This study proposes an effective scheme for high speed positioning control of a piezoelectric actuator. The proposed approach is based on the combination of a feedforward branch and a proportional integral derivative (PID) feedback controller. The feedforward branch consists of an inverse model of the actuator that includes hysteresis compensation, inverse mechanical transfer function, and electrical losses compensation. In order to avoid using a bulky and costly displacement sensor, a detection model has been developed to compute the displacement of the piezoelectric actuator as a function of the current. This approach has been compared with a regular PID feedback control scheme, and with a feedforward/feedback controller using a sensor. Experiments have been carried out for a 2ms pulse excitation of the actuator. It is shown that the proposed approach allows to combine feedforward advantages (quickness and hysteresis compensation) and feedback advantages (static error and creep cancellation). Moreover, it is shown that the detection model allows to smartly avoid using any mechanical sensor.