access icon free Unbiased inversion-based fault estimation of systems with non-minimum phase fault-to-output dynamics

© The Institution of Engineering and Technology
Received 04/11/2018, Accepted 08/04/2019, Revised 12/02/2019, Published 16/04/2019

In this study, the authors propose a framework for inversion-based estimation of certain categories of faults in discrete-time linear systems. The fault signal, as an unknown input, is reconstructed from its projections onto two subspaces. The first projection is achieved through an algebraic operation, whereas the second projection is obtained by a dynamic filter whose poles coincide with the transmission zeros of the system. Feedback is then introduced to stabilise this filter as well as to provide an unbiased estimate of the unknown input. Their proposed methodology has two distinctive and practical advantages. First, it represents a unified approach to the problem of inversion of both minimum and non-minimum phase systems as well as systems having transmission zeros on the unit circle. Second, the feedback structure ensures that the proposed scheme is robust to noise. They have shown that the proposed inversion filter is unbiased for certain categories of faults. Finally, they have demonstrated the capabilities and performance of the proposed methodology through several numerical simulation case studies.

Inspec keywords: fault diagnosis; filtering theory; linear systems; discrete time systems; feedback

Other keywords: dynamic filter; inversion-based estimation; practical advantages; fault signal; unknown input; distinctive advantages; unbiased estimate; nonminimum phase systems; discrete-time linear systems; transmission zeros; inversion filter; phase fault-to-output dynamics; algebraic operation; projections; unbiased inversion-based fault estimation

Subjects: Filtering methods in signal processing; Algebra; Discrete control systems; Linear control systems; Control system analysis and synthesis methods

References

    1. 1)
      • 6. Figueroa, M., Bonilla, M., Malabre, M., et al: ‘On failure detection by inversion techniques’. 43rd IEEE Conf. on Decision and Control, vol. 5, Nassau, The Bahamas, 2004, pp. 4770–4775.
    2. 2)
      • 7. Kulcsár, B., Verhaegen, M.: ‘Robust inversion based fault estimation for discrete-time lpv systems’, IEEE Trans. Autom. Control, 2012, 57, (6), pp. 1581–1586.
    3. 3)
      • 19. Patton, R.J., Frank, P.M., Clark, R.N.: ‘Issues of fault diagnosis for dynamic systems’ (Springer Science & Business Media, 2013).
    4. 4)
      • 16. Kirtikar, S., Palanthandalam-Madapusi, H., Zattoni, E., et al: ‘l-delay input reconstruction for discrete-time linear systems’. Proc. 48th IEEE Conf. on Decision and Control, held jointly with the 28th Chinese Control Conference (CDC/CCC 2009), Shanghai, China, 2009, pp. 1848–1853.
    5. 5)
      • 21. Sontag, E.D.: ‘Mathematical control theory: deterministic finite dimensional systems,vol. 6’ (Springer Science & Business Media, New York, 2013).
    6. 6)
      • 5. Edelmayer, A., Bokor, J., Szabó, Z.: ‘Inversion-based residual generation for robust detection and isolation of faults by means of estimation of the inverse dynamics in linear dynamical systems’, Int. J. Control, 2009, 82, (8), pp. 1526–1538.
    7. 7)
      • 3. Alwi, H., Edwards, C.: ‘Robust sensor fault estimation for tolerant control of a civil aircraft using sliding modes’. American Control Conf., Minneapolis, USA, 2006, p. 6.
    8. 8)
      • 10. Silverman, L.: ‘Inversion of multivariable linear systems’, IEEE Trans. Autom. Control, 1969, 14, pp. 270–276.
    9. 9)
      • 1. Chen, J., Patton, R., Zhang, H.: ‘Design of unknown input observers and robust fault detection filters’, Int. J. Control, 1996, 63, (1), pp. 85–105.
    10. 10)
      • 12. Moylan, P.: ‘Stable inversion of linear systems’, IEEE Trans. Autom. Control, 1977, 22, pp. 74–78.
    11. 11)
      • 8. Szabo, Z., Edelmayer, A., Bokor, J.: ‘Inversion based FDI for sampled LPV systems’. Conf. on Control and Fault-Tolerant Systems (SysTol), Nice, France, October 2010, pp. 82–87.
    12. 12)
      • 2. Tan, D., Patton, R.J., Wang, X.: ‘A relaxed solution to unknown input observers for state and fault estimation’, IFAC Symp. on Fault Detection, Supervision and Safety for Technical Processes, 2015, 48, (21), pp. 1048–1053.
    13. 13)
      • 17. Floquet, T., Barbot, J.-P.: ‘A sliding mode approach of unknown input observers for linear systems’. 43rd IEEE Conf. on Decision and Control (CDC 2004), vol. 2, Nassau, The Bahamas, 2004, pp. 1724–1729.
    14. 14)
      • 13. Gilijns, S.: ‘Kalman filtering techniques for system inversion and data assimilation’. PhD thesis, K.U. Leuven, Leuven, Belgium, 2007.
    15. 15)
      • 4. Szigeti, F., Vera, C., Bokor, J., et al: ‘Inversion based fault detection and isolation’. Proc. 40th IEEE Conf. on Decision and Control, Orlando, USA, vol. 2, 2001, pp. 1005–1010.
    16. 16)
      • 18. Marro, G., Zattoni, E.: ‘Unknown-state, unknown-input reconstruction in discrete-time nonminimum-phase systems: geometric methods’, Automatica, 2010, 46, (5), pp. 815–822.
    17. 17)
      • 15. Palanthandalam-Madapusi, H.J., Bernstein, D.S.: ‘Unbiased minimum-variance filtering for input reconstruction’. American Control Conf. (ACC'07 2007), New York City, USA, 2007, pp. 5712–5717.
    18. 18)
      • 11. Massey, J., Sain, M.: ‘Inverses of linear sequential circuits’, IEEE Trans. Comput., 1968, C-17, pp. 330–337.
    19. 19)
      • 14. Chavan, R.A., Palanthandalam-Madapusi, H.J.: ‘Delayed recursive state and input reconstruction’, 2015, arXiv preprint arXiv:1509.06226.
    20. 20)
      • 9. Brockett, R., Mesarovic, M.: ‘The reproducibility of multivariable systems’, J. Math. Anal. Appl., 1965, 11, pp. 548–563.
    21. 21)
      • 20. Davison, E., Wang, S.: ‘Properties and calculation of transmission zeros of linear multivariable systems’, Automatica, 1974, 10, (6), pp. 643–658.
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