Robust control of systems with output hysteresis and input saturation using a finite time stability approach

© 2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.This paper presents a robust control approach for a class of nonlinear dynamic systems consisting of a linear plant connected in series with a hysteresis operator, and affected by control input saturation. Such a class of systems commonly appears in applications concerning smart materials, in particular thermal shape memory alloys wire actuators. The goal of this paper is to design a robust controller, in the form of an output PI law, which ensures set-point regulation with a desired decay rate and, at the same time, accounts for the effects of both hysteresis and input saturation. The resulting controller appears as attractive on the implementation stand-point, since no accurate hysteresis compensator is required. In order to deal with the proposed problem, the hysteretic plant is first reformulated as a linear parameter-varying system. Subsequently, a finite time stability approach is used to impose constraints on the control input. A new set of bilinear matrix inequalities is developed, in order to perform the design with reduced conservatism by properly exploiting some structural properties of the model. The effectiveness of the method is finally validated by means of a numerical case of study. © 2018 IEEE.Peer ReviewedPostprint (author's final draft