Structure Preserving Observer Design for Port-Hamiltonian Systems
Authors
Abolfazl Yaghmaei, Mohammad Javad Yazdanpanah
Abstract
In this paper, a full-order observer design method is proposed for port-Hamiltonian systems. The proposed method is based on the notion of contractive port-Hamiltonian systems. It is the first structure preserving observer design for a broad class of input-state-output port-Hamiltonian systems. The design procedure consists of solving a matching equation, similar to the Interconnection and Damping Assignment Passivity-Based Control (IDA-PBC) for controller design. The matching equation, as shown in the paper, has some closed-form solutions for general class of mechanical and electromechanical systems. As another feature of the proposed method, it is shown that the existence of solution of the corresponding matching equation for a linear port-Hamiltonian system is equivalent to the detectability property of that system. Upon these facts, the proposed method can be considered as a counterpart of IDA-PBC for observer design. Simulations for some benchmark examples, including ball and beam, magnetic levitation, and permanent magnetic synchronous motor, show the potency and applicability of the method.
Citation
- Journal: IEEE Transactions on Automatic Control
- Year: 2019
- Volume: 64
- Issue: 3
- Pages: 1214–1220
- Publisher: Institute of Electrical and Electronics Engineers (IEEE)
- DOI: 10.1109/tac.2018.2847904
BibTeX
@article{Yaghmaei_2019,
title={{Structure Preserving Observer Design for Port-Hamiltonian Systems}},
volume={64},
ISSN={2334-3303},
DOI={10.1109/tac.2018.2847904},
number={3},
journal={IEEE Transactions on Automatic Control},
publisher={Institute of Electrical and Electronics Engineers (IEEE)},
author={Yaghmaei, Abolfazl and Yazdanpanah, Mohammad Javad},
year={2019},
pages={1214--1220}
}
References
- LOHMILLER, W. & SLOTINE, J.-J. E. On Contraction Analysis for Non-linear Systems. Automatica vol. 34 683–696 (1998) – 10.1016/s0005-1098(98)00019-3
- Lohmiller, W. & Slotine, J.-J. E. Control system design for mechanical systems using contraction theory. IEEE Transactions on Automatic Control vol. 45 984–989 (2000) – 10.1109/9.855568
- Lynch, A. F. & Bortoff, S. A. Nonlinear observers with approximately linear error dynamics: the multivariable case. IEEE Transactions on Automatic Control vol. 45 927–932 (2001) – 10.1109/9.928597
- Prajna, S., van der Schaft, A. & Meinsma, G. An LMI approach to stabilization of linear port-controlled Hamiltonian systems. Systems & Control Letters vol. 45 371–385 (2002) – 10.1016/s0167-6911(01)00195-5
- Rajamani, R. Observers for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control vol. 43 397–401 (1998) – 10.1109/9.661604
- Rodríguez, H. & Ortega, R. Stabilization of electromechanical systems via interconnection and damping assignment. International Journal of Robust and Nonlinear Control vol. 13 1095–1111 (2003) – 10.1002/rnc.804
- rodríguez, Passivity-based control of magnetic levitation systems: Theory and experiments. Proc 14th Int Symp Math Theory Netw Syst (2000)
- Shim, H., Seo, J. H. & Teel, A. R. Nonlinear observer design via passivation of error dynamics. Automatica vol. 39 885–892 (2003) – 10.1016/s0005-1098(03)00023-2
- Hyungbo Shim & Seo, J. H. Recursive nonlinear observer design: beyond the uniform observability. IEEE Transactions on Automatic Control vol. 48 294–298 (2003) – 10.1109/tac.2002.808485
- Venkatraman, A. & van der Schaft, A. J. Full-order observer design for a class of port-Hamiltonian systems. Automatica vol. 46 555–561 (2010) – 10.1016/j.automatica.2010.01.019
- Califano, C. & Moog, C. H. The Observer Error Linearization Problem via Dynamic Compensation. IEEE Transactions on Automatic Control vol. 59 2502–2508 (2014) – 10.1109/tac.2014.2308606
- Besancon, G. On output transformations for state linearization up to output injection. IEEE Transactions on Automatic Control vol. 44 1975–1981 (1999) – 10.1109/9.793789
- Duindam, V., Macchelli, A., Stramigioli, S. & Bruyninckx, H. Modeling and Control of Complex Physical Systems. (Springer Berlin Heidelberg, 2009). doi:10.1007/978-3-642-03196-0 – 10.1007/978-3-642-03196-0
- Dörfler, F., Johnsen, J. K. & Allgöwer, F. An introduction to interconnection and damping assignment passivity-based control in process engineering. Journal of Process Control vol. 19 1413–1426 (2009) – 10.1016/j.jprocont.2009.07.015
- khalil, Nonlinear Systems (2002)
- Gauthier, J. P., Hammouri, H. & Othman, S. A simple observer for nonlinear systems applications to bioreactors. IEEE Transactions on Automatic Control vol. 37 875–880 (1992) – 10.1109/9.256352
- Arcak, M. & Kokotovic, P. Observer-based control of systems with slope-restricted nonlinearities. IEEE Transactions on Automatic Control vol. 46 1146–1150 (2001) – 10.1109/9.935073
- Aghannan, N. & Rouchon, P. An intrinsic observer for a class of lagrangian systems. IEEE Transactions on Automatic Control vol. 48 936–945 (2003) – 10.1109/tac.2003.812778
- Krener, A. J. & Isidori, A. Linearization by output injection and nonlinear observers. Systems & Control Letters vol. 3 47–52 (1983) – 10.1016/0167-6911(83)90037-3
- Yaghmaei, A. & Yazdanpanah, M. J. Trajectory tracking for a class of contractive port Hamiltonian systems. Automatica vol. 83 331–336 (2017) – 10.1016/j.automatica.2017.06.039