Linear approximation

About: Linear approximation is a research topic. Over the lifetime, 3901 publications have been published within this topic receiving 74764 citations.

Loss Minimizing Control of PMSM with the Use of Polynomial Approximations

Abstract: Normally, look-up table based methods are being utilized for loss minimizing control of permanent magnet synchronous motors (PMSMs). But, numerous repetitive experiments are required to make a look-up table, and the program size becomes bulky. In this work, analytic methods of finding the loss minimizing solution are studied. Since the solution lies either in the interior, or on the voltage limit boundary, two different cases are dealt separately. In both cases, fourth order polynomials are derived. To obtain approximate solutions, methods of order reduction and linear approximation are utilized. The accuracies are good enough for practical use. These approximate solutions are fused into a proposed loss minimizing algorithm (LMA), and implemented in an inverter DSP. Experiments were done with the real PMSM developed for a sport-utility fuel cell electric vehicle (FCEV). The analytically derived minima were justified by experimental evidences, and the dynamic performances over wide speed range were shown to be satisfactory.

Preisach model for the simulation of ferroelectric capacitors

Abstract: The emerging ferroelectric technology needs a reliable model for the simulation of the ferroelectric capacitors. This model would play a crucial role in designing new ferroelectric nonvolatile memories. As a main requirement, such a model must allow the calculation of the polarization variations for an arbitrary voltage applied to the ferroelectric. However, in spite of the large efforts made in modeling, most of the existing solutions fail to satisfy the above requirement or lack a minimal physical background. To address these problems, we developed a model based on a ferroelectric interpretation of the Preisach theory of hysteresis. In this articles, we try to elucidate how this theory, initially developed for ferromagnetic particles, can be adapted to the ferroelectric materials, despite the many differences between the two. Because the Preisach theory assumes a distribution of the coercitive voltages, we try to clarify its physical meaning in the case of the ferroelectric materials and propose a methodology to determine this distribution experimentally. To facilitate the implementation of the model, the experimental results are then fitted by an analytic function and the whole bidimensional distribution is calculated using a linear approximation. To evaluate the validity of the model, we performed simulations using the Spectre® circuit simulator and the results are in very good agreement with the measurements for the saturated hysteresis loops. The differences existing for the partial loops are mainly due to the linear approximation used for the Preisach distribution. This model can be successfully used for the design of the real memories.

A multidimensional upwind scheme for magnetohydrodynamics

Abstract: This paper describes a second-order upwind scheme for multidimensional magnetohydrodynamics, which uses a linear approximation for all Riemann problems except those involving strong rarefactions. This enables it to cope with initial data for which previously published schemes might fail. The condition ▽⊙B = 0 is not enforced in multidimensions, but the numerical problems associated with this are dealt with by adding source terms to the equations, as suggested by Powell. We also show that there are advantages to adding second-order artificial dissipation at shocks.

Exact Solutions of Regge-Wheeler Equation and Quasi-Normal Modes of Compact Objects

Abstract: The well-known Regge–Wheeler equation describes the axial perturbations of the Schwarzschild metric in the linear approximation. From a mathematical point of view it presents a particular case of the confluent Heun equation and can be solved exactly, due to recent mathematical developments. We present the basic properties of its general solution. A novel analytical approach and numerical techniques to study the boundary problems which correspond to quasi-normal modes of black holes and other simple models of compact objects are developed.

Comparison of monolithic and splitting solution schemes for dynamic porous media problems

Abstract: 5 SUMMARY Proceeding from the governing equations describing a saturated poroelastic material with intrinsically 7 incompressible solid and fluid constituents, we compare the monolithic and splitting solution of the different multi-field formulations feasible in porous media dynamics. Because of the inherent solid-fluid momentum 9 interactions, one is concerned with the class of volumetrically coupled problems involving a potentially strong coupling of the momentum equations and the algebraic incompressibility constraint. Here, the 11 resulting set of differential-algebraic equations (DAE) is solved by the finite element method (FEM) following two different strategies: (1) an implicit monolithic approach, where the equations are first 13 discretized in space using stable mixed finite elements and second in time using stiffly accurate implicit time integrators; (2) a semi-explicit-implicit splitting scheme in the sense of a fractional-step method, 15 where the DAE are first discretized in time, split using intermediate variables, and then discretized in space using linear equal-order approximations for all primary unknowns. Finally, a one- and a two-dimensional 17 wave propagation example serve to reveal the pros and cons in regard to accuracy and stability of both solution strategies. Therefore, several test cases differing in the used multi-field formulation, the 19 monolithic time-stepping method, and the approximation order of the individual unknowns are analyzed for varying degrees of coupling controlled by the permeability parameter. In the end, we provide a 21 reliable recommendation which of the presented strategies and formulations is the most suitable for which particular dynamic porous media problem. Copyright q 2009 John Wiley & Sons, Ltd. 23