Operator-based robust control for nonlinear systems with Prandtl–Ishlinskii hysteresis

This article presents an operator-based robust control method for nonlinear systems with Prandtl–Ishlinskii (PI) hysteresis. On the existence of the hysteresis, the system usually exhibits undesirable oscillations and even instability. While addressing the hysteresis, PI model is adopted to describe it. Especially, the PI model is decomposed into two terms: an invertible part and a disturbance part. In this way, the invertible part could be considered as a part of the nonlinear system. Based on the concept of Lipschitz's operator and the robust right coprime factorisation condition, a robust control design scheme is given to guarantee the bounded input bounded output stability of the obtained system. Further, a tracking operator design method is given to ensure the control system output-tracking performance under the existence of the disturbance part. Numerical simulation results are presented to validate the effectiveness of the proposed method.