scispace - formally typeset
Search or ask a question
Book

Mathematical models of hysteresis and their applications

01 Jan 2003-Iss: 1
TL;DR: The classical Preisach model of hysteresis, Generalized scalar preisach models of hystresis (GSPH), Vector PREISACH models of HSTs, Stochastic aspects of HS, Superconducting HS, Eddy current HSTS, core losses as mentioned in this paper.
Abstract: The classical Preisach model of hysteresis, Generalized scalar Preisach models of hysteresis, Vector Preisach models of hysteresis, Stochastic aspects of hysteresis, Superconducting hysteresis, Eddy current hysteresis. Core losses.
Citations
More filters
Journal ArticleDOI
TL;DR: The progresses of different modeling and control approaches for piezo-actuated nanopositioning stages are discussed and new opportunities for the extended studies are highlighted.
Abstract: Piezo-actuated stages have become more and more promising in nanopositioning applications due to the excellent advantages of the fast response time, large mechanical force, and extremely fine resolution. Modeling and control are critical to achieve objectives for high-precision motion. However, piezo-actuated stages themselves suffer from the inherent drawbacks produced by the inherent creep and hysteresis nonlinearities and vibration caused by the lightly damped resonant dynamics, which make modeling and control of such systems challenging. To address these challenges, various techniques have been reported in the literature. This paper surveys and discusses the progresses of different modeling and control approaches for piezo-actuated nanopositioning stages and highlights new opportunities for the extended studies.

458 citations

Book
13 Aug 2007
TL;DR: In this article, the authors present a formal analysis of the BIBO stability of the Bouc-Wen model in the limit case n = 1 2.5.1 The limit case (r) = 0 2.3.1 Numerical simulations 5.2.
Abstract: Preface. List of Figures. List of Tables. 1. Introduction 1.1 Objective and contents of the book 1.2 The Bouc-Wen model: origin and literature review 2. Physical consistency of the Bouc-Wen model 2.1 Introduction 2.2 BIBO stability of the Bouc-Wen model 2.2.1 The model 2.2.2 Problem statement 2.2.3 Classi ~ cation of the BIBO stable Bouc-Wen models 2.2.4 Practical remarks 2.3 Free motion of a hysteretic structural system 2.3.1 Problem statement 2.3.2 Asymptotic trajectories 2.3.3 Practical remarks 2.4 Passivity of the Bouc-Wen model 2.5 Limit cases 2.5.1 The limit case n = 1 2.5.2 The limit case (r) = 1 2.5.3 The limit case (r) = 0 2.5.4 The limit case ~ + - = 0 2.6 Conclusion 3 Forced limit cycle characterization of the Bouc-Wen model 3.1 Introduction 3.2 Problem statement 3.2.1 The class of inputs 3.2.2 Problem statement 3.3 The normalized Bouc-Wen model 3.4 Instrumental functions 3.5 Characterization of the asymptotic behavior of the hysteretic output 3.5.1 Technical Lemmas 3.5.2 Analytic description of the forced limit cycles for the Bouc-Wen model 3.6 Simulation example 3.7 Conclusion 4 Variation of the hysteresis loop with the Bouc-Wen model parameters 4.1 Introduction 4.2 Background results and methodology of the analysis 4.2.1 Background results 4.2.2 Methodology of the analysis 4.3 Maximal value of the hysteretic output 4.3.1 Variation with respect to 4.3.2 Variation with respect to 4.3.3 Variation with respect to n 4.3.4 Summary of the obtained results 4.4 Variation of the zero of the hysteretic output 4.4.1 Variation with respect to 4.4.2 Variation with respect to 4.4.3 Variation with respect to n 4.4.4 Summary of the obtained results 4.5 Variation of the hysteretic output with the Bouc-Wen model parameters 4.5.1 Variation with respect to 4.5.2 Variation with respect to 4.5.3 Variation with respect to n 4.5.4 Summary of the obtained results 4.6 The four regions of the Bouc-Wen model 4.6.1 The linear region Rl 4.6.2 The plastic region Rp 4.6.3 The transition regions Rt and Rs 4.7 Interpretation of the normalized Bouc-Wen model parameters 4.7.1 The parameters and 4.7.2 The parameter 4.7.3 The parameter n 4.8 Conclusion 5 Robust identification of the Bouc-Wen model parameters 5.1 Introduction 5.2 Parameter identi ~ cation for the Bouc-Wen model 5.2.1 Class of inputs 5.2.2 Identi ~ cation methodology 5.2.3 Robustness of the identi ~ cation method 5.2.4 Numerical simulation example 5.3 Modeling and identi ~ cation of a magnetorheological damper 5.3.1 Some insights into the viscous + Bouc-Wen model for shear mode MR dampers 5.3.2 Alternatives to the viscous + Bouc-Wen model for shear mode MR dampers 5.4 Identi ~ cation methodology for the viscous + Dahl model . . 5.4.1 Numerical simulations 5.5 Conclusion 6 Control of a system with a Bouc-Wen hysteresis 6.1 Introduction and problem statement 6.2 Control design and stability analysis 6.3 Numerical simulation 6.4 Conclusion A Mathematical background A.1 Existence and uniqueness of solutions A.2 Concepts of stability A.3 Passivity and absolute stability A.3.1 Passivity in mechanical systems A.3.2 Positive realness A.3.3 Sector functions A.3.4 Absolute stability A.4 Input-output properties References. Index.

299 citations

Journal ArticleDOI
TL;DR: This paper presents a modified Prandtl-Ishlinskii (P-I) (MPI) model for the asymmetric hysteresis description and compensation of piezoelectric actuators, and a generalized input function is introduced to replace the linear input function in the CPI model.
Abstract: This paper presents a modified Prandtl-Ishlinskii (P-I) (MPI) model for the asymmetric hysteresis description and compensation of piezoelectric actuators. Considering the fact that the classical P-I (CPI) model is only efficient for the symmetric hysteresis description, the MPI model is proposed to describe the asymmetric hysteresis nonlinearity of piezoceramic actuators (PCAs). Different from the commonly used approach for the development of asymmetric P-I models by replacing the classical play operator with complex nonlinear operators, the proposed MPI model still utilizes the classical play operator as the elementary operator, while a generalized input function is introduced to replace the linear input function in the CPI model. By this way, the developed MPI model has a relative simple mathematic format with fewer parameters to characterize the asymmetric hysteresis behavior of PCAs. The benefit for the developed MPI model also lies in the fact that an analytic inverse model of the CPI model can be directly applied for the inverse compensation of the asymmetric hysteresis nonlinearity represented by the developed MPI model in real-time applications. To validate the developed MPI model and the inverse hysteresis compensator, simulation, and experimental results on a piezoceramic actuated platform are presented.

279 citations


Cites background or methods from "Mathematical models of hysteresis a..."

  • ...Inspired by the validation approach of the wiping-out property for the operator-based hysteresis models [15], [27], [28], [39], the wiping-out property of the proposed MPI model is asserted in a geometrical interpretation with the memory curve structure....

    [...]

  • ...By adopting the memory curve [15], [27], [28], [39], it can be shown that the MPI model possesses the congruency property as well....

    [...]

  • ...The wiping-out property and congruency property are essential properties for the validity of the operator-based hysteresis models [15], [28]....

    [...]

Journal Article
TL;DR: An overview of available iron loss models for analytical and numerical machine design methods can be found in this article, where the authors compare different models for numerical and analytical machine design of electrical machines.
Abstract: One important factor in the design process and optimization of electrical machines and drives are iron losses in the core. By using new composite materials and low-loss electrical SiFe steels, the losses in the magnetic flux conducting parts of the machine can be reduced significantly. However, it is necessary to have accurate but also easy implementable iron loss models to take the loss effects into account, preferable already during the first design steps and simulations of new electrical machines.The goal of this paper is to give an overview of available iron loss models and to summarize and compare certain models for analytical and numerical machine design methods.

212 citations

Journal ArticleDOI
TL;DR: In this paper, the application of a generalized play operator capable of characterizing symmetric as well as asymmetric hysteresis properties with output saturation is explored in formulating a generalized Prandtl-Ishlinskii model.
Abstract: Smart actuators, such as shape memory alloy (SMA) and magnetostrictive actuators, exhibit saturation nonlinearity and hysteresis that may be symmetric or asymmetric The Prandtl–Ishlinskii model employing classical play operators has been used to describe the hysteresis properties of smart actuators that are symmetric in nature In this study, the application of a generalized play operator capable of characterizing symmetric as well as asymmetric hysteresis properties with output saturation is explored in formulating a generalized Prandtl–Ishlinskii model The generalized play operator employs different envelope functions under increasing and decreasing inputs to describe asymmetric and saturated output–input hysteresis loops The validity of the proposed generalized model to characterize symmetric and asymmetric hysteresis properties is demonstrated by comparing the model responses with the measured major and minor hysteresis loops of three different types of actuator, namely SMA, magnetostrictive, and piezoceramic actuators The simulation results suggest that the proposed generalized Prandtl–Ishlinskii model can be directly applied for modeling the hysteresis loops of different smart actuators together with the output saturation

182 citations