Operator-based Robust Nonlinear Control for System with Generalized PI Hysteresis

In this paper, robust nonlinear control for nonlinear uncertain systems preceded by hysteresis is considered by using operator based robust right coprime factorization approach. Since not all hysteresis model is suitable in operator-theoretic based settings, one generalized Prandtl-Ishlinskii hysteresis model and its inverse model are introduced. The properties of the models are summarized, which imply the availability of the generalized PI model. Then, an operator based control design with feedforward and feedback control operators is proposed. Based on operator based robust right coprime factorization condition, the system is robustly stable and output tracking performance can be realized by designing the feedforward controller. Moreover, as for the modelling error and other uncertainties, a tracking operator can be added for realizing the perfect tracking performance. Finally, the effectiveness of the proposed method is confirmed by numerical simulations.