Conference Paper

# Sufficient conditions for dissipativity on Duhem hysteresis model

Dept. Discrete Technol. & Production Autom., Univ. of Groningen, Groningen, Netherlands

DOI: 10.1109/CDC.2009.5400790 Conference: Decision and Control, 2009 held jointly with the 2009 28th Chinese Control Conference. CDC/CCC 2009. Proceedings of the 48th IEEE Conference on Source: OAI

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**ABSTRACT:**In this paper, we discuss the dissipativity property of the counterclockwise Duhem operator. Sufficient conditions on the functions which define the Duhem operator are given such that the Duhem operator has counterclockwise input–output dynamics. In particular, an explicit construction of the storage functions satisfying the counterclockwise dissipation inequality is given. The constructed storage function is also related to the underlying anhysteresis function which is commonly used to describe hysteresis in magnetic materials. The results can thus facilitate analysis of systems with the counterclockwise Duhem operator via the dissipativity approach.Automatica 10/2012; 48(10). · 3.13 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we present conditions for the stabilization and regulation of the tracking error for annn-dimensional minimum-phase system preceded by a Prandtl–Ishlinskii hysteresis operator. A general controller structure is considered; however, we assume that an integral action is present. The common Lyapunov function theorem is utilized together with a Linear Matrix Inequality (LMI) condition to show that, under suitable conditions, the tracking error of the system goes to zero exponentially fast when a constant reference is considered. A key feature of this LMI condition is that it does not require the hysteresis effect to be small, meaning that hysteresis inversion is not required. We use this condition together with a periodicity assumption to prove that a servocompensator-based controller can stabilize the system without using hysteresis inversion. Additionally, we draw parallels between our LMI condition and passivity-based results achieved in the literature. We then verify our LMI results in simulation, where we show that the LMI condition can accurately predict the stability margins of a system with hysteresis. Finally, we conduct experiments using a servocompensator-based controller, where we verify the stability of the system and achieve a mean tracking error of 0.5%0.5% for a 200200 Hz sinusoidal reference.Proceedings of the American Control Conference 04/2014; - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper, we discuss the dissipativity property of Duhem hysteresis models. Under some sufficient conditions on the functions which defines the Duhem model, an explicit construction of the storage functions is given which takes into account the data on the anhysteresis function. We present an example on the semi-linear Duhem model.01/2011;

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