Stability analysis of repetitive control: The port-Hamiltonian approach

Authors

Federico Califano, Alessandro Macchelli, Claudio Melchiorri

Abstract

This paper deals with two different topics that, at a first sight, could look quite unrelated. The first one is about repetitive control: the scope is to determine a class of linear systems for which such control technique can be successfully applied, i.e. the resulting closed-loop system is stable. In repetitive control schemes, coupled PDEs and ODEs are present, and the idea is to rely on a port-Hamiltonian formulation, and on the properties of passive/dissipative systems to study the behaviour of the closed-loop dynamic. To perform this analysis, novel results dealing with the exponential stabilisation of linear boundary control system with one-dimensional spatial domain in port-Hamiltonian form via finite dimensional linear controllers are presented. This is in fact the second topic discussed in this paper, and the achieved results are applied in order to characterise a class of linear systems for which repetitive control schemes exponentially converge.

Citation

• Journal: 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
• Year: 2017
• Volume:
• Issue:
• Pages: 1894–1899
• Publisher: IEEE
• DOI: 10.1109/cdc.2017.8263926

BibTeX

@inproceedings{Califano_2017,
  title={{Stability analysis of repetitive control: The port-Hamiltonian approach}},
  DOI={10.1109/cdc.2017.8263926},
  booktitle={{2017 IEEE 56th Annual Conference on Decision and Control (CDC)}},
  publisher={IEEE},
  author={Califano, Federico and Macchelli, Alessandro and Melchiorri, Claudio},
  year={2017},
  pages={1894--1899}
}

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References

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