Decompositions and coalescing eigenvalues of symmetric definite pencils depending on parameters

In this work, we consider symmetric positive definite pencils depending on two parameters. That is, we are concerned with the generalized eigenvalue problem $A(x)-\lambda B(x)$, where $A$ and $B$ are symmetric matrix valued functions in ${\mathbb R}^{n\times n}$, smoothly depending on parameters $x\in \Omega\subset {\mathbb R}^2$; further, $B$ is also positive definite. In general, the eigenvalues of this multiparameter problem will not be smooth, the lack of smoothness resulting from eigenvalues being equal at some parameter values (conical intersections). We first give general theoretical results on the smoothness of eigenvalues and eigenvectors for the present generalized eigenvalue problem, and hence for the corresponding projections, and then perform a numerical study of the statistical properties of coalescing eigenvalues for pencils where $A$ and $B$ are either full or banded, for several bandwidths. Our numerical study will be performed with respect to a random matrix ensemble which respects the underlying engineering problems motivating our study.Comment: 34 pages, 4 figure

A Thermal Analysis of Direct Driven Hydraulics

This paper focuses on thermal analysis of a direct driven hydraulic setup (DDH). DDH combines the benefits of electric with hydraulic technology in compact package with high power density, high performance and good controllability. DDH enables for reduction of parasitic losses for better fuel efficiency and lower operating costs. This one-piece housing design delivers system simplicity and lowers both installation and maintenance costs. Advantages of the presented architecture are the reduced hydraulic tubing and the amount of potential leakage points. The prediction of the thermal behavior and its management represents an open challenge for the system as temperature is a determinant parameter in terms of performance, lifespan and safety. Therefore, the electro-hydraulic model of a DDH involving a variable motor speed, fixed-displacement internal gear pump/motors was developed at system level for thermal analysis. In addition, a generic model was proposed for the electric machine, energy losses dependent on velocity, torque and temperature was validated by measurements under various operative conditions. Results of model investigation predict ricing of temperature during lifting cycle, and flattened during lowering in pimp/motor. Conclusions are drawn concerning the DDH thermal behavior

Active Magnetic Bearing system design featuring a Predictive current control

Active Magnetic Bearing (AMB) technology is becoming attractive for several reasons such as high speed operations, high reliability and vibrations exemption. Moreover, AMB can behave as active vibration dampers and provide a real-time control of the shaft. For all these advantages, AMBs are particularly attractive for high power - high speed applications. These desirable features come at the cost of an increased complexity of the system, which now includes a power electronic converter and a control system dedicated to the AMBs. This paper focus on the overall system design, from the AMB design, to the power electronic converter design and control, for an AMB featuring Wheatstone bridge winding configuration. The magnetic design has been developed analytically and validated by means of Finite Elements simulation, to generate up to 2kN of axial forces. The power conversion system is based on three full bridges, one to magnetize the bearing and two to control the axial forces independently on the x and y axes. In order to achieve high bandwidth current control able to generate the desired orthogonal forces, a predictive control strategy has been proposed, for the several advantages it can provides such as fast dynamic response, no need of modulation, easy inclusion of nonlinearities and constraints of the system, possibility of incorporating nested control loops in only one loop and the flexibility to include other system requirements in the controller. The control system has been validated in Matlab/PLECS simulation, including the effect of parameters mismatches in the coils

Fast magnetic reconnection: The "ideal" tearing instability in classic, Hall, and relativistic plasmas

Magnetic reconnection is believed to be the driver of many explosive phenomena in Astrophysics, from solar to gamma-ray flares in magnetars and in the Crab nebula. However, reconnection rates from classic MHD models are far too slow to explain such observations. Recently, it was realized that when a current sheet gets sufficiently thin, the reconnection rate of the tearing instability becomes "ideal", in the sense that the current sheet destabilizes on the "macroscopic" Alfv\'enic timescales, regardless of the Lundquist number of the plasma. Here we present 2D compressible MHD simulations in the classical, Hall, and relativistic regimes. In particular, the onset of secondary tearing instabilities is investigated within Hall-MHD for the first time. In the frame of relativistic MHD, we summarize the main results from Del Zanna et al. [1]: the relativistic tearing instability is found to be extremely fast, with reconnection rates of the order of the inverse of the light crossing time, as required to explain the high-energy explosive phenomena.Comment: 12 pages, 6 figures, submitted to the Proceedings of the 12th International Conference on Numerical Modeling of Space Plasma Flows (ASTRONUM-2017

A high-speed permanent-magnet machine for fault-tolerant drivetrains

This paper details the design considerations of a permanent magnet (PM), three phase, high speed, synchronous machine for fault tolerant operation. A multidisciplinary approach to the optimal design of the machine is adopted targeted at minimising the additional losses resulting from faulty operating conditions and accounting for the remedial control strategy implemented. The design of a closed slot, 6 slots, 4 pole machine is presented. The machine is prototyped and tested to validate the analytical-computational performances predicted in the design and analysis stage under healthy and faulty condition