonlinear adaptive control algorithm based on dynamic surface control and neural networks for ship course-keeping controller. Journal of Applied Science and Engineering, 20(2), (2017), 157-163. DOI: 10.6180/jase.2017.20.2.03.
• [3] S. Guo, F. Zhu, W. Zhang, S. H. Zak and J. Zhang: Fault detection and reconstruction for discrete nonlinear systems via Takagi-Sugeno fuzzy models. International Journal of Control, Automation and Systems, 16(4), (2018), 2676-2687. DOI: 10.1007/s12555-017-0582-4.
• [4] Y. Wang, D. Rotondo, V. Puig and G. Cembrano: Fault-tolerant control based on virtual actuator and sensor for discrete-time descriptor systems. IEEE Transactions on Circuits and Systems, 67(12), (2020), 5316-5325. DOI: 10.1109/TCSI.2020.3015887.
• [5] A. Zhirabok, A. Zuev, V. Filaretov and A. Shumsky: Sliding mode observers for fault identification in linear systems not satisfying matching and minimum phase conditions. Archives of Control Sciences, 31(2), (2021), 253-266. DOI: 10.24425/acs.2021.137417.
• [6] R.B. Kumar, P. Suresh and V.S. Hemakumar: Automated anesthesia level controller using fuzzy logic for injectable type. Journal of Applied Science and Engineering, 24(5), (2021), 749-755. DOI: 10.6180/jase.20211024(5).0009.
• [7] G. Zheng and F.J. Bejarano: Observer design for linear singular time-delay systems. Automatica, 80 (2017), 1-9. DOI: 10.1016/j.automatica.2017.01.025.
• [8] X.T. Wang and H.H. Yu: Generalized PI observer design for descriptor linear system. Archives of Control Sciences, 29(4), (2019), 585-601. DOI: 10.24425/acs.2019.131227.
• [9] J. Zhang, M. Chadli and F. Zhu: Finite-time observer design for singular systems subject to unknown inputs. The Institution of Engineering and Technology, IET Control Theory & Applications, 13(14), (2019), 2289-2299. DOI: 10.1049/iet-cta.2018.6038.
• [10] A.T. Nguyen, V. Campos, T.M. Guerra, J. Pan and W. Xie: Takagi-Sugeno fuzzy observer design for nonlinear descriptor systems with unmeasured premise variables and unknown inputs. International Journal of Robust and Nonlinear Control, 31(17), (2021), 8353-8372. DOI: 10.1002/rnc.5453.
• [11] C.M.A. Zaragoza, D. Theilliol, J.C. Ponsart and M. Rodrigues: Fault diagnosis for a class of descriptor linear parameter-varying systems. International Journal of Adaptive Control and Signal Processing, 26(3), (2012), 208-223. DOI: 10.1002/acs.1259.
• [12] Z. Wang, M. Rodrigues, D. Theilliol and Y. Shen: Fault estimation filter design for discrete-time descriptor systems. IET Control Theory Applications, 9(10), (2015), 1587-1594. DOI: 10.1049/iet-cta.2014.0641.
• [13] W. Han, Z. Wang, Y. Shen and Y. Liu: 𝐻𝐿1 fault detection for linear discrete-time descriptor systems. The Institution of Engineering and Technology, IET Control Theory & Applications, 12(15), (2018), 2156-2163. DOI: 10.1049/iet-cta.2017.1408.
• [14] T. Kaczorek: Observers of fractional linear continuous-time systems. Archives of Control Sciences, 32(1), (2022), 73-84. DOI: 10.24425/acs.2022.140865.
• [15] L. Moysis, M. Tripathi, M.K. Gupta, M. Marwan and C. Volos: Adaptive observer design for systems with incremental quadratic constraints and nonlinear outputs: application to chaos synchronization. Archives of Control Sciences, 32(1), (2022), 105-121. DOI: 10.24425/acs.2022.140867.
• [16] V. Novak, I. Perfilieva and A. Dvorak: What is Fuzzy Modeling. Insight into Fuzzy Modeling. Wiley Online Library, First Edition, 2016, 3-10. DOI: 10.1002/9781119193210.ch1.
• [17] J. Soulami, A. El Assoudi, M. Essabre, M. Habibi and E. El Yaagoubi: Observer design for a class of nonlinear descriptor systems: A Takagi-Sugeno approach with unmeasurable premise variables. Journal of Control Science and Engineering, 2015 (2015), 1-10. DOI: 10.1155/2015/636909.
• [18] V.E. Manzo, Zs. Lendek and T.M. Guerra: An alternative LMI static output feedback control design for discrete-time nonlinear systems represented by Takagi-Sugeno models. ISA Transactions, 84 (2019), 104-110. DOI: 10.1016/j.isatra.2018.08.025.
• [19] I. Hmaiddouch, M. Essabre, A. El Assoudi, J. Soulami and E. El Yaagoubi: Observer design for a class of discrete-time Takagi-Sugeno models with unmeasurable premise variables: Application to an asynchronous motor. International Conference on Intelligent Systems and Computer Vision(ISCV), (2020), 1-6. DOI: 10.1109/ISCV49265.2020.9204333.
• [20] F. Delmotte, M.A. Hammani and N.E. Rettab: On the state estimation for nonlinear continuous-time fuzzy systems. Archives of Control Sciences, 32(1), (2022), 57-72. DOI: 10.24425/acs.2022.140864.
• [21] A. Louzimi, A. El Assoudi, J. Soulami and E. El Yaagoubi: Observer design for a class of discrete-time Takagi-Sugeno implicit models subject to unknown inputs. American Journal of Computational and Applied Mathematics, 7(4), (2017), 115-122. DOI: 10.5923/j.ajcam.20170704.03.
• [22] M. Essabre, E.M. El Bouatmani, J. Soulami, A. El Assoudi and E. El Yaagoubi: Unknown input observer design for a class of discretetime Takagi-Sugeno implicit systems. International Conference on Control, Automation and Diagnosis, (ICCAD), (2018), 1-6. DOI: 10.1109/CA-DIAG.2018.8751310.
• [23] K. Bouassem, E. El Bouatmani, A. El Assoudi and E. El Yaagoubi: State and unknown input simultaneous estimation for a class of discrete time linear implicit models: A heat exchanger pilot process application. E3S Web of Conferences, The 4th International Conference of Computer Science and Renewable Energies (ICCSRE’2021), 297 (2021), 1-6. DOI:10.1051/e3sconf/202129701011.
• [24] M. Ouzaz, A. El Assoudi, J. Soulami and E. El Yaagoubi: Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints. International Journal of Optimization and Control: Theories & Applications (IJOCTA), 11(1), (2021), 100-108. DOI: 10.11121/ijocta.01.2021.00877.
• [25] K. Ouarid, A. El Assoudi, J. Soulami and E. El Yaagoubi: Observer design for simultaneous state and fault estimation for a class of discrete-time descriptor linear models. E3S Web of Conferences, The 3rd International Conference of Computer Science and Renewable Energies (ICCSRE’2020), 229 (2021), 1-6. DOI: 10.1051/e3sconf/202122901020.
• [26] S.G. Penate, F.R.L. Estrada, G.V. Palomo, D. Rotondo and M.E.G. Sanchez: Actuator and sensor fault estimation based on a proportional multipleintegral sliding mode observer for linear parameter varying systems with inexact scheduling parameters. International Journal of Robust and Non-linear Control, 31(17), (2020), 8420-8441. DOI: 10.1002/rnc.5371.
• [27] J. Guzman, F.R.L. Estrada, V.E. Manzo and G.V. Palomo: Actuator fault estimation based on a proportional-integral observer with nonquadratic Lyapunov functions. International Journal of Systems Science, 52(9), (2021), 1938-1951. DOI: 10.1080/00207721.2021.1873451.
• [28] R. Yang, D. Rotondo and V. Puig: Observer-based model reference control of Takagi-Sugeno-Lipschitz systems affected by disturbances using quadratic boundedness. Asian Journal of Control, 23(1), (2021), 42-56. DOI: 10.1002/asjc.2391.
• [29] N. Karmarkar: A new polynomial time algorithm for linear programming. Combinatorica, 4 (1984), 373-395. DOI: 10.1007/BF02579150.
• [30] M.J. Todd: An extension of Karmarkar’s algorithm for linear programming using dual variables. Algorithmica, 1 (1986), 409-424. DOI: 10.1007/bf01840455.
• [31] Y. Nesterov and A. Nemirovskii: Interior-Point Polynomial Algorithms in Convex Programming. SIAM Studies in Applied and Numerical Mathematics, 1994. DOI: 10.1137/1.9781611970791.
• [32] J.G. VanAntwerp and R.D. Braatz: A tutorial on linear and bilinear matrix inequalities. Journal of Process Control, 10(4), (2000), 363-385. DOI: 10.1016/S0959-1524(99)00056-6.
• [33] F.R.L. Estrada, C.M.A. Zaragoza, D. Theilliol, J.C. Ponsart, G.V. Palomo and L. Torres: Observer synthesis for a class of Takagi-Sugeno descriptor system with unmeasurable premise variable. Application to fault diagnosis. International Journal of Systems Science, 48(16), (2017), 3419-3430. DOI: 10.1080/00207721.2017.1384517.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2024).