On the Characterization of Butterfly and Multiloop Hysteresis Behavior

Vasquez-Beltran, M. A.; Jayawardhana, Bayu; Peletier, Reynier F.

doi:10.1109/tac.2021.3109533

Cited by 8 publications

(2 citation statements)

References 36 publications

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“…The first simple mathematical modeling, analysis, and identification of hysteresis with butterfly loops is presented in [23], where a convex function is added to the output of standard hysteresis operator in order to enforce two inflection points to the standard loop and thereby creating butterfly loops. A general modeling and analysis of a butterfly hysteresis operator based on the Preisach model is presented in [24] and [25]. This class of Preisach operator was first reported in [26], where it is used to describe the shape memory property of a newly purposely-designed piezoelectric materials.…”

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confidence: 99%

Modeling and Analysis of Duhem Hysteresis Operators With Butterfly Loops

Vasquez-Beltran

Jayawardhana

Peletier

2023

IEEE Trans. Automat. Contr.

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In this work, we study and analyze a class of Duhem hysteresis operators that can exhibit butterfly loops. We study first 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.

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confidence: 99%

Modeling and Analysis of Duhem Hysteresis Operators With Butterfly Loops

Vasquez-Beltran

Jayawardhana

Peletier

2023

IEEE Trans. Automat. Contr.

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“…Based on Preisach operators with sign indefinite weighting functions, a number of sufficient conditions on the weighting functions have been introduced that allow to obtain butterfly hysteresis loops [61]. These results were proven and extended in [62].…”

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confidence: 99%

Distributed actuation systems for adaptive optics: from structural modeling to design optimization

Schmerbauch¹

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1 introduction 1 1.1 Adaptive optics 1 1.2 Hysteretic deformable mirror 3 1.3 Outline and contributions 5 1.3.1 Publications 8 2 preliminaries 9 2.1 Design parameters and performance measures 9 2.2 Actuator technologies for deformable mirrors 12 2.3 Space-based applications and deformable mirror technology 17 2.3.1 Deformable mirror requirements 17 2.3.2 State of the art 18 2.4 Hysteresis models for asymmetric butterfly loops 19 2.4.1 Preisach model 19 2.4.2 Duhem model 20 3 semi-analytical plate model 23 3.1 Overview of plate models 23 3.2 Influence functions for the hysteretic deformable mirror 26 3.2.1 Determination of the influence matrix 26 3.2.2 Actuator model 31 3.3 Results and discussion 33 3.3.1 2D pattern for influence functions (Case 1 -5) 33 3.3.2 Least-square fitting 33 3.3.3 Simulation results 34 3.3.4 Comparison to conventional modeling approaches 41 3.4 Concluding remarks 43 4 investigation of the electrical coupling phenomenon 45 4.1 Consideration of the phenomenon in surface fitting process 46 4.2 Fundamental analysis of the electrical coupling 48 4.3 Theoretical frameworks for detailed analysis 50 4.3.1 Model of the hysteretic deformable mirror 51 4.3.2 Modeling of the memory material 53 4.3.3 Sensitivity analysis of the facesheet 56 4.4 Implementation and results 57 4.4.1 Hysteretic deformable mirror model in 3D 57 xi xii contents 4.4.2 Memory material implementation 58 4.4.3 Sensitivity of the facesheet 60 4.4.4 Discussion 63 4.5 Concluding remarks 64 5 development of 2.5d metamaterial actuation array 67 5.1 Introduction 67 5.2 Modular actuation array based on kirigami 68 5.2.1 Design of cut patterns 69 5.2.2 Numerical validation of cut patterns 69 5.2.3 Proof of concept experiments 70 5.3 Application of kirigami array in adaptive optics 74 5.3.1 Design concept of a deformable mirror 74 5.4 Discussion and concluding remarks 81 6 conclusions and outlook 87 a coefficient calculation by solution to poisson's equation 91 a.1 Respective formulas 91 a.2 Numerical integration 91 a.3 Coefficient calculation in Case 1 91 a.3.1 Sub-functions of f 1 94 a.3.2 Sub-functions of f 2 94 a.4 Coefficient calculation in Case 2 95 a.4.1 Sub-functions of f 1 95 a.4.2 Sub-functions of f 2 95 a.5 Coefficient calculation in Case 3 96 a.5.1 Sub-functions of f 1 97 a.5.2 Sub-functions of f 2 97 a.6 Coefficient calculation in Case 4 98 a.6.1 Sub-functions of f 1 99 a.6.2 Sub-functions of f 2 99 a.7 Coefficient calculation in Case 5 100 a.7.1 Sub-functions of f 1 101 a.7.2 Sub-functions of f 2 101 bibliography 103 summary 117 samenvatting 119 zusammenfassung 123

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