Generalized regression neural network modeling based on inverse Duhem operator and adaptive sliding mode control for hysteresis in piezoelectric actuators

A dynamic generalized regression neural network model based on inverse Duhem operator is proposed to characterize the rate-dependent hysteresis in piezoelectric actuators. As hysteresis is multi-valued mapping, and traditional neural network can only model the system with one-to-one mapping. An inverse Duhem operator is proposed to extract the dynamic property of the hysteresis. Moreover, it can transform the multi-valued mapping of the hysteresis into a one-to-one mapping to suit the input of neural network. In order to compensate the effect of the hysteresis in piezoelectric actuator, the adaptive sliding mode controller with a feedforward hysteresis compensator is developed for the tracking control of the piezoelectric actuator. Experimental results demonstrate superior tracking performance, which validate the practicability and effectiveness of the presented approach.