Modelling and neural adaptive vibration control for three-dimensional Timoshenko beam with output restrictions and external disturbances

Abstract

In this paper, the dynamic modelling and adaptive boundary control of a three-dimensional Timoshenko beam are presented for vibration suppression. In order to ensure that no modal information is left out, partial differential equations (PDEs) are employed to describe the nonlinear dynamic characteristics of the system by applying the extended Hamilton’s principle. Based on the established model, barrier Lyapunov functions (BLFs) are utilised for dealing with system output restrictions. For practical consideration, parameter uncertainties and external disturbances are also taken into account. Under the proposed neural adaptive control scheme, undesirable elastic vibration of the three-dimensional Timoshenko beam is restricted and constrained within given bounds even subject to external perturbations, without needing to know any system parameters. The system stability is proved by the Lyapunov’s direct method. The control performance is verified via using numerical simulations.

KEYWORDS:

• Three-dimensional Timoshenko beam
• PDE modelling
• neural adaptive boundary control
• output restrictions
• vibration suppression
• external disturbances

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61873296].

Notes on contributors

Xueyan Xing

Xueyan Xing received the B.S. degree from Northeastern University, Shenyang, China, in 2015, and the M.S. degree from the Harbin Institute of Technology, Harbin, China, in 2017, the Ph.D. degree from Beihang University, Beijing, China. She is now a research fellow in Univeristy of Sussex. Her current research interests include distributed-parameter systems, human-robot interaction control and vibration control.

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 Beihang University. His research interests include motion control, intelligent control and robust control.