Biblio

To decouple the multi-axis motion in the 6 degrees of freedom magnetically levitated actuators (MLAs), this paper introduces a numerical method to model the force and torque distribution. Taking advantage of the Gaussian quadrature, the concept of coil node is developed to simplify the Lorentz integral into the summation of the interaction between each magnetic node in the remanence region and each coil node in the coil region. Utilizing the coordinate transformation in the numerical method, the computation burden is independent of the position and the rotation angle of the moving part. Finally, the experimental results prove that the force and torque predicted by the numerical model are rigidly consistent with the measurement, and the force and torque in all directions are decoupled properly based on the numerical solution. Compared with the harmonic model, the numerical wrench model is more suitable for the MLAs undertaking both the translational and rotational displacements.

This paper presents a novel sensor parameter fault diagnosis method for generally multiple-input multiple-output (MIMO) affine nonlinear systems based on adaptive observer. Firstly, the affine nonlinear systems are transformed into the particular systems via diffeomorphic transformation using Lie derivative. Then, based on the techniques of high-gain observer and adaptive estimation, an adaptive observer structure is designed with simple method for jointly estimating the states and the unknown parameters in the output equation of the nonlinear systems. And an algorithm of the fault estimation is derived. The global exponential convergence of the proposed observer is proved succinctly. Also the proposed method can be applied to the fault diagnosis of generally affine nonlinear systems directly by the reversibility of aforementioned coordinate transformation. Finally, a numerical example is presented to illustrate the efficiency of the proposed fault diagnosis scheme.