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A neural network-based distributed parameter model identification approach for microcantilever

The microcantilever used in micro–nanomanipulator is a spatially distributed and flexible mechanical system. An accurate model of the microcantilever is essential for the accurate tip positioning and force sensing. Traditional lumped parameter model will lose the spatial dynamics. Though the nominal Euler–Bernoulli model is a distributed parameter model, in practice there are still some unknown nonlinear dynamics. In this study, a neural network-based distributed parameter model identification approach is proposed for modelling the microcantilever. First, a nominal Euler–Bernoulli beam model is derived. To compensate unknown nonlinear dynamics, a nonlinear term that needs to be estimated is added in the nominal model. For finite-dimensional implementation, the infinite-dimensional partial differential equation model is reduced into a finite-dimensional ordinary differential equation model using the Galerkin method. Next, a neural network-based intelligent learning approach is developed to learn the unknown nonlinearities from the input–output data. A radial basis function recurrent neural network observer is designed to estimate the finite-dimensional states from a few sensors of measurements. After that, a general regression neural network model is identified to establish the nonlinear spatiotemporal dynamic model between the inputs and outputs. The effectiveness of the proposed neural network-based distributed parameter modelling approach is verified by the simulations on a typical microcantilever.