Robust adaptive vibration control of nonlocal strain gradient nanobeams

In this paper, a robust adaptive sliding mode controller is designed to suppress the nonlinear vibration of an uncertain Euler–Bernoulli nanobeam with immovable ends. The Galerkin scheme is applied to convert the obtained non-dimensional partial differential equation to a nonlinear ordinary differential equation. Then, the robust sliding mode controller is designed to stabilize the nonlinear vibration of un-certain nanobeam. Then, considering the fact that most of micro/nano-systems have uncertain dynamics, and there is a paucity of accurate infor-mation about their states, the proposed con-troller is equipped with an extended Kalman filter. Actually, the extended Kalman filter algo-rithm is used to estimate the states of the considered system. Finally, simulation results with various initial conditions are presented to illustrate the effectiveness of the designed control scheme as well as the estimation algorithm