Active Vibration Control Using On–line Algebraic Identification and Sliding Modes
Control Activo de Vibraciones Usando Identificación Algebraica en Línea y Modos Deslizantes
Francisco Beltrán Carbajal1*, Gerardo Silva Navarro2, Hebertt Sira Ramírez2 and Andrés Blanco Ortega1
1 ITESM, Campus Guadalajara. Escuela de Ingeniería y Arquitectura C.P. 45201 Zapopan, Jalisco, México. *francisco.beltran@itesm.mx
2 CINVESTAV–IPN. Departamento de Ingeniería Eléctrica – Sección de Mecatrónica Apdo. Postal 14–740 C.P. 07360 México, D.F.
]]>Article received on March 10, 2008
Accepted on September 04, 2008
Abstract
In this paper is described the application of an on–line algebraic identification methodology for parameter and signal estimation in vibrating systems. The algebraic identification is employed to estimate the frequency and amplitude of exogenous vibrations affecting the mechanical system using only position measurements. The algebraic identification is combined with an adaptive–like sliding mode control scheme to asymptotically stabilize the system response and, simultaneously, cancel the harmonic vibrations. Numerical and experimental results show the dynamic and robust performance of the algebraic identification and the active vibration control scheme.
Keywords: Active vibration control, On–line algebraic identification, Sliding mode control.
Resumen
En este artículo se describe la aplicación de una metodología para la identificación algebraica en línea para estimación de parámetros y señales en sistemas vibratorios. La identificación algebraica se utiliza para estimar la frecuencia y la amplitud de vibraciones exógenas que afectan a un sistema mecánico, usando únicamente mediciones de posición. La identificación algebraica se combina con un esquema de control por modos deslizantes del tipo adaptable para estabilizar asintóticamente la respuesta del sistema y, simultáneamente, cancelar las vibraciones armónicas. Resultados numéricos y experimentales muestran el desempeño dinámico y robusto de la identificación algebraica y del esquema de control activo.
]]> Palabras clave: Control activo de vibraciones, Identificación algebraica en línea, Control por modos deslizantes.
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References
1. Fliess, M. and Sira–Ramírez, H., "An algebraic framework for linear identification", ESAIM: Control, Optimization and Calculus of Variations, 9: 151–168 (2003). [ Links ]
2. Korenev, B. G. and Reznikov, L. M., Dynamic Vibration Absorbers: Theory and Technical Applications, London: Wiley, 1993. [ Links ]
3. Rao, S. S., Mechanical Vibrations, New York: Addison–Wesley, 1995. [ Links ]
4. Fliess, M., Lévine, J., Martin, P. and Rouchon, P., "Flatness and defect of nonlinear systems: Introductory theory and examples", International Journal of Control, 61(6): 1327–1361 (1993). [ Links ]
5. Beltrán–Carbajal, F., Silva–Navarro, G. and Sira–Ramírez, H., "Active Vibration Control Using On–line Algebraic Identification of Harmonic Vibrations", Proceedings of the American Control Conference 2005, Portland, OR, USA, 4820–4825 (2005). [ Links ]
6. Beltrán–Carbajal, F., Silva–Navarro, G. and Sira–Ramírez, H., "Active Vibration Absorbers Using Generalized PI and Sliding–Mode Control Techniques", Proceedings of the American Control Conference 2003, Denver, Colorado, USA, 791–796 (2003). [ Links ]
7. Beltrán–Carbajal, F., Sira–Ramírez, H. and Silva–Navarro, G., "Robust Active Vibration Absorption Using Sliding Modes, Delta–Modulators and Generalized PI Control", Proceedings of the Tenth International Congress on Sound and Vibration, Stockholm, Sweden, 117–122 (2003). [ Links ]
8. Fliess, M., Márquez, R, Delaleau E. and Sira–Ramírez, H., "Correcteurs Proportionnels–Integraux Généralisés", ESAIM Control, Optimisation and Calculus of Variations, 7: 23–41 (2002). [ Links ]
9. Ljung, L., Systems Identification: Theory for the User, Englewood Cliffs, New Jersey: Prentice–Hall, 1987. [ Links ]
10. T. Soderstrom and P. Stoica, System Identification, New York: Prentice–Hall, 1989. [ Links ]
11. Sagara, S. and Zhao, Z. Y., "Numerical integration approach to on–line identification of continuous systems", Automática, 26(1): 63–74 (1990). [ Links ]
12. Sagara, S. and Zhao, Z. Y., "Recursive identification of transfer function matrix in continuous systems via linear integral filter", International Journal of Control, 50(2): 457–477 (1989). [ Links ] ]]>