The paper presents a modelling and identification of a piezoelectric actuator followed by the feed-forward controller design. A commercial piezoelectric bender, model PL140, from Physik Instrumente Co. is considered. Its physical model is derived using Euler-Bernoulli beam theory. This model is designed to produce accurate data for experiments without risking harm to the actual actuator. Nevertheless, the acquired model, due to its complex structure, is unsuitable for control design. For this purpose, a Hammerstein model is proposed. Its structure comprises a static non-linear component that characterizes hysteresis and a dynamic linear component represented by a stochastic auto-regressive model with external inputs (ARX model). The non-linear component of the Hammerstein model is represented by a shallow neural network. The parameters of the ARX model are estimated by the Bayesian approach. The feedforward controller is based on the independently inverted part of the developed Hammerstein model. The results are illustrated by simulations using the proposed physical model.