Observer design for a class of irreversible port Hamiltonian systems
Authors
Saida Zenfari, Mohamed Laabissi, Mohammed Elarbi Achhab
Abstract
In this paper we address the state estimation problem of a particular class of irreversible port Hamiltonian systems (IPHS), which are assumed to be partially observed. Our main contribution consists to design an observer such that the augmented system (plant + observer) is strictly passive. Under some additional assumptions, a Lyapunov function is constructed to ensure the stability of the coupled system. Finally, the proposed methodology is applied to the gas piston system model. Some simulation results are also presented.
Citation
- Journal: An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
- Year: 2023
- Volume: 13
- Issue: 1
- Pages: 26–34
- Publisher: AccScience Publishing
- DOI: 10.11121/ijocta.2023.1072
BibTeX
@article{Zenfari_2023,
title={{Observer design for a class of irreversible port Hamiltonian systems}},
volume={13},
ISSN={2146-0957},
DOI={10.11121/ijocta.2023.1072},
number={1},
journal={An International Journal of Optimization and Control: Theories & Applications (IJOCTA)},
publisher={AccScience Publishing},
author={Zenfari, Saida and Laabissi, Mohamed and Achhab, Mohammed Elarbi},
year={2023},
pages={26--34}
}
References
- 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
- Maschke, B. M., Van Der Schaft, A. J. & Breedveld, P. C. An intrinsic hamiltonian formulation of network dynamics: non-standard poisson structures and gyrators. Journal of the Franklin Institute vol. 329 923–966 (1992) – 10.1016/s0016-0032(92)90049-m
- van der Schaft, A., & Maschke, B. (1995). The Hamiltonian formulation of energy conserving physical systems with external ports. Arch, fur Elektron, Ubertragungstech. 49(5-6), 362- 371.
- van der Schaft, A. & Jeltsema, D. Port-Hamiltonian Systems Theory: An Introductory Overview. Foundations and Trends® in Systems and Control vol. 1 173–378 (2014) – 10.1561/2600000002
- 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
- Hangos, K. M., Bokor, J. & Szederkényi, G. Hamiltonian view on process systems. AIChE Journal vol. 47 1819–1831 (2001) – 10.1002/aic.690470813
- Ramirez, H., Maschke, B. & Sbarbaro, D. Irreversible port-Hamiltonian systems: A general formulation of irreversible processes with application to the CSTR. Chemical Engineering Science vol. 89 223–234 (2013) – 10.1016/j.ces.2012.12.002
- Biedermann, B. & Meurer, T. Observer design for a class of nonlinear systems combining dissipativity with interconnection and damping assignment. International Journal of Robust and Nonlinear Control vol. 31 4064–4080 (2021) – 10.1002/rnc.5461
- Karagiannis, D. & Astolfi, A. Nonlinear observer design using invariant manifolds and applications. Proceedings of the 44th IEEE Conference on Decision and Control 7775–7780 doi:10.1109/cdc.2005.1583418 – 10.1109/cdc.2005.1583418
- 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
- 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
- Zenfari, S., Laabissi, M. & Achhab, M. E. Proportional observer design for port Hamiltonian systems using the contraction analysis approach. International Journal of Dynamics and Control vol. 10 403–408 (2021) – 10.1007/s40435-021-00830-3
- Ramírez, H., Le Gorrec, Y., Maschke, B. & Couenne, F. On the passivity based control of irreversible processes: A port-Hamiltonian approach. Automatica vol. 64 105–111 (2016) – 10.1016/j.automatica.2015.07.002
- Zenfari, S., Laabissi, M. & Achhab, M. E. Passivity Based Control method for the diffusion process. IFAC-PapersOnLine vol. 52 80–84 (2019) – 10.1016/j.ifacol.2019.07.014
- Villalobos Aguilera, I. (2020). Passivity based control of irreversible port Hamiltonian system: An energy shaping plus damping injection approach. Master Thesis, Universidad T ?ecnica Federico Santa Maria.
- Ramirez, H., Maschke, B. & Sbarbaro, D. Modelling and control of multi-energy systems: An irreversible port-Hamiltonian approach. European Journal of Control vol. 19 513–520 (2013) – 10.1016/j.ejcon.2013.09.009
- Lieb, E. H. & Yngvason, J. The entropy concept for non-equilibrium states. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences vol. 469 20130408 (2013) – 10.1098/rspa.2013.0408
- Byrnes, C. I., Isidori, A. & Willems, J. C. Passivity, feedback equivalence, and the global stabilization of minimum phase nonlinear systems. IEEE Transactions on Automatic Control vol. 36 1228–1240 (1991) – 10.1109/9.100932
- van der Schaft, A. L2 - Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer London, 2000). doi:10.1007/978-1-4471-0507-7 – 10.1007/978-1-4471-0507-7
- Agarwal, P. & Choi, J. FRACTIONAL CALCULUS OPERATORS AND THEIR IMAGE FORMULAS. Journal of the Korean Mathematical Society 53, 1183–1210 (2016) – 10.4134/jkms.j150458
- Baleanu, D., Sajjadi, S. S., Jajarmi, A. & Defterli, Ö. On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control. Advances in Difference Equations vol. 2021 (2021) – 10.1186/s13662-021-03393-x
- Baleanu, D., Sajjadi, S. S., Asad, J. H., Jajarmi, A. & Estiri, E. Hyperchaotic behaviors, optimal control, and synchronization of a nonautonomous cardiac conduction system. Advances in Difference Equations vol. 2021 (2021) – 10.1186/s13662-021-03320-0
- Chu, Y.-M., Ali Shah, N., Agarwal, P. & Dong Chung, J. Analysis of fractional multi-dimensional Navier–Stokes equation. Advances in Difference Equations vol. 2021 (2021) – 10.1186/s13662-021-03250-x
- Jajarmi, A., Baleanu, D., Zarghami Vahid, K. & Mobayen, S. A general fractional formulation and tracking control for immunogenic tumor dynamics. Mathematical Methods in the Applied Sciences vol. 45 667–680 (2021) – 10.1002/mma.7804
- Qureshi, S. & Jan, R. Modeling of measles epidemic with optimized fractional order under Caputo differential operator. Chaos, Solitons & Fractals vol. 145 110766 (2021) – 10.1016/j.chaos.2021.110766
- Qureshi, S., Chang, M. M. & Shaikh, A. A. Analysis of series RL and RC circuits with time-invariant source using truncated M, Atangana beta and conformable derivatives. Journal of Ocean Engineering and Science vol. 6 217–227 (2021) – 10.1016/j.joes.2020.11.006
- Wang, B. et al. A New RBF Neural Network-Based Fault-Tolerant Active Control for Fractional Time-Delayed Systems. Electronics vol. 10 1501 (2021) – 10.3390/electronics10121501
- Yusuf, A., Qureshi, S., Mustapha, U. T., Musa, S. S. & Sulaiman, T. A. Fractional Modeling for Improving Scholastic Performance of Students with Optimal Control. International Journal of Applied and Computational Mathematics vol. 8 (2022) – 10.1007/s40819-021-01177-1