Modeling and Analysis of Permanent Magnet Spherical Motors by A Multi-task Gaussian Process Method and Finite Element Method for Output Torque

Permanent magnet spherical motors (PMSMs) operate on the principle of the dc excitation of stator coils and three freedom of motion in the rotor. Each coil generates the torque in a specific direction, collectively they move the rotor to a direction of motion. Modeling and analysis of the output torque are of critical importance for precise position control applications. The control of these motors requires precise output torques by all coils at a specific rotor position, which is difficult to achieve in the three-dimension space. This article is the first to apply the Gaussian process to establish the relationship of the rotor position and the output torque for PMSMs. Traditional methods are difficult to resolve such a complex three-dimensional problem with a reasonable computational accuracy and time. This article utilizes a data-driven method using only input and output data validated by experiments. The multitask Gaussian process is developed to calculate the total torque produced by multiple coils at the full operational range. The training data and test data are obtained by the finite-element method. The effectiveness of the proposed method is validated and compared with existing data-driven approaches. The results exhibit superior performance of accuracy

Covariance localization in the ensemble transform Kalman filter based on an augmented ensemble

With the increased density of available observation data, data assimilation has become an increasingly important tool in marine research. However, the success of the ensemble Kalman filter is highly dependent on the size of the ensemble. A small ensemble used in data assimilation could cause filter divergence, undersampling and spurious correlations. The primary method to alleviate these problems is localization. It can eliminate some spurious correlations and increase the rank of the forecast error covariance matrix. The ensemble transform Kalman filter has been widely used in various studies as a deterministic filter. Unfortunately, the covariance localization cannot be directly applied to ensemble transform Kalman filter. The new covariance localization needs to be presented to adapt the ensemble transform Kalman filter. Based on the method of expanded ensemble and eigenvalue decomposition, this study describes a variation of covariance localization that takes advantage of an unbiased covariance matrix from the expanded ensemble. Experiments described herein show that the new method outperforms the localization methods proposed by others when used in the ensemble transform Kalman filter. The new method yields an analysis estimate that is closer to the true state under different experimental conditions