Boundary output tracking for a flexible beam with tip payload and boundary nonlinear disturbance

Abstract

We study boundary output tracking for a flexible beam with tip payload and boundary nonlinear disturbance. By constructing an infinite-dimensional extended state observer (ESO), the total disturbance is estimated on line. A servomechanism corresponding to the reference signal and servomechanism-based output feedback control law are designed. Under such control law, we prove that the performance boundary output tracks exponentially the reference signal. By virtue of the Riesz basis approach, the Riesz basis generation and exponential stability of an coupled system are verified, and thereby the boundedness of closed-loop system is obtained. Some numerical simulations are presented to illustrate the effectiveness.

Keywords:

• Performance output tracking
• infinite-dimensional extended state observer
• Riesz basis
• flexible beam equation

2020 Mathematics Subject Classifications:

• 37L15
• 93D15
• 93B51
• 93B52

Acknowledgments

The authors would like to thank the anonymous reviewer for their careful reading and constructive suggestions, which substantially improved this paper. This work does not have any conflicts of interest.

Disclosure statement

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

Additional information

Funding

This work was supported by the Natural Science Foundation of Shaanxi Province [grant number 2018JM1051] and the National Natural Science Foundation of China [grant number 61973338].