Adaptive boundary control of a vibrating cantilever nanobeam considering small scale effects

Xinling Yue; Yuhua Song; Jianxiao Zou; We He

doi:10.1016/j.isatra.2020.05.038

Adaptive boundary control of a vibrating cantilever nanobeam considering small scale effects

ISA Trans. 2020 Oct:105:77-85. doi: 10.1016/j.isatra.2020.05.038. Epub 2020 Jun 16.

Authors

Xinling Yue¹, Yuhua Song², Jianxiao Zou¹, We He³

Affiliations

¹ School of Automation Engineering, University of Electronic Science and Technology of China, Chengdu 611731, China.
² The Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China; The School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
³ The Institute of Artificial Intelligence, University of Science and Technology Beijing, Beijing 100083, China; The School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China. Electronic address: weihe@ieee.org.

PMID: 32616355
DOI: 10.1016/j.isatra.2020.05.038

Abstract

This paper presents vibration control analysis for a cantilever nanobeam system. The dynamics of the system is obtained by the non-local elastic relationship which characterizes the small scale effects. The boundary conditions and governing equation are respectively expressed by several ordinary differential equations (ODE) and a partial differential equation (PDE) with the help of the Hamilton's principle. Model-based control and adaptive control are both designed at the free end to regulate the vibration in the control section. By employing the Lyapunov stability approach, the system state can be proven to be substantiated to converge to zero's small neighbourhood with appropriate parameters. Simulation results illustrate that the designed control is feasible for the nanobeam system.

Keywords: Adaptive control; Cantilever nanobeam; Nonlocal elastic theory; Partial differential equation; Vibration control.