A hamiltonian control approach for the stabilization of the angular velocity of a rigid body system controlled by two torques
C. Aguilar–Ibáñeza,*, M.S. Suárez–Castañónb and F. Guzmán–Aguilarc
ª Centro de Investigación en Computación, Instituto del Politécnico Nacional, Av. Juan de Dios Bátiz s/n ,Esq. Miguel Othón de M., Unidad Profesional Adolfo López Mateos, Col. Nueva Industrial Vallejo, Apartado Postal 75476 México, D.F. 07738, México, FAX: +(52) 55 5586–2936.
b Escuela Superior de Cómputo del Instituto Politécnico Nacional.
c Escuela Superior de Física y Matemáticas del Instituto Politécnico Nacional.
]]> * To whom correspondence should be addressed:
Recibido el 30 de julio de 2007
Aceptado el 29 de julio de 2008
Abstract
We present a Hamiltonian control approach for the stabilization of a rigid body system that is controlled by two torques. The stabilization strategy consists in solving a feasible matching condition in order to derive a feedback controller which forces the closed–loop system to be globally asymptotically stable.
Keywords: Control of rigid body system; nonlinear control; Lyapunov stability.
]]> Resumen
Presentamos un enfoque de control Hamiltoniano para la estabilización de un sistema de cuerpo rígido que es controlado por dos torques. La estrategia de control consiste en resolver una condición de acoplamiento conveniente con el fin de derivar un eontrolador de retroalimentaeión que haga al sistema en lazo cerrado global y asintóticamente estable.
Descriptores: Control de un sistema de cuerpo rígido; control no–lineal; estabilidad de Lyapunov.
PACS: 05.45.–a; 45.40.–f; 45.20.Jj; 45.40.Cc
DESCARGAR ARTÍCULO EN FORMATO PDF
Acknowledgements
This work was supported by the Centro de Investigación en Computación del Instituto Politécnico Nacional and by the Secretaría de Investigación y Posgrado (SIP-IPN) under research grants 20071088, 20071109, 20082694 and 200882887.
]]> Florencio Guzmán wishes to thank the Escuela Superior de Física y Matemáticas of the Instituto Politécnico Nacional, where he is a doctoral student.Miguel S. Suárez wishes to thank the Instituto Politécnico Nacional and the Fondo para el Desarrollo de Recursos Humanos del Banco de México for on his postdoctoral stay at the University of Houston possible. Part of this work was done while M. Suárez was making its posdoctoral stay.
References
1. R. Ortega, M. Spong, F. Gomez, and G. Blankenstein, IEEE Trans. Aut. Control 47 (2002) 1218. [ Links ]
2. M. Galaz, R. Ortega, A. Bazanella, and A. Stankovic, Automática 39 (2003) 111. [ Links ]
3. A.M. Bloch, D.E. Chang, and J.E. Marsden, IEEE Transactions on Automatic Control 46 (2001) 1556. [ Links ]
4. C.I. Byrnes and A. Isidori, IEEE Automática 27 (1991) 87. [ Links ]
5. H. Sira–Ramirez and S.K. Agrawal, Differentially flat systems (Marcel Dekker, New York, 2004). [ Links ]
6. C. Aguilar, O. Gutierrez, and M.S. Suarez, Nonlinear Dynamics 40 (2005) 367. [ Links ]
7. H. Sira–Ramirez and H. Siguerdidjane, Int. J. Control 65 (1996) 901. [ Links ]
8. J.T. Y. Wen and K. Kreutz–Delgado, IEEE Transactions on Automatic Control 36 (1991) 1148. [ Links ]
9. O.E. Fjeslltad and T.I. Fossen, IEEE Transactions on Automatic Control 39 (1994) 699. [ Links ]
10. A.M. Bloch and J.E. Marsden, Syst. Control Lett. 14 (1990) 341. [ Links ]
11. R.W. Brockett, Asymptotic Stability and Feedback Stabilization, Differential geometric control theory (Birkhauser, 1983) p. 181. [ Links ]
12. D. Aeyels, Syst. Control Lett. 5 (1985) 59. [ Links ]
13. E.D. Sontag and H.J. Sussmann, Syst. Control Lett. 12 (1989) 213. [ Links ]
14. D. Aeyels and M. Szafranski, Syst. Control Lett. 12 (1988) 213. [ Links ]
15. P. Morin, V. Samson, J.B. Pormet, and Z.P Jiang, Syst. Control Lett. 25 (1995) 375. [ Links ]
16. A. Astolfi and A. Rapaport, Syst. Control Lett. 34 (1998) 257. [ Links ]
17. T. Floquet, W. Perruquetti, and J.P Barbot, Journal of Dynamic Systems, Measurement and Control 122 (2000) 669. [ Links ]
18. M. Reyhanoglu, Discontinues Feedback Stabilization of the Angular Velocity of a Rigid Body with two control Torques Proceeding of the 35th CDCD–IEEE , Kobe Japan, December 1996. [ Links ]
19. H. Siguerdidjane, Kybernetica 5 (1994) 341. [ Links ]
20. M.J. Sidi, Spacecraft Dynamics and control. (Cambridge University Press, 1997). [ Links ]
21. J. Zabczyk, Applied Mathematics and Optimization 19 (1989) 1. [ Links ]
22. D.E. Chang, A.M. Bloch, N.E. Leonard, J.E. Marsden, and CA. Woolsey, ESAIM: Control, Optimisation and Calculus of Variations 8 (2002) 393. [ Links ]
23. R. Ortega, M. Spong, F. Gomez, and G. Blankenstein, IEEE Trans. Autom. Control 47 (2002) 1218. [ Links ]
24. A.M. Bloch, N.E. Leonard, and J.E. Marsden, Open problem in Mathematical System and Control Theory, Edited by V.D. Blondel, Sontag E. Vidyasagar and J.C. Willems (Springer–Verlag London, 1999). [ Links ]
25. H.K. Khalil, Non–linear Systems, 2nd. Edition. (Prentice Hall, N.J., 2002). [ Links ] ]]>