Inverse neural networks modelling of a piezoelectric stage with dominant variable

This paper presents an approach for developing a neural network inverse model of a piezoelectric positioning stage, which exhibits rate-dependent, asymmetric hysteresis. Unlike most piezoelectric actuators being investigated, the stage involves sliding motion with a maximum range of travel of over 10cm and, therefore, frictional disturbances are significant. The proposed inverse model is a feedforward neural network trained using the Levenberg–Marquardt algorithm. Such a static network is capable of modelling the dynamic features of the hysteresis using the velocity signals. However, using both the velocity and the acceleration as inputs results in overfitting. With a rough analytical model of the actuator and by measuring its response to excitation, velocity was identified as the dominant variable. By setting the input space of the neural network to only this dominant variable, an inverse model with good predictive ability is obtained. Its effectiveness in feedforward compensation for position control is experimentally demonstrated by tracking the positioning reference signal with an amplitude of 20 mm and a period of 0.5 and 1 Hz, respectively.