Modelling and Passivity Based Control of switched systems from bond graph formalism: Application to multicellular converters

Authors

H. Cormerais, J. Buisson, P.Y. Richard, C. Morvan

Abstract

This paper addresses the modelling and control of switched systems with Boolean inputs. A generalization of Passivity Based Control (PBC) is proposed and fitted to bond graph formalism. The state equations of the equivalent average model are first deduced from the original bond graph using the notion of commutation cells and then interpreted according to Port Controlled Hamiltonian formalism. The whole approach is presented in a formal way. This method is then applied on a multicellular serial converter, which is widespread in power systems and of growing interest. The application of PBC associated to a modelling approach using commutation cells on a non-trivial example shows its efficiency to determine a generic controller, the number of elementary cells being considered as a parameter.

Keywords

bond graph, commutation cells, passivity based control, power converter

Citation

Journal: Journal of the Franklin Institute
Year: 2008
Volume: 345
Issue: 5
Pages: 468–488
Publisher: Elsevier BV
DOI: 10.1016/j.jfranklin.2008.01.001

BibTeX

@article{Cormerais_2008,
  title={{Modelling and Passivity Based Control of switched systems from bond graph formalism: Application to multicellular converters}},
  volume={345},
  ISSN={0016-0032},
  DOI={10.1016/j.jfranklin.2008.01.001},
  number={5},
  journal={Journal of the Franklin Institute},
  publisher={Elsevier BV},
  author={Cormerais, H. and Buisson, J. and Richard, P.Y. and Morvan, C.},
  year={2008},
  pages={468--488}
}

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References

Morvan C, Richard PY, Cormerais H, Buisson J (2004) Sliding mode control of switching systems with boolean inputs. IFAC Proceedings Volumes 37(13):591–596. https://doi.org/10.1016/s1474-6670(17)31288- – 10.1016/s1474-6670(17)31288-0
Buisson J, Richard P-Y, Cormerais H (2005) On the Stabilisation of Switching Electrical Power Converters. Lecture Notes in Computer Science 184–19 – 10.1007/978-3-540-31954-2_12
Sira-Ramirez H, Perez-Moreno RA, Ortega R, Garcia-Esteban M (1997) Passivity-based controllers for the stabilization of Dc-to-Dc Power converters. Automatica 33(4):499–513. https://doi.org/10.1016/s0005-1098(96)00207- – 10.1016/s0005-1098(96)00207-5
Ortega R, Loría A, Nicklasson PJ, Sira-Ramírez H (1998) Passivity-based Control of Euler-Lagrange Systems. Springer Londo – 10.1007/978-1-4471-3603-3
Ortega R, van der Schaft A, Maschke B, Escobar G (2002) Interconnection and damping assignment passivity-based control of port-controlled Hamiltonian systems. Automatica 38(4):585–596. https://doi.org/10.1016/s0005-1098(01)00278- – 10.1016/s0005-1098(01)00278-3
Perez M, Ortega R, Espinoza J (2003) Passivity-based PI control of switched power converters. 2003 European Control Conference (ECC) 542–54 – 10.23919/ecc.2003.7085012
Karnopp, (1990)
Buisson, Analysis of the bond graph model of hybrid physical systems with ideal switches. J. Syst. Control Eng. (2002)
Cormerais H, Buisson J (2000) A Mathematical Criteria to Determine the Valid Modes of a Hybrid System. IFAC Proceedings Volumes 33(5):239–244. https://doi.org/10.1016/s1474-6670(17)40966- – 10.1016/s1474-6670(17)40966-9
Slupphaug O, Foss BA (1997) Model predictive control for a class of hybrid systems. 1997 European Control Conference (ECC) 3095–310 – 10.23919/ecc.1997.7082584
Edwards C, Spurgeon S (1998) Sliding Mode Contro – 10.1201/9781498701822
Jeltsema D, Ortega R, Scherpen JMA (2003) An Energy-Balancing Perspective of Interconnection and Damping Assignment Control of Nonlinear Systems 1. IFAC Proceedings Volumes 36(2):105–110. https://doi.org/10.1016/s1474-6670(17)38875- – 10.1016/s1474-6670(17)38875-4
Morvan C, Cormerais H, Richard PY, Buisson J (2004) Extending passivity based control to dae systems with boolean inputs. IFAC Proceedings Volumes 37(13):1229–1234. https://doi.org/10.1016/s1474-6670(17)31395- – 10.1016/s1474-6670(17)31395-2