Discrete-time Control by Interconnection using energy-preserving collocation methods

Authors

Maximilian Mogler, Paul Kotyczka, Laurent Lefèvre

Abstract

The energy-preserving collocation methods combine a high order of accuracy with an exact discrete-time energy balance equation when discretizing port-Hamiltonian systems. We show how they can be used to translate Control by Interconnection to the discrete-time setting. We set up the discrete-time plant and controller model and compute the discrete-time inputs for which the desired equilibrium of the continuous-time closed-loop system becomes a stable equilibrium of the discrete-time models. To obtain a continuous-time control signal for the plant system in the sampling interval, these discrete inputs are then interpolated by a polynomial. The advantages of the proposed approach at large sampling times are illustrated in simulations using the example of the controlled pendulum.

Keywords

Sampled systems; discrete-time control; Control by Interconnection; energy-preserving collocation methods; energy shaping

Citation

• Journal: IFAC-PapersOnLine
• Year: 2024
• Volume: 58
• Issue: 6
• Pages: 172–177
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2024.08.276
• Note: 8th IFAC Workshop on Lagrangian and Hamiltonian Methods for Nonlinear Control LHMNC 2024- Besançon, France, June 10 – 12, 2024

BibTeX

@article{Mogler_2024,
  title={{Discrete-time Control by Interconnection using energy-preserving collocation methods}},
  volume={58},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2024.08.276},
  number={6},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Mogler, Maximilian and Kotyczka, Paul and Lefèvre, Laurent},
  year={2024},
  pages={172--177}
}

Download the bib file

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