Modeling and identification of nonlinear distributed parameter dynamics of the micro-cantilever

The micro-cantilever used in atomic force microscopy is a spatially distributed and flexible mechanical system. An accurate model of the micro-cantilever is essential for the accurate tip positioning and force sensing. Traditional lumped parameter model will lose the spatial dynamics. There are also some unknown nonlinear dynamics in the nominal Euler-Bernoulli distributed parameter model. In this study, an intelligent distributed parameter modeling approach is proposed for the micro-cantilever. A nominal Euler-Bernoulli beam model is derived first. To compensate unknown nonlinear dynamics, a nonlinear term is added in the nominal model. To implement numerically, the infinite-dimensional partial differential equation (PDE) model is reduced into a finite-dimensional ordinary differential equation (ODE) model based on the Galerkin method. Finally, a neural network based intelligent learning approach is developed to learn the unknown nonlinearities from the input-output data. The effectiveness of the proposed intelligent modeling approach is verified by the simulations.