Jinchun Hu

Analysis and Optimization of a New 2-D Magnet Array for Planar Motor

This paper presents a new 2-D permanent-magnet array for a planar motor, in which the angle between the magnetization directions of any two adjacent magnets is 45°. The harmonic model for flux density distribution of the array is solved by the scalar magnetic potential equation and validated by the finite-element method. An analytical model for real-time control is derived by taking the first harmonic of the magnetic flux density distribution. The ignored higher harmonics in z-component of the magnetic flux density distribution is minimized by the genetic algorithm such that the analytical model becomes more accurate. Compared with the well-known Halbach magnet array, the proposed magnet array has lower higher harmonic components and higher z -component of the magnetic flux density, which will reduce the force ripples of the planar motor.

Mean-Square Convergence Analysis of ADALINE Training With Minimum Error Entropy Criterion

Recently, the minimum error entropy (MEE) criterion has been used as an information theoretic alternative to traditional mean-square error criterion in supervised learning systems. MEE yields nonquadratic, nonconvex performance surface even for adaptive linear neuron (ADALINE) training, which complicates the theoretical analysis of the method. In this paper, we develop a unified approach for mean-square convergence analysis for ADALINE training under MEE criterion. The weight update equation is formulated in the form of block-data. Based on a block version of energy conservation relation, and under several assumptions, we carry out the mean-square convergence analysis of this class of adaptation algorithm, including mean-square stability, mean-square evolution (transient behavior) and the mean-square steady-state performance. Simulation experimental results agree with the theoretical predictions very well.

Accuracy- and Simplicity-Oriented Self-Calibration Approach for Two-Dimensional Precision Stages

Departing from previous complicated attempts, this paper studies the self-calibration of 2-D precision metrology stages seriously from an accuracy- and simplicity-oriented perspective. Based on three measurement views with different permutations of an artifact plate on the metrology stage, symmetry, transitivity, and redundance are obtained and utilized to exactly extract the stage error from the measurement data. Particularly, as the determination of the misalignment-error components of the translation measurement view is rather complicated but important in previous research studies, the proposed scheme does not need this costly computation, which significantly simplifies the calculation process. The algorithm is tested by computer simulation, and the results validate that the proposed method can exactly realize the stage error even under the existence of various random measurement noises. The procedure for performing a standard 2-D self-calibration following the proposed scheme is finally introduced for engineers in practical implementations.

Analysis and Design of Novel Overlapping Ironless Windings for Planar Motors

This paper presents novel overlapping ironless windings for permanent magnet planar motors, which have high winding factors and make full use of the magnetic field of the magnet array in the planar motor. A simple analytical model of the planar motors is developed and validated by finite-element method first. Then the winding factors of the ironless windings are derived and used to simplify the analytical model. Furthermore, the design rules of the ironless windings for the planar motor are obtained from the analytical model with winding factors and the ironless windings are optimized for maximum steepness of the planar motor. Compared with the nonoverlapping ironless windings, the novel overlapping ironless windings have a much (up to 25%) larger force with the same copper loss and nearly the same size when the coils of the windings have a large length/width ratio.

A Holistic Self-Calibration Algorithm for

Self-calibration technology is an important approach with the utilization of an artifact plate with mark positions that are not precisely known to calibrate the precision metrology system. In this paper, we study the self-calibration of xy precision metrology systems and present a holistic self-calibration algorithm based on the least squares method. The proposed strategy utilizes three traditional measurement views of an artifact plate on the xy metrology stage and provides relevant symmetry, transitivity, and redundancy. The misalignment errors of all measurement views, particularly errors of the translation view, are totally determined by detailed mathematical manipulations. Consequently, a least-squares-based robust estimation law is synthesized to calculate the stage error even under the existence of random measurement noise. Computer simulation validates that the proposed method can accurately realize the stage error when there is no random measurement noise. Furthermore, the calculation accuracy of the proposed scheme under various random measurement noises is studied, and the results verify that the proposed algorithm can effectively attenuate the effects of random measurement noise. The proposed strategy, in fact, provides a well-understood solution to the xy self-calibration problem for engineers in practical applications.

xy

Recently, the minimum error entropy criterion, an information theoretic alternative to the traditional mean square error criterion, has been successfully used in the contexts of machine learning and signal processing. For system identification, however, the MEE criterion will be no longer suitable if the training data are discrete-valued, since minimizing errors discrete entropy cannot constrain errors dispersion. In this paper, to make the MEE criterion suitable for the discrete-valued data cases, we give a new entropy definition for the discrete random variables, i.e. the @D-entropy, based on Riemann sums for finite size partitions. A probability weighted formula is established to calculate the average partition.This new entropy retains some important properties of the differential entropy and reduces to discrete entropy under certain conditions. Unlike discrete entropy, the @D-entropy is sensitive to the dynamic range of the data, and can be used as a superior optimality criterion in system identification problems. Also, we present a plug-in estimate of @D-entropy, analyze its asymptotic behavior and explore the links to the kernel based and m-spacing based estimates for differential entropy. Finally, the @D-entropy criterion is applied in system identification with coarsely quantized input-output data to search for the optimum parameter set. Monte Carlo simulations demonstrate the performance improvement that may be achieved with the @D-entropy criterion.

Precision Metrology Systems

This paper investigates the robustness, uniqueness, sufficient condition and the necessary condition for the minimum error entropy (MEE) estimation. For the robustness aspect, we show that the MEE estimator for a Gaussian nominal model is robust with respect to a relative entropy mismodeling criterion as well as the minimum mean-square error (MMSE) estimations. For the uniqueness aspect, we demonstrate by means of examples that for the singular case, the optimum solution of the MEE estimation will be nonunique. For the sufficient and the necessary condition, the former is established by the independence condition, and the later by score orthogonality condition. A specific example illustrates that the score orthogonality condition is just a necessary condition and not a sufficient one, because if an estimator satisfies the score orthogonality condition, it may be a local minimum or even a local maximum of the error entropy in a certain direction.

Δ-Entropy: Definition, properties and applications in system identification with quantized data

Informational correlation coefficient (ICC) can be used to measure the degree of observability for a system. In this paper, we define the generalized informational correlation coefficient (GICC), which is suitable for both discrete and continuous random variables. For the case in which the probability density functions (PDFs) are regularly supersummable, we obtain the exact value of GICC. Moreover, for the linear, stochastically autonomous system, we derive the explicit formula for the degree of observability, and prove the equivalence between the proposed measure and the traditional rank condition. Finally, a simple example is given to compare the discrete state case and the continuous state case.

On optimal estimations with minimum error entropy criterion

An optimal synchronous trajectory tracking controller was developed for multi-axis systems. The position synchronization error on each axis was defined as the position difference between this axis and the following axes. The following error of each axis, the synchronization error, and its derivative were considered in the cost function. A Riccati equation was deduced from the Hamilton-Pontryagin equation. The optimal control law was set up from the Riccati equation solution. Simulations of a two-axis system show that the synchronization error can be significantly reduced and the synchronization performance can be adjusted based on the parameters in the cost function.

Measure observability by the generalized informational correlation

As previous self-calibration technologies are mostly limited to 1-D or 2-D metrology systems, a holistic and explicit self-calibration strategy is proposed for 3-D precision metrology stages in this paper. With different alignments of a rigid cubic artifact on the uncalibrated 3-D stage, four measurement views are constructed to provide the symmetry, transitivity, and redundancy of the 3-D stage error. The first-order components of the stage error, i.e., the nonorthogonality and the scale difference, are determined through the first three measurement views with mathematical processing. The residual components of the stage error are then determined through a least square-based calculation law. Additionally, the misalignment error and the artifact error are all identified through rigorous algebraic manipulation, which may be useful as foundation for synthesis of other self-calibration algorithms. Computer simulation is carried out, and the results validate that the proposed scheme can achieve good calibration accuracy even under the existence of various random measurement noises. Experimental results are also presented to provide a preliminary illustration and validation of the proposed approach in practical applications.