A Fault Diagnosis in Non-Stationary Systems via Interval Observers
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Published
May 30, 2025
Alexey Zhirabok
Alexander Zuev
Abstract
The paper is devoted to the problem of fault diagnosis in technical systems described by non-stationary linear dynamic equations under unmatched disturbances and measurement noise via interval observers. The problem is to design the observer insensitive to the disturbances and having fewer dimension than that of the original system. Such an observer generates two (upper and lower) residuals such that if zero is between these residuals, then the faults in the system are absent; if zero is out of these residuals, one concludes that a fault has occurred. The interval observer consists of two subsystems: the first one generates the lower residual, the second one the upper residual. The relations describing both subsystems are given. Theoretical results are illustrated by practical example of the electric servoactuator for which the fault diagnosis problem is solved.
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Keywords
Fault diagnosis, non-stationary linear models, interval observers
References
Alives, J., Moreno, J., Davila, J., Becerra, G., Flores, F., Chavez, C., & Marquez, C. (2022). Stability radii-based interval observes for discrete-time nonlinear systems. IEEE Access, 10, 3216-3227.
Blesa, J., Rotondo, D., & Puig, V. (2014). Fdi and ftc of wind turbines using the interval observer approach and virtual actuators/sensors. Control Eng. Pract., 24, 138-155.
Chebotarev, S., Efimov, D., Räıssi, T., & Zolghadri, A. (2015). Interval observers for continous-time lpv systems with l1/l2 performance. Automatica, 58, 82-89.
Degue, K., Efimov, D., & Richard, J.-P. (2016). Interval observers for linear impulsive system. IFACPapersOnLine, 49-18, 867-872.
Dinh, T., Mazenc, F., & Niculescu, S. (2014). Interval observer composed of observers for nonlinear systems. In Proceedings of 2014 european control conference.
Edwards, C., Spurgeon, S.,&Patton, R. (2000). Sliding mode observers for fault detection and isolation. Automatica, 36, 541-553.
Efimov, D., Perruquetti, W., Räıssi, T., & Zolghadri, A. (2013). Interval observers for time-varying discrete-time systems. IEEE Trans. Automatic Control, 58(12), 3218-3224.
Efimov, D., Polyakov, A., & Richard, J.-P. (2015). Interval observer design for estimation and control of time-delay descriptor systems. European J. Control, 23(5), 26-35.
Efimov, D., & Räıssi, T. (2015). Design of interval state observers for uncertain dynamical systems. Autom. Remote Control, 72(2), 191-225.
Efimov, D., Räıssi, T., Chebotarev, S., & Zolghadri, A. (2013). Interval state observer for nonlinear time-varying systems. Automatica, 49, 200-206.
Khan, A., Xie,W., Zhang, B., & Liu, L.-W. (2021). A survey of interval observers design methods and implementation for uncertain systems. J. Franklin Institute, 358, 3077-3126.
Khan, A., Xie, W., Zhang, L., & Liu, L.-W. (2020). Design and applications of interval observers for uncertain dynamical systems. IET Circuits Devices Syst., 14(6), 721-740.
Kravaris, C., & Venkateswaran, S. (2021). Functional observers with linear error dynamics for nonlinear systems. Systems and Control Letters, 157, 105021.
Liu, L., Xie, W., Khan, A., & Zhang, L. (2021). Finite-time functional interval observer for linear systems with uncertainties. IET Control Theory and Appl., 14, 2868-2878.
Marouani, G., Dinh, T., Ra¨ıssi, T., Wang, X., & H., M. (2021). Unknown input interval observers for discrete-time linear switched systems. European J. Control, 59, 165-174.
Mazenc, F., & Bernard, O. (2011). Interval observers for linear time-invariant systems with disturbances. Automatica, 47(1), 140-147.
Mazenc, F., Dinh, T., & Niculescu, S. (2014). Interval observers for discrete-time systems. Inter. J. Robust and Nonlinear Control, 24, 2867-2890.
Räıssi, T., Efimov, D., & Zolghadri, A. (2012). Interval state estimation for a class of nonlinear systems. IEEE Trans. Automatic Control, 57(1), 260-265.
Rotondo, D., Fernandez-Canti, R., Tornil-Sin, S., Blesa, J., & Puig, V. (2016). Robust fault diagnosis of proton exchange membrane fuel cells using a takagi-sugeno interval observer approach. Int. J. Hydrog. Energy, 41, 2875-2886.
Yi, Z., Xie, W., Khan, A., & Xu, B. (2020). Fault detection and diagnosis for a class of linear time-varying discrete-time uncertain systems using interval observers. In Proceedings of 39th chinese control conference.
Zhang, Z.-H., & Yang, G.-H. (2017a). Fault detection for discrete-time lpv systems using interval observers. Int. J. Systems Science, 48, 1-15.
Zhang, Z.-H., & Yang, G.-H. (2017b). Interval observer-based fault isolation for discrete-time fuzzy interconnected systems with unknown interconnections. IEEE Trans. on Cybernetics, 47, 2413-2424.
Zhirabok, A., Shumsky, A., Solyanik, S., & Suvorov, A. (2017). Design of nonlinear robust diagnostic observers. Autom. Remote Control, 78(9), 1572-1584.
Zhirabok, A., Zuev, A., & Kim, C. (2022). Method to design interval observers for linear time-invariant systems. J. Comput. Systems Sciences Int., 61(5), 485-495.
Zhirabok, A., Zuev, A., & Shumsky, A. (2024). Interval observer design for fault diagnosis. IFAC-PapersOnLine, 58(4), 688-692.
Blesa, J., Rotondo, D., & Puig, V. (2014). Fdi and ftc of wind turbines using the interval observer approach and virtual actuators/sensors. Control Eng. Pract., 24, 138-155.
Chebotarev, S., Efimov, D., Räıssi, T., & Zolghadri, A. (2015). Interval observers for continous-time lpv systems with l1/l2 performance. Automatica, 58, 82-89.
Degue, K., Efimov, D., & Richard, J.-P. (2016). Interval observers for linear impulsive system. IFACPapersOnLine, 49-18, 867-872.
Dinh, T., Mazenc, F., & Niculescu, S. (2014). Interval observer composed of observers for nonlinear systems. In Proceedings of 2014 european control conference.
Edwards, C., Spurgeon, S.,&Patton, R. (2000). Sliding mode observers for fault detection and isolation. Automatica, 36, 541-553.
Efimov, D., Perruquetti, W., Räıssi, T., & Zolghadri, A. (2013). Interval observers for time-varying discrete-time systems. IEEE Trans. Automatic Control, 58(12), 3218-3224.
Efimov, D., Polyakov, A., & Richard, J.-P. (2015). Interval observer design for estimation and control of time-delay descriptor systems. European J. Control, 23(5), 26-35.
Efimov, D., & Räıssi, T. (2015). Design of interval state observers for uncertain dynamical systems. Autom. Remote Control, 72(2), 191-225.
Efimov, D., Räıssi, T., Chebotarev, S., & Zolghadri, A. (2013). Interval state observer for nonlinear time-varying systems. Automatica, 49, 200-206.
Khan, A., Xie,W., Zhang, B., & Liu, L.-W. (2021). A survey of interval observers design methods and implementation for uncertain systems. J. Franklin Institute, 358, 3077-3126.
Khan, A., Xie, W., Zhang, L., & Liu, L.-W. (2020). Design and applications of interval observers for uncertain dynamical systems. IET Circuits Devices Syst., 14(6), 721-740.
Kravaris, C., & Venkateswaran, S. (2021). Functional observers with linear error dynamics for nonlinear systems. Systems and Control Letters, 157, 105021.
Liu, L., Xie, W., Khan, A., & Zhang, L. (2021). Finite-time functional interval observer for linear systems with uncertainties. IET Control Theory and Appl., 14, 2868-2878.
Marouani, G., Dinh, T., Ra¨ıssi, T., Wang, X., & H., M. (2021). Unknown input interval observers for discrete-time linear switched systems. European J. Control, 59, 165-174.
Mazenc, F., & Bernard, O. (2011). Interval observers for linear time-invariant systems with disturbances. Automatica, 47(1), 140-147.
Mazenc, F., Dinh, T., & Niculescu, S. (2014). Interval observers for discrete-time systems. Inter. J. Robust and Nonlinear Control, 24, 2867-2890.
Räıssi, T., Efimov, D., & Zolghadri, A. (2012). Interval state estimation for a class of nonlinear systems. IEEE Trans. Automatic Control, 57(1), 260-265.
Rotondo, D., Fernandez-Canti, R., Tornil-Sin, S., Blesa, J., & Puig, V. (2016). Robust fault diagnosis of proton exchange membrane fuel cells using a takagi-sugeno interval observer approach. Int. J. Hydrog. Energy, 41, 2875-2886.
Yi, Z., Xie, W., Khan, A., & Xu, B. (2020). Fault detection and diagnosis for a class of linear time-varying discrete-time uncertain systems using interval observers. In Proceedings of 39th chinese control conference.
Zhang, Z.-H., & Yang, G.-H. (2017a). Fault detection for discrete-time lpv systems using interval observers. Int. J. Systems Science, 48, 1-15.
Zhang, Z.-H., & Yang, G.-H. (2017b). Interval observer-based fault isolation for discrete-time fuzzy interconnected systems with unknown interconnections. IEEE Trans. on Cybernetics, 47, 2413-2424.
Zhirabok, A., Shumsky, A., Solyanik, S., & Suvorov, A. (2017). Design of nonlinear robust diagnostic observers. Autom. Remote Control, 78(9), 1572-1584.
Zhirabok, A., Zuev, A., & Kim, C. (2022). Method to design interval observers for linear time-invariant systems. J. Comput. Systems Sciences Int., 61(5), 485-495.
Zhirabok, A., Zuev, A., & Shumsky, A. (2024). Interval observer design for fault diagnosis. IFAC-PapersOnLine, 58(4), 688-692.
Section
Technical Papers