Abstract
This paper presents an approach to diagnose faults on systems with Descriptor Takagi–Sugeno representation. This approach is focused on simultaneously estimate states and actuator faults. Not only the estimation algorithm is designed to estimate actuator time-varying faults, but also it is useful for abrupt faults. The observer considered has additional degrees of freedom to estimate, and it is called as generalized observer, where the proportional and proportional-integral observers are particular cases. The convergence analysis is given through the Lyapunov approach. A continuous stirred tank reactor is used as a case study to evaluate the capabilities of the observer.
Similar content being viewed by others
References
Krokavec, D., Filasová, A.: Design of PD observer-based fault estimator for a class of takagi-sugeno descriptor systems. IFAC-PapersOnLine, pp. 754–759 (2015). https://doi.org/10.1016/j.ifacol.2015.09.280
Hamdi, H., Rodrigues, M., Mechmeche, C., Braiek, N.B.: Robust fault detection and estimation for descriptor systems based on multi-models concept. Int. J. Control Autom. Syst. 6(10), 1260–1266 (2012). https://doi.org/10.1007/s12555-012-0622-z
Osorio-Gordillo, G.-L., Astorga-Zaragoza, C.-M., Pérez-Estrada, A.-J., Vargas-Méndez, R.-A., Darouach, M., Boutat-Baddas, L.: Fault estimation for descriptor linear systems based on the generalised dynamic observer. Int. J. Syst. Sci. 9, 2398–2409 (2018). https://doi.org/10.1080/00207721.2018.1503357
Jia, Q., Chen, W., Zhang, Y., Li, H.: Fault reconstruction and fault-tolerant control via learning observers in Takagi–Sugeno fuzzy descriptor systems with time delays. IEEE Trans. Ind. Electron. 62(6), 3885–3895 (2015). https://doi.org/10.1109/TIE.2015.2404784
Shaker, M.S.: A Robust adaptive observer-based time varying fault estimation. Amirkabir Int. J. Model. Identif. Simul. Control 47(2), 11–19 (2015). https://doi.org/10.22060/MISCJ.2015.566
Sun, K., Mou, S., Qiu, J., Wang, T., Gao, H.: Adaptive fuzzy control for nontriangular structural atochastic switched nonlinear systems with full state constraints. IEEE Trans. Fuzzy Syst. 27(8), 1587–1601 (2018). https://doi.org/10.1109/TFUZZ.2018.2883374
Kong, F., Zhu, Q., Huang, T.: Application to the discontinuous fuzzy inertial neural networks. IEEE Trans. Fuzzy Syst. 29, 3711–3722 (2021)
Qiu, J., Sun, K., Wang, T., Gao, H.: Observer-based fuzzy adaptive event-triggered control for pure-feedback nonlinear systems with prescribed performance. IEEE Trans. Fuzzy Syst. (2019). https://doi.org/10.1109/TFUZZ.2019.2895560
Li, J., Zhou, S., Xu, S.: Fuzzy control system design via fuzzy lyapunov functions. IEEE Trans. Syst. Man Cybernet. B 38(6), 1657–1661 (2008). https://doi.org/10.1109/TSMCB.2008.928224
Kong, F., Rajan, R.: Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen–Grossberg neural networks with uncertain external perturbations and mixed time delays. Fuzzy Sets Syst. 411, 105–135 (2021). https://doi.org/10.1016/j.fss.2020.07.009
Kong, F., Zhu, Q., Sakthivel, R.: Finite-time and fixed-time synchronization control of discontinuous fuzzy Cohen–Grossberg neural networks. Fuzzy Sets Syst. 394, 87–109 (2020). https://doi.org/10.1016/j.fss.2019.12.002
Luenberger, D.G.: Dynamic equations in descriptor form. IEEE Trans. Automat. Control AC-22, 312–321 (1977). https://doi.org/10.1109/TAC.1977.1101502
Araujo, J.M., Barros, P.R., Dorea, C.E.T.: Design of observers with error limitation in discrete-time descriptor systems: a case study of a hydraulic tank system. IEEE Trans. Control Syst. Technol. 20, 1041–1047 (2012). https://doi.org/10.1109/TCST.2011.2159719
Boulkroune, B., Darouach, M., Zasadzinski, M., Gillé, S., Fiorelli, D.: A nonlinear observer design for an activated sludge wastewater treatment process. J. Process Control 19, 1558–1565 (2009). https://doi.org/10.1109/ACC.2009.5160499
Boutayeb, M., Darouach, M.: Observers Design for Non Linear Descriptor Systems. In: Procees. of IEEE Conf. Decis. and Control, New Orleand, LA, pp. 2369–2374 (1995). https://doi.org/10.1109/CDC.1995.480692
Fridman, E., Shaked, U.: A descriptor system approach to \({H}_\infty \) control of linear time-delay systems. IEEE Trans. Automat. Control 47, 253–270 (2002). https://doi.org/10.1109/9.983353
Liu, P., Zhang, E., Yang, X., Yang, L.: Passivity and optimal control of descriptor biological complex systems. IEEE Trans. Automat. Control 53, 122–125 (2008). https://doi.org/10.1109/TAC.2007.911341
Osorio-Gordillo, G.L., Darouach, M., Astorga-Zaragoza, C.M., Boutat-Baddas, L.: New dynamical observers design for linear descriptor systems. IET Control Theory Appl. 10(17), 2223–2232 (2016). https://doi.org/10.1049/iet-cta.2016.0431
Osorio-Gordillo, G.L., Darouach, M., Astorga-Zaragoza, C.M.: \({H}_\infty \) dynamical observers design for linear descriptor systems. application to state and unknown input estimation. Eur. J. Control, 35–43 (2015). https://doi.org/10.1016/j.ejcon.2015.07.001
Müller, P.C.: Modelling and control of mechatronic systems by the descriptor approach. J. Theoretic. Appl. Mech. 43, 593–607 (2005)
Rajiv, C.: Model predictive control of high-index DAE systems without index reduction. PhD thesis, COPPE UFRJ (2019)
Taniguchi, T., Tanaka, K., Yamafuji, K., Wang, H.O.: Fuzzy Descriptor systems: satability analysis and design via LMIs. In: Am. Control Conf. (ACC), San Diego, USA, pp. 1827–1831 (1999). https://doi.org/10.1109/ACC.1999.786165
Taniguch, T., Tanaka, K., Wang, H.O.: Fuzzy descriptor systems and nonlinear model following control. IEEE Trans. Fuzzy Syst. 8, 442–452 (2000). https://doi.org/10.1109/91.868950
Yoneyama, J., Ichikawa, I.: \({H}_\infty \) control for Takagi Sugeno descriptor systems. In: IEEE Int. Conf. on Syst., Man, and Cybernetics, Tokio, Japan, pp. 28–33 (1999)
Skelton, R.E., Iwasaki, T., Grigoriadis, K.: A Unified Algebraic Approach to Linear Control Design. Taylor & Francis, London (1998)
Lendek, Z., Guerra, T.M., Babuska, R., De Schutter, B.: Stability Analysis and Nonlinear Observer Design Using Takagi–Sugeno Fuzzy Models. Springer, Berlin (2011)
Pérez-Estrada, A.J., Osorio-Gordillo, G.L., Darouach, M., Alma, M.: Adaptive observer design for LPV systems. IFAC-PapersOnLine 52(28), 140–145 (2019). https://doi.org/10.1016/j.ifacol.2019.12.361
Boukas, E.K.: Control of Singular Systems with Random Abrupt Changes. Springer, Berlin, Heidelberg (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Osorio-Gordillo, GL., Mujica-Campos, VE., Vargas-Méndez, RA. et al. Descriptor Takagi-Sugeno Approach Used to Diagnose Faults on a CSTR Reactor. Int. J. Fuzzy Syst. 24, 3469–3482 (2022). https://doi.org/10.1007/s40815-022-01340-w
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40815-022-01340-w