Discrete-Time Flatness-Based Feedforward Control for the 1D Shallow Water Equations

Authors

Paul Kotyczka

Abstract

Flatness of given outputs for quasilinear 1D hyperbolic systems is conserved under an appropriate port-Hamiltonian spatial discretization. Combining the spatial with a structure-preserving temporal scheme leads to a fully discretized control model of the infinite-dimensional system, which can be exploited for discrete-time trajectory planning. We show that with a suitable approximation of the continuous nonlinear equations, a stable explicit numerical scheme is obtained for flatness-based feedforward control of quasilinear hyperbolic systems. As an example, we consider the 1D shallow water equations and the inverse flow routing problem, i. e. the computation of the upstream discharge trajectory from a given downstream hydrograph. We compare our approach with known results based on the method of characteristics.

Keywords

Port-Hamiltonian systems; nonlinear conservation laws; structure-preserving discretization; geometric integration; discrete-time systems; flatness-based trajectory planning

Citation

• Journal: IFAC-PapersOnLine
• Year: 2019
• Volume: 52
• Issue: 16
• Pages: 42–47
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2019.11.753
• Note: 11th IFAC Symposium on Nonlinear Control Systems NOLCOS 2019- Vienna, Austria, 4–6 September 2019

BibTeX

@article{Kotyczka_2019,
  title={{Discrete-Time Flatness-Based Feedforward Control for the 1D Shallow Water Equations}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.11.753},
  number={16},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Kotyczka, Paul},
  year={2019},
  pages={42--47}
}

Download the bib file

References

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