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

Authors: Mingcong Deng, Changan Jiang, Akira Inoue

Addresses: Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-Naka, Kita-Ku, Okayama 700-8530, Japan. ' Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-Naka, Kita-Ku, Okayama 700-8530, Japan. ' Graduate School of Natural Science and Technology, Okayama University, 3-1-1 Tsushima-Naka, Kita-Ku, Okayama 700-8530, Japan

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.

Keywords: robust control; Prandtl-Ishlinskii hysteresis model; right coprime factorisation; non-symmetric play hysteresis operator; robust tracking; robust stability; nonlinear systems; modelling; tracking control; controller design; simulation.

DOI: 10.1504/IJMIC.2010.033841

International Journal of Modelling, Identification and Control, 2010 Vol.10 No.1/2, pp.29 - 36

Published online: 02 Jul 2010 *

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