Neural modeling of rate-dependent and asymmetric hysteresis in ultrasonic motors

Usually, rotary travelling wave ultrasonic motor (RTWUSM) is involved with complex characteristic such as non-symmetric and rate-dependent hysteresis due to the inverse piezoelectric effect in the stator and the dynamics containing in the rotor. It is known that the hysteresis existing in RTWUSM is also a non-smooth nonlinearity with multi-valued mapping. Thus, the modeling of such characteristic of the RTWUSM is a real challenge. In this paper, a rate-dependent hysteretic operator is proposed to extract the rate-dependent and hysteretic features of the motor. Moreover, considering the friction between the rotor and the stator that causes the asymmetry of the minor-loop of the hysteresis, a compensation method is introduced in the neural model. Then, an extended input space involved with the proposed hysteretic operator is constructed to transform the multi-valued of the hysteresis into a one-to-one mapping. Based on the obtained expanded input space, the neural networks can be utilized for modeling of the behavior of the RTWUSM.