A survey of the hysteretic Duhem model

The Duhem model is a simulacrum of a com- plex and hazy reality: hysteresis. Introduced by Pierre Duhem to provide a mathematical representation of thermodynamical irreversibility, it is used to describe hysteresis in other areas of science and engineering. Our aim is to survey the relationship between the Duhem model as a mathematical representation, and hysteresis as the object of that representation.Peer ReviewedPostprint (author's final draft

On the characterization of the Duhem hysteresis operator with clockwise input-output dynamics

In this paper we investigate the dissipativity property of a certain class of Duhem hysteresis operator, which has clockwise (CW) input-output (I/O) behavior. In particular, we provide sufficient conditions on the Duhem operator such that it is CW and propose an explicit construction of the corresponding storage function satisfying dissipation inequality of CW systems. The result is used to analyze the stability of a second order system with hysteretic friction which is described by a Dahl model.Comment: Pre-print, revised manuscript, 19 page

Model Predictive Control with Fatigue-Damage Minimization through the Dissipativity Property of Hysteresis Operators

In this paper, we propose an approximation method for the well-known fatigue-damage estimation of rainflow counting (RFC) using the dissipativity property of hysteresis operators that can be embedded in model predictive control (MPC) frameworks. Firstly, we revisit results that establish the equivalence between RFC to an energy dissipation property of an infinite-dimensional operator of the Preisach hysteresis model. Subsequently, we approximate the Preisach model using a finite- dimensional differential Duhem hysteresis model and propose an extended MPC scheme that takes into account the dissipated energy of Duhem hysteresis model as a damage proxy in the optimization problem formulation. Lastly, we present an example of control design for damage minimization in the shaft of a wind turbine where we illustrate the proposed strategy

Characterization of the hysteresis Duhem model

The Duhem model, widely used in structural, electrical and mechanical engineering, gives an analytical description of a smooth hysteretic behavior. In practice, the Duhem model is mostly used within the following black-box approach: given a set of experimental input-output data, how to tune the model so that its output matches the experimental data. It may happen that a Duhem model presents a good match with the experimental real data for a specific input, but does not necessarily keep signi cant physical properties which are inherent to the real data, independently of the exciting input. This paper presents a characterization of different classes of Duhem models in terms of their consistency with the hysteresis behavior.Postprint (published version

Modeling and analysis of Duhem hysteresis operators with butterfly loops

In this work we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study firstly the consistency property of such operator which corresponds to the existence of an attractive periodic solution when the operator is subject to a periodic input signal. Subsequently, we study the two defining functions of the Duhem operator such that the corresponding periodic solutions can admit a butterfly input-output phase plot. We present a number of examples where the Duhem butterfly hysteresis operators are constructed using two zero-level set curves that satisfy some mild conditions