This paper is addressed to proving a new Carleman estimate for stochastic parabolic equations. Compared to the existing Carleman estimate in this respect (see [S. Tang and X. Zhang, SIAM J. Control Optim. 48 (2009) 2191–2216.], Thm. 5.2), one extra gradient term involving in that estimate is eliminated. Also, our improved Carleman estimate is established by virtue of the known Carleman estimate for deterministic parabolic equations. As its application, we prove the existence of insensitizing controls for backward stochastic parabolic equations. As usual, this insensitizing control problem can be reduced to a partial controllability problem for a suitable cascade system governed by a backward and a forward stochastic parabolic equation. In order to solve the latter controllability problem, we need to use our improved Carleman estimate to establish a suitable observability inequality for some linear cascade stochastic parabolic system, while the known Carleman estimate for forward stochastic parabolic equations seems not enough to derive the desired inequality.

An improved target field method is proposed for cylindrical coil design to meet the constraint of limited coil volume. It realizes the design of uniform magnetic field coil by predetermining the coil configuration and optimizing the coordinate positions of target field points. Compared with conventional methods, this current density distribution is divided into two symmetric subregions to solve the problem of reserving a gap in the coil center for setting light-passing holes. Therefore, this method is more applicable in miniature atomic devices with optical paths. Moreover, the overall coil performance can be significantly improved using the optimized configuration of coil design parameters. The numerical evaluation shows that the coil designed by this method has remarkable advantages over the nested saddle coil, whose uniformity performance can be improved by about one order of magnitude. Measurements show that relative magnetic field uniformities of the proposed coils reach to 4×10-4 and 3×10-4 along the z-axis in the range of ±0.24 R. The measurement results match well with the theoretical simulation.

Temperature rise caused by losses is a key issue for a high-speed machine. This paper deals with loss calculation and thermal analysis of a high-speed magnetically suspended PM machine (MSPMM) with an actual power of 33 kW and rotation speed of 55 332 r/min. The temperature distribution based on the finite element method is obtained by accounting for various losses, which consist of air friction losses, copper losses, and iron losses of a radial magnetic bearing, a combined radial/axial magnetic bearing, and high-speed permanent magnet machine (PMM). A back-to-back test setup with two MSPMM is fabricated for verifying the calculation results. The predicted maximum temperature of rotor is located in the center of the cylindrical permanent magnet, and the value is 143 °C. Except for the rotor, the estimated maximum temperature of the stator parts is located in tooth tips of the motor stator core, the value is 92 °C, and the error between the predicted temperature and the measured one is 9.3%. Total measured losses are 1644.4 W, the estimated total losses are 1536.7 W, the error is 6.5%, and the efficiency of the machine under test is 94.6%. The loss calculation and thermal analysis results are verified by the measured ones.

Varieties of loss should be optimized to be as less as possible for the stability of permanent magnet in high speed magnetic levitated permanent magnet synchronous motor (HSMLPMSM) rotor and ensure the high efficiency and low temperature of the motor. First, This paper analyzes loss distribution in motor, whose power and rated speed are 100kW 32000rpm, by calculation method. Then, separation of losses of HSMLPMSM is implemented based on drag system without torque meter accounting for its particularity of high power and high speed level. In all kinds of losses, core loss and coil loss can be separated by traditional calculation method with related parameters being tested actually. Besides, windage loss and magnetic bearing (MB) loss can be obtained by deceleration test. Resulting from power balance equations deduced by relationship of drag system's power input and output, eddy current loss (ECL) of rotor can be separated, with compare to its finite element analysis (FEA) results and analytical results. In the end, with thermal-electromagnetic coupled (TEC) analysis, loss separation results are validated via temperature rise experiment indirectly.

The magnetic bearing's (MB) performance is determined by its electromagnetic and mechanical parameters, which should be optimized to meet the working requirements. Many optimal methods of MB have been only focused on a single objective, which may be limited to a small amount of aspects, while other important ones are ignored. A multiobjective optimization (MOO) model to design the MB considered for a better comprehensive property is proposed in this paper. After modeling the equivalent circuit model whose simplification has been clarified by finite element method, we provide the constraints and optimal objectives in the shape of analytical expression. First, every single objective is solved to get utilization by complex method, then, a novel concept of utilization vector is proposed to calculate the weighting coefficients to resolve the MOO problem, by chaotic local search particle swarm optimization with the constraints as penalty functions. MOO design methods are applied for one type of two-degree-of-freedom hybrid MB, and this method could obtain a better balanced overall result, improving the levitated force and decreasing flux density in the air gap.

In this Note, we study the local null controllability and the cost estimate for a class of multidimensional quasilinear parabolic equations with homogeneous Dirichlet boundary conditions and an arbitrary located internal controller. Unlike the known result for one space dimension, we need to consider the problem in the frame of classical solutions. The key point is to improve the regularity of control function for smooth data, which is a consequence of a new observability inequality for linear parabolic equations with an explicit estimate on the observability constant in terms of the $C^1$-norm of the principle part coefficients. The later is based on a new global Carleman estimate for the linear parabolic equation. To cite this article: X. Liu, X. Zhang, C. R. Acad. Sci. Paris, Ser. I 347 (2009). Dans cette Note, nous étudions la contrôlabilité locale vers zéro et son coût pour une classe d'équations quasi-linéaires paraboliques multidimensionnelles avec une condition homogène de Dirichlet et un contrôle interne. À la différence des résultats connus dans le cas monodimensionel, nous avons besoin de considérer le problème dans le cadre des solutions classiques. Le point clé consiste à améliorer la régularité de la fonction contrôle pour des données régulières. Ceci découle d'une nouvelle inégalité d'observabilité pour les équations linéaires paraboliques dans laquelle la constante d'observabilité est explicite vis-à-vis de la norme $C^1$ des coefficients de la partie principale. À cette fin, on établit une nouvelle inégalité de Carleman globale pour les équations linéaires paraboliques. Pour citer cet article : X. Liu, X. Zhang, C. R. Acad. Sci. Paris, Ser. I 347 (2009).