Tip Tracking Control of Piezoelectric Nano-Actuator with Flexoelectric Size-Dependent Theory

In this paper, feedback control algorithms to tracking a desired path of a piezoelectric size dependent cantilever nanobeam as a nano-actuator are developed. In size dependent piezoelectric nanobeam, the governing Partial Differential Equation (PDE) of motion is obtained based on the non-classical continuum mechanics which introduces material length scale parameters. Nonlinear formulation of isotropic piezoelectric Euler-Bernoulli nanobeam is derived based on consistent size-dependent piezoelectricity theory. By considering geometrically nonlinear and axial displacement of the centroid of nanobeam section, basic nonlinear equations are obtained by Hamilton’s principle and variational approach. In order to reduce the governing partial differential equations into a set of ordinary differential equations (ODEs) the Galerkin method is applied. By introducing the new set of variables the state space model of nanobeam is derived. The control algorithms are employed to achieve an output tracking control based on the state space model of the nanobeam, for the supply voltage as a control input. The effectiveness of the proposed control algorithms and input voltage are illustrated by some numerical simulations.