Neural networks based identification and compensation of rate-dependent hysteresis in piezoelectric actuators

Abstract This paper presents a method of the identification for the rate-dependent hysteresis in the piezoelectric actuator (PEA) by use of neural networks. In this method, a special hysteretic operator is constructed from the Prandtl–Ishlinskii (PI) model to extract the changing tendency of the static hysteresis. Then, an expanded input space is constructed by introducing the proposed hysteretic operator to transform the multi-valued mapping of the hysteresis into a one-to-one mapping. Thus, a feedforward neural network is applied to the approximation of the rate-independent hysteresis on the constructed expanded input space. Moreover, in order to describe the rate-dependent performance of the hysteresis, a special hybrid model, which is constructed by a linear auto-regressive exogenous input (ARX) sub-model preceded with the previously obtained neural network based rate-independent hysteresis sub-model, is proposed. For the compensation of the effect of the hysteresis in PEA, the PID feedback controller with a feedforward hysteresis compensator is developed for the tracking control of the PEA. Thus, a corresponding inverse model based on the proposed modeling method is developed for the feedforward hysteresis compensator. Finally, both simulations and experimental results on piezoelectric actuator are presented to verify the effectiveness of the proposed approach for the rate-dependent hysteresis.