Observer-Based State Feedback Controller for a class of Distributed Parameter Systems

Authors

Jesus Toledo, Yongxin Wu, Hector Ramirez, Yann Le Gorrec

Abstract

This paper aims to propose a finite-dimensional observer-based state feedback controller to stabilize a class of boundary controlled system. To this end, we propose to use an early-lumping approach, where the infinite-dimensional port-Hamiltonian system is first discretized using a structure-preserving method. Then, we build a passive observed-based controller using a Linear Matrix Inequality (LMI) and finally, the controller is interconnected with the infinite-dimensional system in a passive way. Due to its passivity and Hamiltonian structure, this observer-based controller can stabilize not only the discretized lumped parameter system but also the original distributed parameter system. This approach avoids the intrinsic drawback of early lumping approach and spillover effects. Finally, the boundary controlled undamped wave equation is used to illustrate the effectiveness of the proposed controller.

Keywords

Port-Hamiltonian Systems (PHS); Boundary Control Systems (BCS); Linear Matrix Inequalities (LMI)

Citation

• Journal: IFAC-PapersOnLine
• Year: 2019
• Volume: 52
• Issue: 2
• Pages: 114–119
• Publisher: Elsevier BV
• DOI: 10.1016/j.ifacol.2019.08.020
• Note: 3rd IFAC Workshop on Control of Systems Governed by Partial Differential Equations CPDE 2019- Oaxaca, Mexico, 20–24 May 2019

BibTeX

@article{Toledo_2019,
  title={{Observer-Based State Feedback Controller for a class of Distributed Parameter Systems}},
  volume={52},
  ISSN={2405-8963},
  DOI={10.1016/j.ifacol.2019.08.020},
  number={2},
  journal={IFAC-PapersOnLine},
  publisher={Elsevier BV},
  author={Toledo, Jesus and Wu, Yongxin and Ramirez, Hector and Gorrec, Yann Le},
  year={2019},
  pages={114--119}
}

Download the bib file

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