Vibration control of a flexible aerial refuelling hose with input saturation

ABSTRACT

In this study, we consider a boundary control problem of a flexible aerial refuelling hose in the presence of input saturation. To provide an accurate and concise representation of the hose's behaviour, the flexible hose is modelled as a distributed parameter system described by partial differential equations (PDEs). By using the backstepping method, a boundary control scheme is proposed based on the original PDEs to regulate the hose's vibration. An auxiliary system based on a smooth hyperbolic function and a Nussbaum function is designed to handle the effect of the input saturation. Then based on Lyapunov's direct method, the state of the system is proven to converge to a small neighbourhood of zero by appropriately choosing design parameters. Finally, the results are illustrated using numerical simulations for control performance verification.

KEYWORDS:

• Flexible hose
• input saturation
• backstepping
• distributed parameter system
• vibration control

Acknowledgments

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 authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61374048].

Notes on contributors

Zhijie Liu

Zhijie Liu received his B.S. degree from China university of Mining and Technology, Beijing, in 2014. He is currently a Ph.D. student in Beihang University. His research interests include distributed parameter systems.

Jinkun Liu

Jinkun Liu received his B.S., M.S. and Ph.D. degrees from Northeastern University, China, in 1989, 1994 and 1997, respectively. He is currently a professor in Behang University. His research interests include motion control, intelligent control and robust control.

Wei He

Wei He received his B.Eng. degree from College of Automation Science and Engineering, South China University of Technology (SCUT), China, in 2006, and his Ph.D. degree from Department of Electrical & Computer Engineering, the National University of Singapore (NUS), Singapore, in 2011. He worked as a Research Fellow in the Department of Electrical and Computer Engineering, NUS, Singapore, from 2011 to 2012. He is currently working as a full professor in School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China. He has co-authored one book published in Springer and published over 100 international journal and conference papers. He is a senior member of IEEE. His current research interests include robotics, distributed parameter systems and intelligent control systems.