Adaptive boundary control of a vibrating cantilever nanobeam considering small scale effects. (October 2020) - Yue, Xinling; Song, Yuhua; Zou, Jianxiao; He, We
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. Highlights: Considering small scale effects, the non-local theory is used. The system is expressed by PDE system. Two controls are designed. Employing Lyapunov functions to prove the ultimate boundedness and system states. Simulation results demonstrate that the effectiveness of the designed controls.