Robust stability and tracking of non-linear systems with modified Prandtl-Ishlinskii hysteresis model

Abstract

This paper introduces a method to guarantee robust stability of nonlinear systems with modified Prandtl-Ishlinskii (PI) hysteresis model and presents a tracking controller design method to compensate the effect of hysteretic non-linearity. In order to make hysteresis model closer to the real hysteretic behaviour, a modified PI hysteresis model which is described by a non-symmetric play operator with unknown slopes is adopted. Using an operator theoretic approach, the modified PI hysteresis model is represented as a generalised Lipschitz operator and a bounded parasitic term. To guarantee robust stability of the controlled systems with hysteresis, a robust condition using robust right coprime factorisation is used. To ensure the output tracking performance, a non-linear tracking controller is designed. Simulation results are presented to validate the effectiveness of the proposed control design method.