Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation

Authors

Joel Ferguson, Alejandro Donaire, Richard H. Middleton

Abstract

In this paper we present a method for the addition of integral action to nonpassive outputs of a class of port-Hamiltonian (pH) systems. The proposed integral controller is a dynamic extension, constructed from the open-loop system, such that the closed loop preserves the pH form. It is shown that the controller is able to reject the effects of both matched and unmatched disturbances, preserving the regulation of the nonpassive outputs. Previous solutions to this problem have relied on a change of coordinates whereas the presented solution is developed using the original state vector and, therefore, retains its physical interpretation. In addition, the resulting closed-loop dynamics have a natural interpretation as a control by interconnection scheme.

Citation

• Journal: IEEE Transactions on Automatic Control
• Year: 2017
• Volume: 62
• Issue: 11
• Pages: 5947–5953
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/tac.2017.2700995

BibTeX

@article{Ferguson_2017,
  title={{Integral Control of Port-Hamiltonian Systems: Nonpassive Outputs Without Coordinate Transformation}},
  volume={62},
  ISSN={1558-2523},
  DOI={10.1109/tac.2017.2700995},
  number={11},
  journal={IEEE Transactions on Automatic Control},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Ferguson, Joel and Donaire, Alejandro and Middleton, Richard H.},
  year={2017},
  pages={5947--5953}
}

Download the bib file

References

• Ortega, R. & Romero, J. G. Robust integral control of port-Hamiltonian systems: The case of non-passive outputs with unmatched disturbances. Systems & Control Letters vol. 61 11–17 (2012) – 10.1016/j.sysconle.2011.09.015
• Romero, J. G., Donaire, A. & Ortega, R. Robust energy shaping control of mechanical systems. Systems & Control Letters vol. 62 770–780 (2013) – 10.1016/j.sysconle.2013.05.011
• The Behavioral Approach to Open and Interconnected Systems. IEEE Control Systems vol. 27 46–99 (2007) – 10.1109/mcs.2007.906923
• Brogliato, B., Maschke, B., Lozano, R. & Egeland, O. Dissipative Systems Analysis and Control. Communications and Control Engineering (Springer London, 2007). doi:10.1007/978-1-84628-517-2 – 10.1007/978-1-84628-517-2
• Nicklasson, P. J., Ortega, R. & Espinosa-Perez, G. Passivity-Based Control of a Class of Blondel-Park Transformable Electric Machines. Modeling, Identification and Control: A Norwegian Research Bulletin vol. 18 273–305 (1997) – 10.4173/mic.1997.4.3
• Alonso, A. A. & Ydstie, B. E. Stabilization of distributed systems using irreversible thermodynamics. Automatica vol. 37 1739–1755 (2001) – 10.1016/s0005-1098(01)00140-6
• Ferguson, J., Middleton, R. H. & Donaire, A. Disturbance rejection via control by interconnection of port-Hamiltonian systems. 2015 54th IEEE Conference on Decision and Control (CDC) 507–512 (2015) doi:10.1109/cdc.2015.7402279 – 10.1109/cdc.2015.7402279
• Ortega, R., van der Schaft, A., Castanos, F. & Astolfi, A. Control by Interconnection and Standard Passivity-Based Control of Port-Hamiltonian Systems. IEEE Transactions on Automatic Control vol. 53 2527–2542 (2008) – 10.1109/tac.2008.2006930
• Ortega, R. & García-Canseco, E. Interconnection and Damping Assignment Passivity-Based Control: A Survey. European Journal of Control vol. 10 432–450 (2004) – 10.3166/ejc.10.432-450
• Pavlov, A. & Marconi, L. Incremental passivity and output regulation. Systems & Control Letters vol. 57 400–409 (2008) – 10.1016/j.sysconle.2007.10.008
• Koopman, J. & Jeltsema, D. Casimir-Based Control Beyond the Dissipation Obstacle. IFAC Proceedings Volumes vol. 45 173–177 (2012) – 10.3182/20120829-3-it-4022.00046
• Jayawardhana, B. & Weiss, G. A class of port-controlled Hamiltonian systems. Proceedings of the 44th IEEE Conference on Decision and Control 5630–5632 doi:10.1109/cdc.2005.1583059 – 10.1109/cdc.2005.1583059
• Jayawardhana, B., Ortega, R., García-Canseco, E. & Castaños, F. Passivity of nonlinear incremental systems: Application to PI stabilization of nonlinear RLC circuits. Systems & Control Letters vol. 56 618–622 (2007) – 10.1016/j.sysconle.2007.03.011
• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• 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
• Donaire, A. & Junco, S. On the addition of integral action to port-controlled Hamiltonian systems. Automatica vol. 45 1910–1916 (2009) – 10.1016/j.automatica.2009.04.006