Observer design for a class of nonlinear Hamiltonian systems based on energy function structure

https://doi.org/10.58571/CNCA.AMCA.2022.042

Resumen: In this paper the observer design problem for a class of nonlinear port-Hamiltonian system is addressed. The class of nonlinear Hamiltonian system is based on the structure of energy function where it is possible to pull the state apart at measured and unmeasured states which generates two interconnected Hamiltonian systems. Exploiting the properties of the class of nonlinear Hamiltonian systems a reduced order observation scheme is proposed. Finally the observer design proposed in this paper is evaluated in a magnetic levitator in order to prove its the convergence properties, also it is comparing the observer convergence characteristics and the observer performance among the observation schemes that are reported in the literature.

¿Cómo citar?

Granados-Salazar, C., Rojas, M. & Espinosa-Pérez, G. Observer design for a class of nonlinear Hamiltonian systems based on energy function structure. Memorias del Congreso Nacional de Control Automático, pp. 193-198, 2022. https://doi.org/10.58571/CNCA.AMCA.2022.042

Palabras clave

Control de Sistemas Lineales; Control Basado en pasividad; Otros Tópicos Afines

• Astolfi, Alessandro y Ortega, R. (2003). Immersion and invariance: a new tool for stabilization and adaptive control of nonlinear systems. IEEE Transactions on Automatic control, 48(4), 590–606.
• Biedermann, B., Rosenzweig, P., and Meurer, T. (2018). Passivity-based observer design for state affine systems using interconnection and damping assignment. In 2018 IEEE Conference on Decision and Control (CDC), 4662–4667. doi:10.1109/CDC.2018.8619143.
• Fu, B., Wang, Q., and He, W. (2018). Nonlinear disturbance observer-based control for a class of port-controlled hamiltonian disturbed systems. IEEE Access, 6, 50299–50305. doi: 10.1109/ACCESS.2018.2868919.
• Maschke, B. and van der Schaft, A. (1993). Portcontrolled hamiltonian systems: Modelling origins and system theoretic properties. In M. Fliess (ed.), Nonlinear Control Systems Design 1992., IFAC Symposia Series, 359–365. Pergamon, Oxford. doi: https://doi.org/10.1016/B978-0-08-041901-5.50064-6.
• Maya-Ortiz, P. and Espinosa-P´erez, G. (2004). Output feedback excitation control of synchronous generators. International Journal of Robust and Nonlinear Control: IFAC-Affiliated Journal, 14(9-10), 879–890.
• Pfeifer, M., Caspart, S., Strehle, F., and Hohmann, S. (2021). Full-order observer design for a class of nonlinear port-hamiltonian systems. IFAC-PapersOnLine, 54(19), 149–154. doi: https://doi.org/10.1016/j.ifacol.2021.11.070. 7th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2021.
• Rojas, M., Granados-Salazar, C., and Espinosa-Perez, G. (2021). Observer design for a class of nonlinear hamiltonian systems. IFAC PapersOnLine., 54(19), 125–130.
• Sundarapandian, V. (2006). Reduced order observer design for nonlinear systems. Applied mathematics letters, 19(9), 936–941.
• Venkatraman, A. and van der Schaft, A. (2010). Fullorder observer design for a class of port-hamiltonian systems. Automatica, 46(3), 555 – 561. doi: https://doi.org/10.1016/j.automatica.2010.01.019.
• Yaghmaei, Abolfazl y Yazdanpanah, M.J. (2018). Structure preserving observer design for port-Hamiltonian systems. IEEE Transactions on Automatic Control, 64(3), 1214–1220.
• Zenfari, S., Laabissi, M., and Achhab, M.E. (2022). Proportional observer design for port hamiltonian systems using the contraction analysis approach. International Journal of Dynamics and Control, 10(2), 403–408.