Fault Diagnosis Operator in Linear Fractional Order Singular Systems Using Singular Observer and Unknown Input
الموضوعات :
F. PourDadashi Komachali
1
(Amirkabir University of Technology, Tehran, Iran.)
M. Shafiee
2
(Amirkabir University of Technology, Tehran, Iran.)
الکلمات المفتاحية: Fault diagnosis, noise separation, singular system, fractional order system, linear matrix inequality.,
ملخص المقالة :
The singular systems appear in many real occasions of system modeling. Fault occurrence is inevitable in real system; thus to avoid their destructive impacts, new design perspective must be taken. Performance and sensitivity of the fault diagnosis model based methods, however, significantly dependent on the accuracy of the model. In the one hand, it has been shown that many systems naturally follows the fractional order behavior, while on the other, in some scenarios, fractional modeling has improved the accuracy of the model. In this paper, we pay attention to the fault diagnosis in the fractional order singular systems. To this end, a singular observer with an unknown input has been used for diagnosis of the fault in the fractional order singular system, and the proposed observer convergence will be derived in the form of a linear matrix inequality. An advantage of the proposed method is separation of noise from the desired signal, both in inputs and outputs, using only the inputs and outputs signals.
[1] Duan, G.-R., D. Howe, and R.J. Patton, Robust fault detection in descriptor linear systems via generalized unknown input observers. International Journal of Systems Science, 2002. 33(5): p. 369-377.
[2] Dai, L., Singular control systems (Lecture notes in control and information sciences). 1989.
[3] Mirmomeni, M., et al., Forecasting sunspot numbers with the aid of fuzzy descriptor models. Space Weather, 2007. 5(8): p. 1-10.
[4] Razzaghi, M. and M. Shafiee, Optimal control of singular systems via Legendre series. International journal of computer mathematics, 1998. 70(2): p. 241-250.
[5] Zamani, I., M. Shafiee, and A. Ibeas, Switched nonlinear singular systems with time‐delay: Stability analysis. International Journal of Robust and Nonlinear Control, 2015: (10) 25, p. 1497-1513.
[6] Shafiee, M. and M. Razzaghi, On the solution of the covariance matrix differential equation for singular systems. International journal of computer mathematics, 1998. 68(3-4): p. 337-343.
[7] Shafiee, M. and P. Karimaghai. Optimal control for singular systems (Rectangular case). in Proc. of ICEE. 1997.
[8] Shafiee, M. and S. Amani, Optimal control for a class of singular systems using neural network. Iranian Journal of Science and Technology, Transaction B, Engineering, 2005. 29(B1(p. 33-48.
[9] Hassanabadi, A.H., M. Shafiee, and V. Puig, UIO design for singular delayed LPV systems with application to actuator fault detection and isolation. International Journal of Systems Science, 2016. 47(1): p. 107-121.
[10] Monje, C.A., et al., Fractional-order systems and controls: fundamentals and applications. 2010: Springer Science & Business Media.
[11] N’Doye, I., et al., Robust stabilization of uncertain descriptor fractional-order systems. Automatica, 2013. 49(6): p. 1907-1913.
[12] Liu, S., et al., Stability of fractional nonlinear singular systems and its applications in synchronization of complex dynamical networks. Nonlinear Dynamics, 2016. 84(4): p. 2377-2385.
[13] Nosrati, K. and M. Shafiee, Dynamic analysis of fractional-order singular Holling type-II predator–prey system. Applied Mathematics and Computation, 2017. 313: p. 159-179.
[14] Kaczorek, T., Reduced-order fractional descriptor observers for a class of fractional descriptor continuous-time nonlinear systems. International Journal of Applied Mathematics and Computer Science, 2016. 26(2): p. 277-283.
[15] Nosrati, K. and M. Shafiee, Kalman filtering for discrete-time linear fractional-order singular systems. IET Control Theory & Applications, 2018.
[16] Ashayeri, L., M. Shafiee, and M. Menhaj, Kalman filter for fractional order singular systems. J. Am. Sci, 2013. 9(1): p. 209-216.
[17] Hotzel, R. and M. Fliess, On linear systems with a fractional derivation: Introductory theory and examples. Mathematics and computers in Simulation, (4-3)45, 1998, p. 385-395
