Construction of Expanded Input Space for Modeling Hysteretic Systems

A neural model for hysteresis based on expanded input space is proposed in this article. In this method, the behavior of hysteresis is considered as a dynamic system that can be described by a nonlinear state space equation containing hysteretic state. In order to transfer the multi-valued mapping of hysteresis into a one-to-one mapping, an expanded input space involving the original input variable and a so-called Duhem operator is constructed. Thus, the neural networks can be employed to approximate the relation between the hysteretic state and the output of the system that is also the output of hysteresis. The proposed model has a simple architecture that can be easily implemented for on-line adaptation for the model in case of the unexpected change of operating environment. Furthermore, the dynamic performance of the model is improved because of the existence of Duhem operator. Finally, the method is used to the modeling of hysteresis in a piezoelectric actuator.