Vibration Control of Strain Gradient Nonlinear Micro-Cantilevers Using Piezoelectric Actuators

Abstract

A closed-loop control algorithm is used for stabilization of a vibrating nonlinearstrain gradient micro Euler-Bernoulli cantilever beam usinglinear piezoelectric actuation.In this paper, the governing partial differential equation (PDE) of the nonlinear strain gradient beam with piezoelectric actuator is obtained. Galerkin projection method is utilized to reduce the system’s PDE equation of motion into a set of nonlinear ordinary differential equation (ODE) model. The nonlinear system is controlled by a robust linear controller which ensures the stability of the nonlinear system. Numerical simulations are investigated to demonstrate the effectiveness and performance of the designed control scheme.