Abstract
This paper investigates the fault detection and isolation (FDI) problem for discrete-time linear repetitive processes using a geometric approach, starting from a 2-D model for these processes that incorporates a representation of the failure. Based on this model, the FDI problem is formulated in the geometric setting and sufficient conditions for solvability of this problem are given. Moreover, the processes’s behaviour in the presence of noise is considered, leading to the development of a statistical approach for determining a decision threshold. Finally, a FDI procedure is developed based on an asymptotic observer reconstruction of the state vector.
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Azevedo-Perdicoulis, T. P., Jank, G., & Lopes dos Santos, P. (2013). The good behaviour of the gas network: Boundary control, observability and stability. In Proceedings of the 8th international workshop on multidimentional systems, Vol. 8, pp. 1–6, September 2013.
Basile, G., & Marro, G. GA toolbox for use with MATLAB. MATH Works Inc. Retrived from http://www3.deis.unibo.it/Staff/FullProf/GiovanniMarro/geometric.htm
Basile, G., & Marro, G. (1969a). Controlled and conditioned invariant subspaces in linear system theory. Journal of Optimization Theory and Applications, 3(5), 306–315.
Basile, G., & Marro, G. (1969b). On the observability of linear time-invariant systems with unknown inputs. Journal of Optimization Theory and Applications, 3(6), 410–415.
Basile, G., & Marro, G. (1992). Controlled and conditioned invariants in linear system theory. Englewood Cliffs: Prentice-Hall.
Beard, R. V. (1971). Failure accommodation in linear systems through self-reorganisation. Ph.D dissertation, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology
Bochniak, J., Galkowski, K., Rogers, E., & Kummert, A. (2007). Control law design for switched repetitive processes with a metal rolling example. IEEE International Conference on Control Applications, 1(3), 700–705.
Boyd, S., Ghaoul, L., Feron, E., & Balakrishnan, V. (1994). Linear matrix inequalities in system and control theory. Philadelphia: SIAM.
Cichy, B., Galkowski, K., & Rogers, E. (2014). 2D systems based robust iterative learning control using noncausal finite-time interval. Systems and Control Letters, 64, 36–42.
Emami-Naeini, A., Akhter, M. M., & Rock, S.M. (1985). Robust detection, isolation, and accommodation for sensor failures. American Control Conference, pp. 1129–1134.
Fernando, K. (1986). Conditions for internal stability of 2D systems. Systems and Control Letters, 7(3), 183–187.
Fornasini, E., & Marchesini, G. (1978). Doubly-indexed dynamical systems: State-space models and structural properties. Mathematical Systems Theory, 12(1), 59–72.
Fornasini, E., & Marchesini, G. (1980). Stability analysis of 2D systems. IEEE Transactions on Electronics, Circuits and Systems, 27, 1210–1217.
Frank, Pl M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy - a survey and some new results. Automatica, 26, 459–474.
Galkowski, K., Lam, J., Xu, S., & Lin, Z. (2003). Lmi approach to state-feedback stabilization of multidimensional systems. International Journal of Control, 76(14), 1428–1436.
Hashemi, A. & Pisu, P. (2011). Adaptive threshold-based fault detection and isolation for automotive electrical systems. WCICA, pp. 1013–1018.
Hwang, I., Kim, S., & Chze Eng, S. (2010). A survey of fault detection, isolation, and reconfiguration methods. IEEE Transactions on Control Systems Technology, 18(3), 636–653.
Jones, H. L. (1973). Failure detection in linear system. Ph. D dissertation, Department Aeronautics and Astronautics, Massachusetts Institute of Technology.
Kar, H., & Singh, V. (2003). Stability of 2D systems described by the Fornasini-Marchesini first model. IEEE Transactions on Signal Processing, 51(6), 1675–1676.
Ma, S., Papadopoulos, D., Gunopulos, D., & Domeniconi, C. (2004). Subspace clustering of high dimensional data. In Proceedings of the 2004 SIAM international conference on data mining, pp. 517–521.
Maleki, S., Rapisarda, P., Ntogramatzidis, L., & Rogers, E. (2015). Fault detection and isolation in 3d linear systems. Multidimensional Systems and Signal Processing, 26, 481–502.
Massoumnia, M. A. (1986). A geometric approach to the synthesis of failure detection filters. IEEE Transactions on Automatic Control, 31, 839–849.
Ntogramatzidis, L., & Cantoni, M. (2012). Detectability subspaces and observer synthesis for two-dimensional systems. Multidimensional Systems and Signal Processing, 23(1–2), 79–96.
Owens, D. H., Amann, N., Rogers, E., & French, M. (2000). Analysis of linear iterative learning control schemes—a 2D systems/repetitive processes approach. Multidimensional Systems and Signal Processing, 11(11), 125–177.
Roberts, P. D. (2002). Two-dimensional analysis of an iterative nonlinear optimal control algorithm. IEEE Transactions on Circuits Systems I: Fundamental Theory and Applications, 49, 872–878.
Rogers, E., & Owens, D. H. (1992). Stability analysis for linear repetitive processes, Vol. 175. Lecture Notes in Control and Information Sciences. Berlin, Germany: Springer.
Rogers, E., Galkowski, K., & Owens, D. H. (2007). Control systems theory and applications for linear repetitive processes. Berlin: Springer.
Willsky, A. S. (1976). A survey of design methods for failure detection in dynamic systems. Automatica, 12, 601–611.
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Maleki, S., Rapisarda, P. & Rogers, E. Failure identification for linear repetitive processes. Multidim Syst Sign Process 26, 1037–1059 (2015). https://doi.org/10.1007/s11045-015-0345-4
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DOI: https://doi.org/10.1007/s11045-015-0345-4