Design and experimental validation of a model reduction algorithm for high-order port-Hamiltonian systems *

Authors

Luca Gentili, Luca Bassi, Alessandro Macchelli, Claudio Melchiorri, Roberto Borsari

Abstract

This paper illustrates a model reduction procedure for port Hamiltonian systems able to preserve the frequency behavior of the original system in a neighborhood of a predefined set of frequencies of interest. This research is part of a wider activity carried out in collaboration with Tetra Pak concerning the modelling and simulation of the Ultrasonic Sealing System (USTS). Due to the presence of a Compact Transducer (CT) that can be modelled only by means of commercial finite element CAE software, which provide extremely high-order dynamical systems, it is not possible to perform a simulation of the complete system to test the validity of the controller and perform the diagnosis of the sealing process in detail. The proposed procedure drastically reduces the simulation time without loosing the essential dynamical information. The model reduction algorithm is experimentally validated.

Citation

• Journal: IFAC Proceedings Volumes
• Year: 2010
• Volume: 43
• Issue: 14
• Pages: 867–872
• Publisher: Elsevier BV
• DOI: 10.3182/20100901-3-it-2016.00207
• Note: 8th IFAC Symposium on Nonlinear Control Systems

BibTeX

@article{Gentili_2010,
  title={{Design and experimental validation of a model reduction algorithm for high-order port-Hamiltonian systems *}},
  volume={43},
  ISSN={1474-6670},
  DOI={10.3182/20100901-3-it-2016.00207},
  number={14},
  journal={IFAC Proceedings Volumes},
  publisher={Elsevier BV},
  author={Gentili, Luca and Bassi, Luca and Macchelli, Alessandro and Melchiorri, Claudio and Borsari, Roberto},
  year={2010},
  pages={867--872}
}

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References

• Amini, Energy dissipation in multi-layered board under ultrasonic sealing (2010)
• Bassi, (2007)
• Fritzson, (2004)
• Gentili, Model reduction for high-order port-Hamiltonian systems. Application to piezo-electric systems. (2009)
• Golo, G., Talasila, V., van der Schaft, A. & Maschke, B. Hamiltonian discretization of boundary control systems. Automatica 40, 757–771 (2004) – 10.1016/j.automatica.2003.12.017
• Krysl, P., Lall, S. & Marsden, J. E. Dimensional model reduction in non‐linear finite element dynamics of solids and structures. Numerical Meth Engineering 51, 479–504 (2001) – 10.1002/nme.167
• Lall, S., Marsden, J. E. & Glavaški, S. A subspace approach to balanced truncation for model reduction of nonlinear control systems. Intl J Robust & Nonlinear 12, 519–535 (2002) – 10.1002/rnc.657
• Lall, S., Krysl, P. & Marsden, J. E. Structure-preserving model reduction for mechanical systems. Physica D: Nonlinear Phenomena 184, 304–318 (2003) – 10.1016/s0167-2789(03)00227-6
• Maschke, Port controlled Hamiltonian systems: modeling origins and system theoretic properties. (1992)
• Nemkov, Development of inductive power transfer for ultrasonic sealing (UIPT) (2008)
• Paynter, (1961)
• Piefort, (2001)
• Polyuga, Structure preserving model reduction for port-Hamiltonian systems. Mathematical Theory of Networks and Systems (2008)
• 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
• Van Der Schaft, A. J. & Maschke, B. M. On the Hamiltonian formulation of nonholonomic mechanical systems. Reports on Mathematical Physics 34, 225–233 (1994) – 10.1016/0034-4877(94)90038-8
• van der Schaft, A. J. & Maschke, B. M. Hamiltonian formulation of distributed-parameter systems with boundary energy flow. Journal of Geometry and Physics 42, 166–194 (2002) – 10.1016/s0393-0440(01)00083-3