Lumped-circuit models for nonlinear inductors exhibiting hysteresis loops
TL;DR: In this article, a new mathematical model of dynamic hysteresis loops is presented, which is completely specified by two strictly monotonically increasing functions: a restoring function f(.) and a dissipation function g(.).
Abstract: A new mathematical model of dynamic hysteresis loops is presented. The model is completely specified by two strictly monotonically increasing functions: a restoring function f(.) and a dissipation function g(.). Simple procedures are given for constructing these two functions so that the resulting model will simulate a given hysteresis loop exactly. The model is shown to exhibit many important hysteretic properties commonly observed in practice such as the presence of minor loops and an increase in area of the loop with frequency. In the case of an iron-core inductor, the mathematical model is shown to be equivalent to a lumped-circuit model, consisting of a nonlinear inductor in parallel with a nonlinear resistor. Extensive experimental investigations using different types of cores show remarkable agreement between results predicted by the model with those actually measured. The most serious limitation of this dynamic model is its inability to predict dc behaviors. For the class of switching circuits where dc solutions are important, a special dc lumped-circuit model is also presented.
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TL;DR: Contrary to what is the case in linear circuit theory, it is shown that an infinite variety of basic algebraic and dynamic elements will be needed in the eventual formulation of a unified theory on device modeling.
Abstract: Two basic approaches to device modeling are presented. The physical approach consists of 4 basic steps: 1) device physics analysis and partitioning, 2) physical equation formulation, 3) equation simplification and solution, and 4) nonlinear network synthesis. The black-box approach consists also of 4 basic steps: 1) experimental observations, 2) mathematical modeling, 3) model validation, and 4) nonlinear network synthesis. Each approach is ilustrated with 2 examples: Gunn Diode and SCR for the physical approach and Hysteretic Inductor and Memristive Device for the black-box approach. While the techniques for carrying out the first 3 steps in each approach presently involve more art than science, a unified theory for carrying out the last step (nonlinear network synthesis) is beginning to emerge. In particular, the universe of all lumped nonlinear circuit elements can now be classified into algebraic and dynamic elements via a completely logical axiomatic approach. Contrary to what is the case in linear circuit theory, it is shown that an infinite variety of basic algebraic and dynamic elements will be needed in the eventual formulation of a unified theory on device modeling. Consequently, these elements are given a complete and in-depth treatment in this paper. This material can also be regarded as a self-contained survey of the state-of-the-art on nonlinear network synthesis.
254 citations
TL;DR: In this paper, the authors derived expressions for various curves of interest to experimenters; among these, the initial magnetization curve, hysteresis loops with specified extremal values of H, and the boundary of the accessible region of the (H, B)-plane.
193 citations
TL;DR: In this paper, the classical Preisach independent domain model is used to capture the essential characteristics of hysteresis nonlinearity in electromagnetic actuators made of soft ferromagnetic material.
Abstract: In this paper, the classical Preisach independent domain model is used to capture the essential characteristics of hysteresis nonlinearity in electromagnetic (EM) actuators made of soft ferromagnetic material. Experimental results demonstrate its ability to accurately model electromagnetic hysteresis for variations in input current, airgap, and orientation. The Preisach model is then inverted and incorporated in an open-loop control strategy that regulates the EM actuator and compensates for hysteretic effects; hysteresis-free regulation of the EM actuator is obtained, for variations in input current, airgap, and orientation. Hysteresis is also effectively compensated for desired force trajectories of frequencies up to 100 Hz. Thus, the experimental results demonstrate consistent performance of the open-loop control strategy based on Preisach model inversion, in satisfactorily regulating the output of the EM actuator to the desired trajectories.
175 citations
Cites background from "Lumped-circuit models for nonlinear..."
...However, these models have limited applicability, as the physical basis of some of the hysteresis characteristics is not completely understood [ 15 ]....
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TL;DR: In this article, a nonlinear dynamic model of a high speed direct acting solenoid valve is presented, which consists of two subsystems ; a proportional Solenoid and a spool assembly.
Abstract: A nonlinear dynamic model of a high speed direct acting solenoid valve is presented. The valve consists of two subsystems ; a proportional solenoid and a spool assembly. These two subsystems are modeled separately. The solenoid is modeled as a nonlinear resistor/inductor combination, with inductance parameters that change with displacement and current. Empirical curve fitting techniques are used to model the magnetic characteristics of the solenoid, enabling both current and magnetic flux to be simulated. The spool assembly is modeled as a spring/mass/damper system. The inertia and damping effects of the armature are incorporated in the spool model. The solenoid model is used to estimate the spool force in order to obtain a suitable damping coefficient value. The model accurately predicts both the dynamic and steady-state response of the valve to voltage inputs. Simulated voltage, current, and displacement results are presented, which agree well with experimental results.
134 citations
TL;DR: In this paper, a new mathematical model of hysteresis, based upon the previous work of Chun and Stromsmoe, is introduced, which not only provides for hystresis loops at frequencies down to dc but allows for extensive control over higher frequency behavior.
Abstract: A new mathematical model of hysteresis, based upon the previous work of Chun and Stromsmoe, is introduced. The model not only provides for hysteresis loops at frequencies down to dc but allows for extensive control over higher frequency behavior. Loop widening with increased frequency can be included, as well as loop narrowing (a phenomenon present in the i-v curves of fluorescent lamps). Loop widening can be reduced to insignificant amounts beyond an upper threshold or can be eliminated all together. Other behavior with frequency variation can be provided once the model is understood. Applications of the model include the simulation of ferrite "memory" cells and the analysis of hysteretic systems capable of operating at arbitrarily low frequencies.
124 citations
References
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01 Jan 1964
TL;DR: Paleomagnetism is the study of the magnetic properties of rocks as discussed by the authors, and it is one of the most broadly applicable disciplines in geophysics, having uses in diverse fields such as geomagnetic, tectonics, paleoceanography, volcanology, paleontology, and sedimentology.
Abstract: Paleomagnetism is the study of the magnetic properties of rocks. It is one of the most broadly applicable disciplines in geophysics, having uses in diverse fields such as geomagnetism, tectonics, paleoceanography, volcanology, paleontology, and sedimentology. Although the potential applications are varied, the fundamental techniques are remarkably uniform. Thus, a grounding in the basic tools of paleomagnetic data analysis can open doors to many of these applications. One of the underpinnings of paleomagnetic endeavors is the relationship between the magnetic properties of rocks and the Earth’s magnetic field. In this chapter, we will review the basic physical principles behind magnetism: what are magnetic fields, how are they produced, and how are they measured? Although many find a discussion of scientific units boring, much confusion arose when paleomagnetists switched from “cgs” to the Système International (SI) units, and mistakes abound in the literature. Therefore, we will explain both unit systems and look at how to convert successfully between them. There is a review of essential mathematical tricks in Appendix A, to which the reader is referred for help.
2,365 citations
Book•
01 Jan 1965
TL;DR: In this paper, the authors present a review of the properties of the magnetic field and its properties in terms of properties such as: 1. The magnetic field, the magnetization vector, the Langevin Formula for Diamagnetic Susceptibility, and the magnetic shell.
Abstract: 1. The Magnetic Field. 1. Historical. 2. The Magnetic field Vector H. 3. The Magnetization Vector M. 4. Magnetic Induction, the Vector B. 5. The Demagnetization Factor D. 6. Energy of Interaction. 7. Magnetic Effects of Currents. The Magnetic Shell. Faradaya s Law. 8. Maxwella s and Lorentza s Equations. 9. The Magnetic Circuit. 10. Dipole in a Uniform Field. 2. Diamagnetic and Paramagnetic Susceptibilities. 1. Introduction. 2. Review of Quantum Mechanical and Other Results. Diamagnetism. 3. The Langevin Formula for Diamagnetic Susceptibility. 4. Susceptibility of Atoms and Ions. 5. Susceptibility of Molecules. Paramagnetism. 6. Curiea s Law. 7. Theoretical Derivations of Curiea s Law. 8. Quantum Mechanical Treatment. 9. Susceptibility of Quasi--free Ions: the Rare Earths. 10. The Effect of the Crystalline Field. 11. The Iron Group Salts. 12. Covalent Binding and the 3d, 4d, 5d, and 5f--6d Transition Groups. 13. Saturation in Paramagnetic Substances. 14. Paramagnetic Molecules. 15. Paramagnetic Susceptibility of the Nucleus. 3. Thermal, Relaxation, and Resonance Phenomena in Paramagnetic Materials. 1. Introduction. Thermal Phenomena. 2. Summary of Thermodynamic Relationships. 3. The Magnetocaloric Effect: The Production and Measurement of Low Temperatures. Paramagnetic Relaxation. 4. The Susceptibility in an Alternating Magnetic Field. 5. Spin--Lattice Relaxation. 6. Spin--spin Relaxation. Paramagnetic Resonance. 7. Conditions for Paramagnetic Resonance. 8. Line Widths: the Effect of Damping. 9. Fine and Hyperfine Structure: the Spin--Hamiltonian. 10. The Spectra of the Transition Group Ions. The 3d group ions. Covalent binding and the 3d, Ad, 5d, and 5f--6d groups. 4/rare earth ions in salts. Transition ions in various host lattices. 11. The Spectra of Paramagnetic Molecules and Other Systems. Paramagnetic gases. Free radicals. Donors and acceptors in semiconductors. Traps, F--centers, etc. Defects from radiation damage. 12. The Three--Level Maser and Laser. 4. Nuclear Magnetic Resonance. 1. Introduction. 2. Line Shapes and Widths. 3. Resonance in Nonmetallic Solids. 4. The Influence of Nuclear Motion on Line Widths and Relaxations. 5. The Chemical Shift: Fine Structure. 6. Transient Effects: the Spin--Echo Method. 7. Negative Temperatures. 8. Quadrupole Effects and Resonance. 9. Nuclear Orientation. 10. Double Resonance. 11. Beam Methods. 5. The Magnetic Properties of an Electron Gas. 1. Statistical and Thermodynamic Functions for an Electron Gas. 2. The Spin Paramagnetism of the Electron Gas. 3. The Diamagnetism of the Electron Gas. 4. Comparison of Susceptibility Theory with Experiment. 5. The De Haas--Van Alphen Effect. 6. Galvanomagnetic, Thermomagnetic, and Magnetoacoustic Effects. 7. Electron Spin Resonance in Metals. 8. Cyclotron Resonance. 9. Nuclear Magnetic Resonance in Metals. 10. Some Magnetic Properties of Superconductors. 6. Ferromagnetism. 1. Introduction. 2. The Classical Molecular Field Theory and Comparison with Experiment. The spontaneous magnetization region. The paramagnetic region. Thermal effects. 3. The Exchange Interaction. 4. The Series Expansion Method. 5. The Bethe--Peierls--Weiss Method. 6. Spin Waves. 7. Band Model Theories of Ferromagnetism. 8. Ferromagnetic Metals and Alloys. 9. Crystalline Anisotropy. 10. Magnetoelastic Effects. 7. The Magnetization of Ferromagnetic Materials. 1. Introduction. 2. Single--Domain Particles. Critical size. Hysteresis loops. Incoherent rotations. Some experimental results. Other effects. 3. Superparamagnetic Particles. 4. Permanent Magnet Materials. 5. Domain Walls. 6. Domain Structure. 7. The Analysis of the Magnetization Curves of Bulk Material. Domain wall movements. Coercive force. Initial permeability. Picture frame specimens. The approach to saturation. Remanence. Nucleation of domains: whiskers. Barkhausen effect. Preisach--type models. External stresses. Minor hysteresis loops. 8. Thermal Effects Associated with the Hysteresis Loop. 9. Soft Magnetic Materials. 10. Time Effects. 11. Thin Films. 8. Antiferromagnetism. 1. Introduction. 2. Neutron Diffraction Studies. 3. Molecular Field Theory of Antiferromagnetism. Behavior above the Neel temperature. The Neel temperature. Susceptibility below the Neel temperature. Sublattice arrangements. The paramagnetic--antiferromagnetic transition in the presence of an applied magnetic field. Thermal effects. 4. Some Experimental Results for Antiferromagnetic Compounds. 5. The Indirect Exchange Interaction. 6. More Advanced Theories of Antiferromagnetism. The series expansion method. The Bethe--Peierls--Weiss method. Spin waves. 7. Crystalline Anisotropy: Spin Flopping. 8. Metals and Alloys. 9. Canted Spin Arrangements. 10. Domains in Antiferromagnetic Materials. 11. Interfacial Exchange Anisotropy. 9. Ferrimagnetism. 1. Introduction. 2. The Molecular Field Theory of Ferrimagnetism. Paramagnetic region. The ferrimagnetic Neel temperature. Spontaneous magnetization. Extension to include additional molecular fields. Triangular and other spin arrangements. Three sublattice systems. Ferromagnetic interaction between sublattices. 3. Spinels. 4. Garnets. 5. Other Ferrimagnetic Materials. 6. Some Quantum Mechanical Results. 7. Soft Ferrimagnetic Materials. 8. Some Topics in Geophysics. 10. Resonance in Strongly Coupled Dipole Systems. 1. Introduction. 2. Magnetomechanical Effects. 3. Ferromagnetic Resonance. 4. Energy Formulation of the Equations of Motion. 5. Resonance in Ferromagnetic Metals and Alloys. 6. Ferromagnetic Resonance of Poor Conductors. 7. Magnetostatic Modes. 8. Relaxation Processes. Relaxation via spin waves in insulators. Relaxation via spin waves in conductors. Fast relaxation via paramagnetic ions. Slow relaxation via electron redistribution. 9. Nonlinear Effects. 10. Spin--Wave Spectra of Thin Films. 11. Electromagnetic Wave Propagation in Gyromagnetic Media. 12. Resonance in Unsaturated Samples. 13. Ferrimagnetic Resonance. 14. Antiferromagnetic Resonance. 15. Nuclear Magnetic Resonance in Ordered Magnetic Materials. 16. The Mossbauer Effect. Appendix I. Systems of Units. Appendix II. Demagnetization Factors for Ellipsoids of Revolution. Appendix III. Periodic Table of the Elements. Appendix IV. Numerical Values for Some Important Physical Constants. Author Index. Subject Index.
1,665 citations
Book•
01 Jan 1958
TL;DR: A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory was given in this article, where the last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases.
Abstract: A series of lectures on the role of nonlinear processes in physics, mathematics, electrical engineering, physiology, and communication theory.From the preface:"For some time I have been interested in a group of phenomena depending upon random processes. One the one hand, I have recorded the random shot effect as a suitable input for testing nonlinear circuits. On the other hand, for some of the work that Professor W. A. Rosenblith and I have been doing concerning the nature of the electroencephalogram, and in particular of the alpha rhythm, it has occurred to me to use the model of a system of random nonlinear oscillators excited by a random input...At the beginning we had contemplated a series of only four or five lectures. My ideas developed pari passu with the course, and by the end of the term we found ourselves with a set of fifteen lectures. The last few of these were devoted to the application of my ideas to problems in the statistical mechanics of gases. This work is both new and tentative, and I found that I had to supplement my course by the writing over of these with the help of Professer Y. W. Lee. "
1,504 citations
Book•
27 Jan 2005
1,152 citations
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TL;DR: In this paper, the main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Abstract: The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
965 citations