A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model

Rodriguez-Alfaro, Luis H.; Alcorta-Garcia, Efrain; Lara, David; Romero, Gerardo

doi:10.1515/amcs-2015-0005

Abstract

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.

References

Ailon, A. (2010). Simple tracking controllers for autonomous VTOL aircraft with bounded inputs, IEEE Transactions on Automatic Control 55(3): 737-743.10.1109/TAC.2010.2040493
Search in Google Scholar
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.
Search in Google Scholar
Alcorta-Garcia, E. and Frank, P.M. (1997). Deterministic nonlinear observer-based approaches to fault diagnosis: A survey, Control Engineering Practice 5(5): 663-670.10.1016/S0967-0661(97)00048-8
Search in Google Scholar
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.
Search in Google Scholar
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.
Search in Google Scholar
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-2013-0031.10.2478/amcs-2013-0031
Search in Google Scholar
Blanke, M., Kinnaert, M. and Staroswiecki, J.L.M. (2006). Diagnosis and Fault-tolerant Control, 2nd Edn., Springer, Berlin.
Search in Google Scholar
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): 510-517.10.1109/TCST.2004.825052
Search in Google Scholar
Castillo., P., Lozano, R. and Dzul, A. (2005). Modelling and Control of Mini-flying Machines, Springer, London.
Search in Google Scholar
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.
Search in Google Scholar
Chen, J. and Patton, R.J. (1999). Robust Model Based Fault Diagnosis for Dynamic Systems, Kluwer Academic Publishers Group, Boston, MA.10.1007/978-1-4615-5149-2
Search in Google Scholar
DePersis, C. and Isidori, A. (2001). A geometric approach to nonlinear fault detection and isolation, IEEE Transactions on Automatic Control 46(6): 853-865.10.1109/9.928586
Search in Google Scholar
Ding, S.X. (2008). Model-Based Fault Diagnosis Techniques, Springer, Berlin/Heidelberg.
Search in Google Scholar
Ding, S.X. (2013). Model-Based Fault Diagnosis Techniques, 2nd Edn., Springer, London.
Search in Google Scholar
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): 2212-2217.10.1109/TAC.2003.820148
Search in Google Scholar
Etkin, B. and Reid, L. (1996). Dynamics of Flight, Stability and control, 3rd Edn., John Wiley and Sons, Hoboken, NJ.
Search in Google Scholar
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.
Search in Google Scholar
Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy-a survey, Automatica 26(3): 459-474.10.1016/0005-1098(90)90018-D
Search in Google Scholar
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): 690-700.10.1049/iet-cta.2009.0158
Search in Google Scholar
Isermann, R. (2006). Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance, 1st Edn., Springer, Berlin/Heidelberg.
Search in Google Scholar
Kościelny, J.M. and Łab˛eda-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-2013-0030.10.2478/amcs-2013-0030
Search in Google Scholar
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/v10006-012-0069-7.10.2478/v10006-012-0069-7
Search in Google Scholar
Lin, F., Zhang, W. and Brandt, R. (1999). Robust hovering control of a PVTOL, IEEE Transactions on Control Systems Technology 7(3): 343-351.10.1109/87.761054
Search in Google Scholar
Murray, R.M., Li, Z. and Sastry, S. (1994). A Mathematical Introduction to Robotic Manipulation, CRC Press, Boca Raton, FL.
Search in Google Scholar
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.10.1007/978-1-4471-3603-3
Search in Google Scholar
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.
Search in Google Scholar
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).
Search in Google Scholar
Seliger, R. and Frank, P.M. (1991). Fault diagnosis by disturbance decoupled nonlinear observers, CDC ’91, Brighton, UK, pp. 2248-2253.
Search in Google Scholar
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): 1381-1395.10.1142/S0218127401002778
Search in Google Scholar
Stevens, B.L. and Lewis, F.L. (2003). Aircraft Control and Simulation, John Wiley and Sons, Hoboken, NJ.
Search in Google Scholar
Thau, F.E. (1973). Observing the state of non-linear dynamic systems, International Journal of Control 17(3): 471-479. 10.1080/00207177308932395
Search in Google Scholar
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.
Search in Google Scholar
Vasiljevic, L.K. and Khalil, H.K. (2008). Error bounds in differentiation of noisy signals by high-gain observers, Systems & Control Letters 57(10): 856-862.10.1016/j.sysconle.2008.03.018
Search in Google Scholar
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): 1282-1287.10.1109/TAC.2007.900831
Search in Google Scholar
Zavala, A., Fantoni, I. and Lozano, R. (2003). Global stabilization of a PVTOL aircraft model with bounded inputs, International Journal of Control 76(18): 1833-1844.10.1080/00207170310001637147
Search in Google Scholar
Zhang, Y. and Jiang., J. (2008). Bibliographical review on reconfigurable fault-tolerant control systems, Annual Reviews in Control 32(2): 229-252. 10.1016/j.arcontrol.2008.03.008
Search in Google Scholar

A Hamiltonian Approach to Fault Isolation in a Planar Vertical Take–Off and Landing Aircraft Model

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