1. bookVolume 31 (2021): Issue 2 (June 2021)
Journal Details
License
Format
Journal
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
access type Open Access

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

Published Online: 08 Jul 2021
Page range: 247 - 258
Received: 18 Aug 2020
Accepted: 28 Jan 2021
Journal Details
License
Format
Journal
First Published
05 Apr 2007
Publication timeframe
4 times per year
Languages
English
Abstract

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.

Keywords

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

Chen, L., Edwards, C. and Alwi, H., (2019) Sensor fault estimation using LPV sliding mode observers with erroneous scheduling parameters, Automatica 101: 66–77. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

Dai, L. (1989) Singular Control Systems, Springer-Verlag, Berlin/New York. Search in Google Scholar

Edwards, C., Spurgeon, S.K. and Patton, R.J. (2000). Sliding mode observers for fault detection and isolation, Automatica 1(36): 511–553. Search in Google Scholar

Fen, W. (1995). Control of Parameter Varying Systems, PhD thesis, University of California, Berkeley. Search in Google Scholar

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. Search in Google Scholar

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 Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

Li, X. and Wang, J. (2020). Fault-tolerant tracking control for a class of nonlinear multi-agent systems, Systems and Control Letters 135: 104576. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

Stefanovski, J. and Juricic, D. (2020). Fault-tolerant control in presence of disturbances based on fault estimation, Systems and Control Letters 138: 104646. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

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. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo