The problem of fault detection and isolation in a class of nonlinear systems having a Hamiltonian representation is considered. In particular, a model of a planar vertical take-off and landing aircraft with sensor and actuator faults is studied. A Hamiltonian representation is derived from an Euler-Lagrange representation of the system model considered. In this form, nonlinear decoupling is applied in order to obtain subsystems with (as much as possible) specific fault sensitivity properties. The resulting decoupled subsystem is represented as a Hamiltonian system and observer-based residual generators are designed. The results are presented through simulations to show the effectiveness of the proposed approach.
@article{bwmeta1.element.bwnjournal-article-amcv25i1p65bwm,
author = {Luis H. Rodriguez-Alfaro and Efrain Alcorta-Garcia and David Lara and Gerardo Romero},
title = {A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model},
journal = {International Journal of Applied Mathematics and Computer Science},
volume = {25},
year = {2015},
pages = {65-76},
zbl = {1322.93051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-amcv25i1p65bwm}
}
Luis H. Rodriguez-Alfaro; Efrain Alcorta-Garcia; David Lara; Gerardo Romero. A Hamiltonian approach to fault isolation in a planar vertical take-off and landing aircraft model. International Journal of Applied Mathematics and Computer Science, Tome 25 (2015) pp. 65-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-amcv25i1p65bwm/
[000] Ailon, A. (2010). Simple tracking controllers for autonomous VTOL aircraft with bounded inputs, IEEE Transactions on Automatic Control 55(3): 737-743.
[001] Al-Hiddabi, S., Shen, J. and McClamroch, N. (1999). A study of flight maneuvers for the PVTOL aircraft model, Proceedings of the American Control Conference, San Diego, CA, USA, Vol. 4, pp. 2727-2731.
[002] Alcorta-Garcia, E. and Frank, P.M. (1997). Deterministic nonlinear observer-based approaches to fault diagnosis: A survey, Control Engineering Practice 5(5): 663-670.
[003] Alcorta Garcia, E. (1999). Modelgestütze Residuengenerierung für die Diagnose von additiven and multiplicativen Fehler in dynamischen Systemen, Ph.D. thesis, Gerhard-Mercator University of Duisburg, Duisburg.
[004] Apostol, T.M. (1967). Calculus I: One-variable Calculus, with an Introduction to Linear Algebra, 2nd Edn., Vol. 1, John Wiley & Sons, New York, NY. | Zbl 0148.28201
[005] Bartyś, M. (2013). Generalized reasoning about faults based on the diagnostic matrix, International Journal of Applied Mathematics Computer Science 23(2): 407-417, DOI: 10.2478/amcs-2013-0031. | Zbl 1282.93091
[006] Blanke, M., Kinnaert, M. and Staroswiecki, J.L.M. (2006). Diagnosis and Fault-tolerant Control, 2nd Edn., Springer, Berlin. | Zbl 1126.93004
[007] Castillo, P., Dzul, A. and Lozano, R. (2004). Stabilization and tracking of a four-rotor mini rotorcraft, IEEE Transactions on Control System Technology 12(4): 510-517.
[008] Castillo., P., Lozano, R. and Dzul, A. (2005). Modelling and Control of Mini-flying Machines, Springer, London.
[009] Castillo, P., Lozano, R., Fantoni, I. and Dzul, A. (2002). Control design for the PVTOL aircraft with arbitrary bounds on the acceleration, Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas, NV, USA, Vol. 2, pp. 1717-1722.
[010] Chen, J. and Patton, R.J. (1999). Robust Model Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers Group, Boston, MA. | Zbl 0920.93001
[011] DePersis, C. and Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control 46(6): 853-865. | Zbl 1009.93003
[012] Ding, S.X. (2008). Model-Based Fault Diagnosis Techniques, Springer, Berlin/Heidelberg.
[013] Ding, S.X. (2013). Model-Based Fault Diagnosis Techniques, 2nd Edn., Springer, London. | Zbl 1293.93003
[014] Do, K.D., Jiang, Z.P. and Pan, J. (2003). On global tracking control of a VTOL aircraft without velocity measurements, IEEE Transactions on Automatic Control 48(12): 2212-2217.
[015] Etkin, B. and Reid, L. (1996). Dynamics of Flight, Stability and control, 3rd Edn., John Wiley and Sons, Hoboken, NJ.
[016] Fantoni, I., Lozano, R. and Castillo, P. (2002). A simple stabilization algorithm for the PVTOL aircraft, 15th IFAC World Congress, Barcelona, Spain, pp. 1225-1225.
[017] Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey, Automatica 26(3): 459-474. | Zbl 0713.93052
[018] Frye, M., Ding, S., Qian, C. and Li, S. (2010). Fast convergent observer design for output feedback stabilisation of a planar vertical takeoff and landing aircraft, IET Control Theory and Applications 4(4): 690-700.
[019] Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, 1st Edn., Springer, Berlin/Heidelberg.
[020] Kościelny, J.M. and Łabęda-Grudziak, Z.M. (2013). Double fault distinguishability in linear systems, International Journal of Applied Mathematics and Computer Science 23(2): 395-406, DOI: 10.2478/amcs-2013-0030. | Zbl 1282.93137
[021] Krokavec, D. and Filasová, A. (2012). Novel fault detection criteria based on linear quadratic control performances, International Journal of Applied Mathematics and Computer Science 22(4): 929-938, DOI: 10.2478/v10006-012-0069-7. | Zbl 1283.93175
[022] Lin, F., Zhang, W. and Brandt, R. (1999). Robust hovering control of a PVTOL, IEEE Transactions on Control Systems Technology 7(3): 343-351.
[023] Murray, R.M., Li, Z. and Sastry, S. (1994). A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL. | Zbl 0858.70001
[024] Ortega, R., Loria, A., Nicklasson, P.J. and Sira Ramirez, H. (1998). Passivity-based Control of Euler Lagrange Systems: Mechanical, Electrical and Electromechanical Applications, Springer, London.
[025] Rejon, V. and Aranda-Bricaire, E. (2006). Discrete-time stabilization of a PVTOL without roll angle and velocities measurement, Proceedings of the 45th IEEE Conference on Decision & Control, San Diego, CA, USA, pp. 1521-1526.
[026] Rodríguez Alfaro, L.H. (2014). Active Fault Tolerant Control of Hamiltonian Convergent Systems, Ph.D. thesis, Autonomous University of Nuevo Leon, San Nicolas de los Garza, (in Spanish).
[027] Seliger, R. and Frank, P.M. (1991). Fault diagnosis by disturbance decoupled nonlinear observers, CDC '91, Brighton, UK, pp. 2248-2253.
[028] Sira Ramírez, H. and Cruz Hernández, C. (2001). Synchronization of chaotic systems: A generalized Hamiltonian systems approach, International Journal of Bifurcation and Chaos 11(5): 1381-1395. | Zbl 1206.37053
[029] Stevens, B.L. and Lewis, F.L. (2003). Aircraft Control and Simulation, John Wiley and Sons, Hoboken, NJ.
[030] Thau, F.E. (1973). Observing the state of non-linear dynamic systems, International Journal of Control 17(3): 471-479. | Zbl 0249.93006
[031] van der Schaft, A. (2000). L2 Gain and Passivity Techniques in Nonlinear Control, Lecture Notes in Control and Information Sciences, Vol. 218, Springer, Berlin/Heidelberg. | Zbl 0937.93020
[032] Vasiljevic, L.K. and Khalil, H.K. (2008). Error bounds in differentiation of noisy signals by high-gain observers, Systems & Control Letters 57(10): 856-862. | Zbl 1162.93011
[033] Wood, R. and Cazzolato, B. (2007). An alternative nonlinear control law for the global stabilization of the PVTOL vehicle, IEEE Transactions on Automatic Control 52(7): 1282-1287.
[034] Zavala, A., Fantoni, I. and Lozano, R. (2003). Global stabilization of a PVTOL aircraft model with bounded inputs, International Journal of Control 76(18): 1833-1844. | Zbl 1073.93041
[035] Zhang, Y. and Jiang., J. (2008). Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control 32(2): 229-252.