On the Representation of Actuator Faults Diagnosis and Systems Invertibility
In this work, the main problem considered is the
detection and the isolation of the actuator fault. A new formulation of
the linear system is generated to obtain the conditions of the actuator
fault diagnosis. The proposed method is based on the representation
of the actuator as a subsystem connected with the process system in
cascade manner. The designed formulation is generated to obtain the
conditions of the actuator fault detection and isolation. Detectability
conditions are expressed in terms of the invertibility notions. An
example and a comparative analysis with the classic formulation
illustrate the performances of such approach for simple actuator fault
diagnosis by using the linear model of nuclear reactor.
 R. Isermann, "Process Fault Detection Based On Modeling and
Estimation Methods - A Survey”. Automatica, 1984, vol. 20, no. 3, pp.
 R. J. Patton, "Robust Model-Based Fault Diagnosis in Dynamic: The
State of Art”, Proceedings of the IFAC Symposium on Fault Detection,
Supervision and Safety for Process (SAFEPROCESS), Espoo, Fnland,
1994, pp. 1-24.
 D. Fragkoulis., G. Roux, B. Dahhou B, « A New Scheme for Detection,
Isolation and Identification of Single and Multiple Actuators Faults”,
IEEE International Conference on Pronostics and Health Management
(PHM 2008), Denver (USA), 6-9 Octobre 2008, 6p.
 J. J. Gertler,. "Fault Detection and Diagnosis in Engineering Systems”,
Marcel Dekker. New York, 1998.
 J. Chen, R. J. Patton, "Robust Model-Based Fault Diagnosis for
Dynamic systems”, Kluwer Academic Publishers. Masssachusetts, 1999.
 A. S. Willsky, "A Survey of Design Methods for Failure Detection in
Dynamic Systems”, Automatica, 12(6), pp. 601-611, 1976.
 H. L. Jones, "Failure Detection in Linear Systems”, Ph.D. Dissertation,
Dep. Aeronautics and Astronautics, Mass. Inst. Technol., Cambridge,
MA, Aug. 1973.
 N. Kabbaj, M. Polit, B. Dahhou and G. Roux, "Adaptive Observers
Based Fault Detection and Isolation for an Alcoholic Fermentation
Process”, 2001, 8th IEEE International Conference on Emerging
Technologies and Factory Automation, October 15-18, 2(2), pp. 669-
673, Antibes - Juan les Pins, France.
 M. A. Massoumnia, "A Geometric Approach to Failure Detection and
Identification in Linear Systems”, Ph.D. dissertation, Dep. Aeronautics
and Astronautics, Mass. Inst. Technol., Feb. 1986.
 Li Z. and Dahhou B.: A New Fault Isolation and Identification Method
for Nonlinear Dynamic Systems: Application to a Fermentation Process.
Applied Mathematical Modelling, 32 (2008), 2806-2830.
 P. M, Frank, "Fault Diagnosis in Dynamic Systems Using Analytical
and Knowledge-Based Redundancy: A Survey and Some New Results”.
Automatica, 26(3), 459–474, 1990.
 R. Isermann, "On the Applicability of Model-Based Fault Detection for
Technical Processes”, Control Engineering Practice, 2, pp. 439-450,
 R, Isermann and P. Balle, "Trends in the Application of Model-Based
Fault Detection and Diagnosis of Technical Processes”, Control
Engineering Practice, 5(5), pp. 709-719, 1997.
 R. J. Patton, P. M. Frank, and, R. N. Clark, "Issues of Fault Diagnosis
for Dynamic Systems”. London Limited: Springer Verlag, 2000.
 C. Bernstein, "Matrix Mathematic, Theory, Facts, and Formulas with
Application to Linear Systems Theory”, Princeton University Press,
Princeton and Oxford, 2005.
 F.Szigeti, A. R. Bolivar, "System Inversion and Fault Detection: The
Failure Affine Nonlinear Case”, Proceedings of the 10th Mediterranean
Conference on Control and Automation - MED2002 Lisbon, Portugal,
July 9-12, 2002.
 R. Kallol, R. N. Banavar, and S. Thangasamy, "Application of Fault
Detection and Identification (FDI) Techniques in Power Regulating
Systems of Nuclear Reactors", IEEE Transactions on Nuclear Science,
Vol. 45, No. 6, December 1998.
 M. K. Sain, J. L. Massey, "Invertibility of Linear Time-Invariant
Dynamical Systems”, IEEE Transactions on Automatic Control, V.AC-
14, No 2, April 1969.