Lumped parameter reduced-order port-Hamiltonian modeling of flexible structures

Authors

Arijit Sarkar, Daniel Dirksz, Jacquelien M.A. Scherpen

Abstract

In this paper, we develop a scalable lumped-parameter model of a flexible structure. We opt for the port-Hamiltonian framework for the representation due to its innate capability of structure-preservation for power-preserving interconnections. We utilize a canonical transformation to reduce the computational burden associated with symbolic computations. Based on the physical discretization, we then validate the applicability of models of different orders on an example of cantilever beam. We also propose a port-Hamiltonian structure-preserving generalized balanced truncation approach for further reduction of the order.

Keywords

flexible structure, model reduction, nonlinear systems, port-hamiltonian systems

Citation

• Journal: IFAC-PapersOnLine
• Year: 2025
• Volume: 59
• Issue: 19
• Pages: 544–549
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2025.11.091
• Note: 13th IFAC Symposium on Nonlinear Control Systems NOLCOS 2025- Reykjavík, Iceland, July 23-25, 2025

BibTeX

@article{Sarkar_2025,
  title={{Lumped parameter reduced-order port-Hamiltonian modeling of flexible structures}},
  volume={59},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2025.11.091},
  number={19},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Sarkar, Arijit and Dirksz, Daniel and Scherpen, Jacquelien M.A.},
  year={2025},
  pages={544--549}
}

Download the bib file

References

• Antoulas, (2005)
• Corbin NA, Sarkar A, Scherpen JMA, Kramer B (2024) Scalable Computation of Input-Normal/Output-Diagonal Balanced Realization for Control-Affine Polynomial System – 10.2139/ssrn.5018659
• Fujimoto K, Sakurama K, Sugie T (2003) Trajectory tracking control of port-controlled Hamiltonian systems via generalized canonical transformations. Automatica 39(12):2059–2069. https://doi.org/10.1016/j.automatica.2003.07.00 – 10.1016/j.automatica.2003.07.005
• Gibson RF (2016) Principles of Composite Material Mechanics. CRC Pres – 10.1201/b19626
• Goubej M, Königsmarková J, Kampinga R, Nieuwenkamp J, Paquay S (2021) Employing Finite Element Analysis and Robust Control Concepts in Mechatronic System Design-Flexible Manipulator Case Study. Applied Sciences 11(8):3689. https://doi.org/10.3390/app1108368 – 10.3390/app11083689
• Gugercin S, Antoulas AC (2004) A Survey of Model Reduction by Balanced Truncation and Some New Results. International Journal of Control 77(8):748–766. https://doi.org/10.1080/0020717041000171344 – 10.1080/00207170410001713448
• Kawano DT, Salsa RG Jr, Ma F, Morzfeld M (2018) A canonical form of the equation of motion of linear dynamical systems. Proc R Soc A 474(2211):20170809. https://doi.org/10.1098/rspa.2017.080 – 10.1098/rspa.2017.0809
• Kim JH, Lee SE, Kim BH (2023) Applications of flexible and stretchable three-dimensional structures for soft electronics. Soft Sci 3(2):16. https://doi.org/10.20517/ss.2023.0 – 10.20517/ss.2023.07
• Maschke, Port-controlled Hamiltonian systems: Modeling origins and systemstheoretic properties. In Proceedings of 2nd IFAC symposium of Nonlinear Control Systems Design, volume 25 (1992)
• Mattioni A, Wu Y, Ramirez H, Le Gorrec Y, Macchelli A (2020) Modelling and control of an IPMC actuated flexible structure: A lumped port Hamiltonian approach. Control Engineering Practice 101:104498. https://doi.org/10.1016/j.conengprac.2020.10449 – 10.1016/j.conengprac.2020.104498
• Moore B (1981) Principal component analysis in linear systems: Controllability, observability, and model reduction. IEEE Trans Automat Contr 26(1):17–32. https://doi.org/10.1109/tac.1981.110256 – 10.1109/tac.1981.1102568
• Rashad R, Califano F, van der Schaft AJ, Stramigioli S (2020) Twenty years of distributed port-Hamiltonian systems: a literature review. IMA Journal of Mathematical Control and Information 37(4):1400–1422. https://doi.org/10.1093/imamci/dnaa01 – 10.1093/imamci/dnaa018
• Sarkar A, Scherpen JMA (2023) Structure-preserving generalized balanced truncation for nonlinear port-Hamiltonian systems. Systems & Control Letters 174:105501. https://doi.org/10.1016/j.sysconle.2023.10550 – 10.1016/j.sysconle.2023.105501
• Scherpen JMA (1993) Balancing for nonlinear systems. Systems & Control Letters 21(2):143–153. https://doi.org/10.1016/0167-6911(93)90117- – 10.1016/0167-6911(93)90117-o
• Scherpen JMA (1996) H∞ balancing for nonlinear systems. Int J Robust Nonlinear Control 6(7):645–668. https://doi.org/10.1002/(sici)1099-1239(199608)6:7<645::aid-rnc179>3.0.co;2- – 10.1002/(sici)1099-1239(199608)6:7<645::aid-rnc179>3.0.co;2-x
• SCHERPEN JMA, VAN DER SCHAFT AJ (1994) Normalized coprime factorizations and balancing for unstable nonlinear systems. International Journal of Control 60(6):1193–1222. https://doi.org/10.1080/0020717940892151 – 10.1080/00207179408921517
• van der Schaft A, Jeltsema D (2014) Port-Hamiltonian Systems Theory: An Introductory Overvie – 10.1561/9781601987877
• van der Schaft A (2017) L2-Gain and Passivity Techniques in Nonlinear Control. Springer International Publishin – 10.1007/978-3-319-49992-5
• Webster RJ III, Jones BA (2010) Design and Kinematic Modeling of Constant Curvature Continuum Robots: A Review. The International Journal of Robotics Research 29(13):1661–1683. https://doi.org/10.1177/027836491036814 – 10.1177/0278364910368147