This paper focuses on a novel polyurethane-based soft actuator that is fabricated by an electrospinning process. The actuator is a bundle of aligned nanofibers of a polyurethane solution and a salt, which acts as a conductive filler. From the same bundle, three actuators are obtained. Electromechanical tests are performed on one specimen to evaluate the axial displacements and axial forces generated by the actuator, when stimulated by an external electric field. The data generated during the electromechanical tests are used to identify the non-linear dynamics of the specimen by means of a multilayer perceptron. Subsequently, the identified dynamic model is used to design a position control architecture that controls the applied electric field to regulate the axial displacement of a second specimen. Finally, as a proof of concept for the usability of the nanofiber bundle soft actuator, a third specimen is tested in a robotic prototype, in which a rigid link moves thanks to the actuator's contraction capability.