A fault estimation and fault-tolerant control based sliding mode observer for LPV descriptor systems with time delay

• Autorzy: Hamdi Habib , Rodrigues Mickael , Rabaoui Bouali , Benhadj Braiek Naceur

Identyfikatory

DOI

10.34768/amcs-2021-0017

• Języki publikacji: EN

Abstrakty

EN

This paper considers the problem of fault-tolerant control (FTC) and fault reconstruction of actuator faults for linear parameter varying (LPV) descriptor systems with time delay. A polytopic sliding mode observer (PSMO) is synthesized to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Exploiting the reconstructed actuator faults and state estimates, a fault-tolerant controller is designed to compensate the impact of actuator faults on system performance by stabilizing the closed-loop LPV delayed descriptor system. Besides, the controller and PSMO gains are obtained throughout the resolution of linear matrix inequalities (LMIs) using convex optimization techniques. The developed PSMO could force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. Simulation results applied to a given numerical system are presented to highlight the superiority and effectiveness of the proposed approach.

Słowa kluczowe

EN

fault estimation; fault-tolerant control; LPV descriptor system; sliding mode observer; time delay; LMIs; linear matrix inequalities

PL

estymacja błędu; sterowanie odporne na uszkodzenia; sterowanie ślizgowe; LMIs; liniowa nierówność macierzowa

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2021
• Tom: Vol. 31, no. 2
• Strony: 247--258
• Opis fizyczny: Bibliogr. 36 poz., wykr.

Twórcy

autor

Hamdi Habib

• Laboratory of Advanced Systems, Polytechnic School of Tunisia, Carthage University, BP 743, 2078 La Marsa, Tunisia

autor

Rodrigues Mickael

• Automation and Process Engineering Laboratory, Claude Bernard University Lyon 1, CNRS UMR 5007, CPE, 43 Boulevard du 11 Novembre 1918, F-69622 Villeurbanne cedex, France

autor

Rabaoui Bouali

• Laboratory of Advanced Systems, Polytechnic School of Tunisia, Carthage University, BP 743, 2078 La Marsa, Tunisia

autor

Benhadj Braiek Naceur

• Laboratory of Advanced Systems, Polytechnic School of Tunisia, Carthage University, BP 743, 2078 La Marsa, Tunisia

Bibliografia

• [1] Alwi, H., Edwards, C. and Marcos, A. (2012) Fault reconstruction using a LPV sliding mode observer for a class of LPV systems, Journal of the Franklin Institute 349(2): 510–530.
• [2] Ben Brahim, A., Dhahri, S., Ben Hmida, F. and Sellami, A. (2015). An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults, International Journal and Applied Mathematics and Computer Science 25(3): 547–559, DOI: 10.1515/amcs-2015-0041.
• [3] Ben Zina, H., Bouattour, M. and Chaabane, M. (2019). Robust Takagi–Sugeno sensor fault tolerant control strategy for nonlinear system, Iranian Journal of Fuzzy Systems 16(6): 177–189.
• [4] Briat, C. (2015). Introduction to LPV time-delay systems, in C. Briat, Linear Parameter-Varying and Time-Delay Systems, Springer, Berlin/Heidelberg, pp. 245–264.
• [5] Chandra, K.P.B., Alwi, H., and Edwards, C., (2017) Fault detection in uncertain LPV systems with imperfect scheduling parameter using sliding mode observers, European Journal of Control 34: 1–15.
• [6] Chen, L., Edwards, C. and Alwi, H., (2019) Sensor fault estimation using LPV sliding mode observers with erroneous scheduling parameters, Automatica 101: 66–77.
• [7] Chan, J.C.L., Tan, C.P., Trinh, H., Kamal, M.A.S. and Chiew, Y.S. (2019). Robust fault reconstruction for a class of non-infinitely observable descriptor systems using two sliding mode observers in cascade, Applied Mathematics and Computation 350: 78–92.
• [8] Chen, W. and Saif, M. (2006). An iterative learning observer for fault detection and accommodation in nonlinear time-delay systems, International Journal of Robust and Nonlinear Control 16(1): 1–19.
• [9] Dai, L. (1989) Singular Control Systems, Springer-Verlag, Berlin/New York.
• [10] Edwards, C., Spurgeon, S.K. and Patton, R.J. (2000). Sliding mode observers for fault detection and isolation, Automatica 1(36): 511–553.
• [11] Fen, W. (1995). Control of Parameter Varying Systems, PhD thesis, University of California, Berkeley.
• [12] Gomez-Penate, S., Valencia-Palomo, G., Lopez-Estrada, F.R., Astorga-Zaragoza, C.M., Osornio-Rios, R.A., Santos-Ruiz, I. (2019). Sensor fault diagnosis based on a H∞ sliding mode and unknown input observer for Takagi–Sugeno systems with uncertain premise variables, Asian Journal of Control 21(1): 339–353.
• [13] Gerland, P., Gross, D., Schulte, H. and Kroll, A. (2010) Design of sliding mode observers for TS fuzzy systems with application to disturbance and actuator fault estimation, 49th IEEE Conference on Decision and Control, Atlanta, USA, pp. 15–17.
• [14] Hamdi, H., Rodrigues, M., Mechmeche, C., Theilliol, D., BenHadj Braiek, N. (2012). Fault detection and isolation in linear parameter-varying descriptor systems via proportional integral observer, International Journal of Adaptive Control and Signal Processing 26(3): 224–240.
• [15] Halalchi, H., Bara, G.I., and Laroche, E. (2011). Observer-based controller synthesis for LPV descriptor systems using dilated LMI conditions, IEEE International Symposium on Computer-Aided Control System Design, Denver, USA, pp. 1044–1049.
• [16] Hamdi, H., Rodrigues, M., Mechmeche, C. and Benhadj Braiek, N. (2019). Fault diagnosis based on sliding mode observer for LPV descriptor systems, Asian Journal of Control 21(1): 89–98.
• [17] Hamdi, H., Rodrigues, M., Mechmeche, C. and Benhadj Braiek, N. (2018). Observer-based fault diagnosis for time-delay LPV descriptor systems, IFAC-PapersOnLine 51(24): 1179–1184.
• [18] Hassanabadi, A.H., Shafiee, M. and Puig, V. (2016). Robust fault detection of singular LPV systems with multiple time-varying delays, International Journal of Applied Mathematics and Computer Science 26(1): 45–61, DOI: 10.1515/amcs-2016-0004.
• [19] Jia, C., Liao, F. and Deng, J. (2019). Impulse elimination and fault-tolerant preview controller design for a class of descriptor systems, Mathematical Problems in Engineering 2019, Article ID: 3857275.
• [20] Jia, Q., Chen, W., Zhang, Y., and Li, H. (2015). Fault reconstruction and fault-tolerant control via learning observers in Takagi–Sugeno fuzzy descriptor systems with time delays, IEEE Transactions on Industrial Electronics 62(6): 3885–3895.
• [21] Lopez-Estrada, F.R., Rotondo, D., Valencia-Palomo, G. (2019). A review of convex approaches for control, observation and safety of linear parameter varying and Takagi–Sugeno systems, Processes 7(11), Article ID: 814.
• [22] Li, X. and Wang, J. (2020). Fault-tolerant tracking control for a class of nonlinear multi-agent systems, Systems and Control Letters 135: 104576.
• [23] Ooi, J.H.T., Tan, C.P., Nurzaman, S.G. and Ng, K.Y. (2017). A sliding mode observers for infinitely unobservable descriptor systems , IEEE Transactions on Automatic Control 62(7): 3580–3587.
• [24] Ooi, J.H.T., Tan, C.P. and Ng, K.Y. (2015). State and fault estimation for infinitely unobservable descriptor systems using sliding mode observers, Asian Journal of Control 17(4): 1458–1461.
• [25] Rodrigues, M., Hamdi, H., Theilliol, D., Mechmeche, C. and Benhadj Braiek, N. (2015). Actuator fault estimation based adaptive polytopic observer for a class of LPV descriptor systems, International Journal of Robust and Nonlinear Control 25(5): 673–688.
• [26] Rodrigues, M., Sahnoun, M., Theilliol, D. and Ponsart, J.C. (2013). Sensor fault detection and isolation filter for polytopic LPV systems: A winding machine application, Journal of Process Control 23(6): 805–816.
• [27] Rabaoui, B., Hamdi, H., BenHadj Braiek, N. and Rodrigues, M. (2020). A reconfigurable PID fault tolerant tracking controller design for LPV systems, ISA Transactions 98: 173–185.
• [28] Rabaoui, B., Rodrigues, M., Hamdi, H. and BenHadj Braiek, N. (2018). A model reference tracking based on an active fault tolerant control for LPV systems, International Journal of Adaptive Control and Signal Processing 32(6): 839–857.
• [29] Shi, F. and Patton, R.J. (2014). Fault estimation and active fault tolerant control for linear parameter varying descriptor systems, International Journal of Robust Nonlinear Control 25(5): 689–706, DOI: 10.1002/rnc.3266.
• [30] Stefanovski, J. and Juricic, D. (2020). Fault-tolerant control in presence of disturbances based on fault estimation, Systems and Control Letters 138: 104646.
• [31] Shahnazi, R. and Zhao, Q. (2016). Adaptive fuzzy descriptor sliding mode observer-based sensor fault estimation for uncertain nonlinear systems, Asian Journal of Control 18(4): 1478–1488.
• [32] Su, X., Wang, J., and Shi, H. (2018). Optimal fault-tolerant control against descriptor time-varying systems with nonlinear input, Mathematical Problems in Engineering 2018, Article ID: 4631371.
• [33] Tabatabaeipour, S.M. and Bak, T. (2013). Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems, Journal of the Franklin Institute 351(1): 277–295.
• [34] Yeu, T.K., Kim, H.S. and Kawaji, S. (2005). Fault detection, isolation and reconstruction for descriptor systems, Asian Journal of Control 7(4): 356–367.
• [35] Zhang, K., Jiang, B. and Shi, P.A. (2009). A new approach to observer-based fault-tolerant controller design for Takagi–Sugeno fuzzy systems with state delay, Circuits Systems and Signal Processing 28(5): 679–697.
• [36] Zhiqiang, Z., Daniel, W.C. Ho and Yijing, W. (2010). A Fault tolerant control for singular systems with actuator saturation and nonlinear perturbation, Automatica 46(3): 569–576.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).