Reduced-order observer based output feedback control for a Timoshenko beam

Abstract

This paper proposes observer based controls for a MIMO Timoshenko beam system with disturbances and references from an exosystem, and by further limiting the references and disturbances, also gives reduced-order controls. At first, we propose state feedback controls to guarantee the output regulation problem of a nominal Timoshenko beam system, which is obtained by specially choosing known disturbances and references. This also makes the PDE observer easily designed based on tracking errors only. Then, exosystem observers and their reduced-order forms are proposed in case of different geometric multiplicities and limited conditions of disturbances, references and system uncertainties. This gives observer based robust controls and reduced-order observer based controls. Robust output regulation is proved for the Timoshenko beam under observer based controls. Simulation examples are provided for a Timoshenko beam system with different references and system uncertainties.

Keywords:

• Output regulation
• observer based control
• reduced-order control
• exponential stability

Acknowledgements

The authors would like to sincerely extend their appreciation to the editor-in-chief, the associate editor, and the anonymous reviewers for their constructive comments which helped improve the quality and presentation of this paper.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper was supported by the National Natural Science Foundation of China [grant number 62103038]; the China National Postdoctoral Program for Innovative Talents [grant number BX2021032]; the China Postdoctoral Science Foundation [grant number 2020M680351]; and the Fundamental Research Funds for the Central Universities [grant number FRF-TP-20-109A1].