Vibration control and stability analysis of a nanobeam with boundary prescribed performance

Abstract

ABSTRACT In this paper, we present dynamics analysis and vibration control for a nanoscale beam. The nanobeam is modelled based on the modified couple stress theory which incorporates small length scale effects. The governing equation and boundary conditions of the nanobeam are obtained by Hamilton's principle. We design model-based control and adaptive control with output constraints for the control part. Employing a time-varying function to the constraint part, the displacement of the nanobeam can be well limited within a trajectory. By choosing designed parameters appropriately, signals in the nanobeam system converge to a small neighbourhood of zero and the vibration of the nanobeam system is suppressed with prescribed performance. Correspondingly, the simulation results of the proposed control are verified suitable.