Piezoelectric motors are resonant vibromotors. They represent a new actuator generation in the field of servo-drives. In particular, the travelling wave ultrasonic motor presents a high torque at low speed, a zero speed torque without feeding, low sensitivity to electromagnetic disturbances as well as being a more compact solution if compared to conventional electromagnetic motors. Much researches has been performed by others to determine an analytical model based on the identification of an electromagnetic equivalent circuit or on exploitation of a theoretical model based on numerical approaches, which use finite elements methods. While leading to satisfactory analysis, these modeling methods can hardly be exploited in the design of control algorithms. Indeed, they require considerable processing resources to generate and visualize the results. For this reason, we introduce in this thesis, an analytical model that is easily adaptable to operational applications and control techniques. The proposed analytical model has been validated by comparing measured characteristics with those obtained in simulations, which was possible thanks to the realization of a modular test bench. The travelling wave ultrasonic motor is characterized by strong non-linearity. It also depends highly on the wear state of the materials, which is difficult to model, and on the contact surface between stator and rotor. In addition, the mechanical resonance frequency experiences drift due to the variations of temperature. These considerations of strong non-linearities and parameter sensitivities of the motor represent a challenge for the study and design of an efficient and robust control strategy. We introduce with this thesis a new control approach that guarantees a closed loop response which is independent of the motor operating point. Moreover, the proposed control method allows to avoid the discontinuities typically present with this type of actuator with a very reasonnable hardware requierments. Finally, an important extension in the product range of the piezoelectric actuators is proposed in the last part of this thesis. It acts to develop an fMRI (functional Magnetic Resonance Imaging) compatible haptic interface with one degree of freedom. The use of a robotic interface in conjunction with an fMRI environment would enable neuroscientists to investigate the brain mechanism used to perform tasks with arbitrary dynamics, and could become a critical tool in neuroscience and rehabilitaiton. There is, however, a major problem for robot working within an fMRI environment : conventional actuators and materials interfere with the strong permanent magnetic field and the fast switching magnetic field gradients. Consequently, non-ferromagnetic materials must be used to avoid forces on the device itself, that can compromise its performance and may result in hazardous conditions for the patient or the medical staff. In addition, the materials should be non-conducting to avoid the generation of eddy currents. The travelling wave ultrasonic motor was used because it provides benefits compared to the conventional electromagnetic actuators. Non-ferromagnetic piezoelectric ceramic material is used and as a result motor operation is not affected by the presence of the strong magnetic fields ecountered in the clinical scanners.