A Monolithic Finite Element Formulation for Magnetohydrodynamics Involving a Compressible Fluid

This work develops a new monolithic finite-element-based strategy for magnetohydrodynamics (MHD) involving a compressible fluid based on a continuous velocity–pressure formulation. The entire formulation is within a nodal finite element framework, and is directly in terms of physical variables. The exact linearization of the variational formulation ensures a quadratic rate of convergence in the vicinity of the solution. Both steady-state and transient formulations are presented for two- and three-dimensional flows. Several benchmark problems are presented, and comparisons are carried out against analytical solutions, experimental data, or against other numerical schemes for MHD. We show a good coarse-mesh accuracy and robustness of the proposed strategy, even at high Hartmann numbers.

NUMERICAL EXPERIMENTS FOR NONLINEAR BURGER’S PROBLEM

The article contains the results of computational experiments for the non-homogeneous Burger’s problem and finding its solution by using the non-classical variational-Cole-Hopf transformation approach. On using exact linearization via Cole-Hopf transformation, as well as the application of the non-classical variational approach, then the non-homogeneous Burger’s problem has been solved. The solution which is obtained by this approach is in a compact form so that the original nonlinear solution is easy to be approximated. The accuracy of this method is dependent on the types of selected basis and its number.

Structural Analysis of 8/6 Switched Reluctance Motor Linear and Non-linear Models

This work presents the process of obtaining the simplified model of a switched reluctance motor (SRM) 8/6. Subsequently, the structure of the single-phase model is analyzed, obtaining an exact linearization and zero dynamics of the system. Finally, the model is linearized at an operating point set at 2000 rpm The model includes Coulomb plus viscous friction nonlinearity and an ideal inverter circuit based on bridge converter topology. The simplified and linear models are simulated and compared in the Matlab®/Simulink software in order to validate the design of a classic controller using the linear model.

On the Backward Path Tracking Control of N-Trailer Systems

This paper considers the lateral control of articulated wheeled vehicles in backward motion. The parameterized articulated vehicle is composed of a car-like truck and N passive trailers, resulting in one single steerable axle. First a nonlinear path tracking control law based on exact linearization of an offset model is reviewed and the general stability conditions of such systems is presented. Second, a stability analysis for some vehicle cases is performed and verified in simulation. The possible application of this path tracking control law in real world articulated vehicles is discussed, and its limitations are shown.

On the Linear Integration of Attraction Choice Models in Business Optimization Problems

Decision problems from various fields (e.g., assortment optimization, product line selection, location planning) require to endogenously incorporate probabilistic choice behavior in dependence of the availability of given choice alternatives. A widely spread demand model in marketing and econometrics to represent such choices is the attraction choice model. Of this model, the well-known multinomial logit model and—in case of multiple latent customer segments—the finite-mixture logit model are special cases. However, integrating such models in optimization problems results in non-linear formulations. Thus, in recent years, several exact linearization approaches have been proposed. These approaches are based on different ideas, and they have appeared independently from each other in different fields of research. Thus, the question arises how these approaches differ and how they relate to each other. In this short communication, we settle this question by arguing that many of the proposed approaches—even though they might seem different at first glance—can be traced back to one of two underlying linearization ideas. Establishing a generic problem, we discuss the two ideas in a unified way by presenting two corresponding general model formulations that are shown to be equivalent. Based upon this, we are able to classify the major publications which integrate some type of attraction choice model in detail. In particular, for each formulation of the analyzed literature, we explain to which extent it is a special case of (one of) the presented generic formulations. This also makes clear under which context-specific conditions certain elements of the generic linearization can be omitted, potentially serving as helpful guideline for future applications of such linearizations.

On the Global Behavior of a Geometric PDAV Controller by Means of a Geometrically Exact Linearization

A complex motion encountered in a number of robotic, industrial and defense applications is the motion of a rigid body when one of its body-fixed axes tracks a desired Pointing Direction while it rotates at high Angular Velocity around the pointing direction (PDAV); during this motion high frequency precession/nutation oscillations arise. This work analyzes the global/local closed-loop behavior induced by a developed geometric, PDAV controller and studies the high frequency precession/nutation oscillations that characterize PDAV motions. This is done via geometrically-exact linearization and via simulation techniques that amount to charting the smooth closed-loop vector fields on the manifold. A method to quickly estimate the frequency of the precession/nutation oscillations is developed and can be used for sizing actuators. A thorough understanding of the behavior of the closed-loop flow induced by the PDAV controller is achieved, allowing the control engineer to anticipate/have a rough estimate of the system closed-loop response.