A Grey-Box Distributed Parameter Modeling Approach for a Flexible Manipulator with Nonlinear Dynamics

The flexible manipulator is a spatially distributed mechanical system. An accurate model of the flexible manipulator is essential for the positioning control of the end effector. In this study, a greybox distributed parameter modeling approach is proposed for the flexible manipulator with unknown nonlinear dynamics. First, a nominal Euler-Bernoulli beam model is derived to describe the linear dynamics. To compensate unknown nonlinear dynamics, a nonlinear term is added in the nominal model.The Galerkin method is used to reduce the infinite-dimensional partial differential equation (PDE) model into a finite-dimensional ordinary differential equation (ODE) model. A neural network is designed to estimate the unknown nonlinearities from the input-output data. The effectiveness of the proposed greybox distributed parameter modeling approach is verified by the simulations on a flexible manipulator.