Interconnection Schemes in Modeling and Control

Authors

Pablo Borja, Joel Ferguson, Arjan van der Schaft

Abstract

Interconnection schemes are ubiquitous in physical systems. For instance, in multi-domain systems consisting of interconnected subsystems from different physical domains. Furthermore, the interconnection of two or more systems has also been exploited to analyze and control dynamical systems, especially passive ones. To this end, the most common interconnection structure is the negative feedback interconnection. However, this approach is unsuitable to directly couple the states of the subsystems in the overall system’s energy as customarily occurs in physical systems. This letter provides two interconnection approaches that overcome this issue. Notably, it is shown that these interconnection structures are suitable for decomposing passive systems into the interconnection of simpler passive subsystems. Moreover, these interconnections schemes allow the interpretation of some existing nonlinear control approaches as the interconnection of a passive plant with a passive controller. Additionally, the interpretation of the proposed interconnection structures is provided via bond graphs.

Citation

• Journal: IEEE Control Systems Letters
• Year: 2023
• Volume: 7
• Issue:
• Pages: 2287–2292
• Publisher: Institute of Electrical and Electronics Engineers (IEEE)
• DOI: 10.1109/lcsys.2023.3286124

BibTeX

@article{Borja_2023,
  title={{Interconnection Schemes in Modeling and Control}},
  volume={7},
  ISSN={2475-1456},
  DOI={10.1109/lcsys.2023.3286124},
  journal={IEEE Control Systems Letters},
  publisher={Institute of Electrical and Electronics Engineers (IEEE)},
  author={Borja, Pablo and Ferguson, Joel and van der Schaft, Arjan},
  year={2023},
  pages={2287--2292}
}

Download the bib file

References

• Putting energy back in control. IEEE Control Systems vol. 21 18–33 (2001) – 10.1109/37.915398
• Ortega, R., Romero, J. G., Borja, P. & Donaire, A. PID Passivity‐Based Control of Nonlinear Systems with Applications. (2021) doi:10.1002/9781119694199 – 10.1002/9781119694199
• Borja, P., Ortega, R. & Scherpen, J. M. A. New Results on Stabilization of Port-Hamiltonian Systems via PID Passivity-Based Control. IEEE Transactions on Automatic Control vol. 66 625–636 (2021) – 10.1109/tac.2020.2986731
• Borja, P. & Scherpen, J. M. A. Stabilization of a Class of Cyclo-Passive Systems Using Alternate Storage Functions. 2018 IEEE Conference on Decision and Control (CDC) 5634–5639 (2018) doi:10.1109/cdc.2018.8619192 – 10.1109/cdc.2018.8619192
• 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
• van der Schaft, A. L2-Gain and Passivity Techniques in Nonlinear Control. Communications and Control Engineering (Springer International Publishing, 2017). doi:10.1007/978-3-319-49992-5 – 10.1007/978-3-319-49992-5
• Bond-graph modeling. IEEE Control Systems vol. 27 24–45 (2007) – 10.1109/mcs.2007.338279
• van der Schaft, A. Interconnections of input-output Hamiltonian systems with dissipation. 2016 IEEE 55th Conference on Decision and Control (CDC) 4686–4691 (2016) doi:10.1109/cdc.2016.7798983 – 10.1109/cdc.2016.7798983
• van der Schaft, A. Cyclo-Dissipativity Revisited. IEEE Transactions on Automatic Control vol. 66 2920–2924 (2021) – 10.1109/tac.2020.3013941
• Venkatraman, A. & van der Schaft, A. Energy Shaping of Port-Hamiltonian Systems by Using Alternate Passive Input-Output Pairs. European Journal of Control vol. 16 665–677 (2010) – 10.3166/ejc.16.665-677
• 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
• van der Schaft, A. J. Positive feedback interconnection of Hamiltonian systems. IEEE Conference on Decision and Control and European Control Conference 6510–6515 (2011) doi:10.1109/cdc.2011.6160395 – 10.1109/cdc.2011.6160395
• Ortega, R. & Borja, L. P. New results on Control by Interconnection and Energy-Balancing Passivity-Based Control of port-hamiltonian systems. 53rd IEEE Conference on Decision and Control 2346–2351 (2014) doi:10.1109/cdc.2014.7039746 – 10.1109/cdc.2014.7039746