Consistency of the Duhem Model with Hysteresis

Abstract

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 significant physical properties which are inherent to the real data, independent of the exciting input. This paper presents a characterization of different classes of Duhem models in terms of their consistency with the hysteresis behavior. * −,

Adaptive Control for Pure-Feedback Nonlinear Systems Preceded by Asymmetric Hysteresis

“…β+γ . Using [52], for every initial condition h(t 0 ) and h 0 m A bw −δ β+γ , it comes that h ≤ max{|h(t 0 )|, h 0 }. Therefore, the proof is completed.…”

Modeling and analysis of Duhem hysteresis operators with butterfly loops

“…The next three lemmas present properties of the sequences (ζ n ) n∈N 0 and (γ n ) n∈N 0 generated by the recursive composition of the function Y u p+ and Y u p− that will be used in the proof of the main result of this section. Lemma 3.2: Let γ 0 ∈ R. The sequences (ζ n ) n∈N 0 and (γ n ) n∈N 0 generated by (10) and (11) are monotonic in the same direction (i.e. both increasing or both decreasing).…”

“…1 M. A. Vasquez Beltran and B. Jayawardhana are with the Engineering and Technology Institute Groningen, Faculty of Science and Engineering, University of Groningen, 9747AG Groningen, The Netherlands {m.a.vasquez.beltran;b.jayawardhana} @rug.nl 2 R. Peletier is with the Kapteyn Astronomical Institute, Faculty of Science and Engineering, University of Groningen, 9747AG Groningen, The Netherlands r.peletier@rug.nl thorough exposition of these properties and other fundamental mathematical properties can be found in [7], [10], [11]. Control systems properties, where Duhem operator is feedback interconnected with other nonlinear systems, have been studied in literature.…”

Piezoelectric Hysteresis Modeling of Hybrid Driven Three-Dimensional Elliptical Vibration Aided Cutting System Based on an Improved Flower Pollination Algorithm

“…At present, experts and scholars have proposed many mathematical models to describe the nonlinear phenomenon of piezoelectric hysteresis. For example: Arindam Bhattacharjee et al [8] use the Preisach model, which mainly uses multiple Preisach operators and weighted superposition to describe the hysteresis characteristics; Zhou et al [9] use the KP model to describe and model the hysteresis characteristics of piezoelectric materials; Kim et al [10] used the Bouc-Wen model to describe the relationship between the restoring force and displacement of the hysteresis system to describe the piezoelectric hysteresis characteristics; Naser M F et al [11] used the Duhem model, which has clear equations. The hysteresis nonlinearity can be described by adjusting the parameters of the equation; Qing et al [12] proposes a PI mathematical model based on the improvement of the traditional Preisach model to describe the hysteresis characteristics of the piezoelectric actuator.…”