Wensheng Yin

A novel synchronous permanent magnet planar motor and its model for control applications

A novel synchronous permanent magnet planar motor (SPMPM) with iron core is proposed. It has higher continuous force compared to the coreless SPMPM. In the novel SPMPM, two sets of windings for generating x-direction thrust and y-direction thrust are perpendicularly fixed in the x-direction slots and y-direction slots of a mover core, respectively. For control system development applications, an electromagnetic model is derived and the analytical method for calculating the model parameters is also reported. The model describes an important characteristic of the novel SPMPM that the x-direction thrust and y-direction thrust are independent of each other. To verify the model and the parameter calculation method, the finite element method (FEM) is used for calculating the phase inductances and electromagnetic forces of an example SPMPM. The results from FEM are in good agreement with the results from the analytical equations. It demonstrates the feasibility and credibility of the proposed model and parameter calculation method to a certain extent.

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.

Electromagnetic Forces Acting on the Planar Armature of a Core-Type Synchronous Permanent-Magnet Planar Motor

The core-type synchronous permanent-magnet planar motor (SPMPM) discussed in this paper includes one or more planar armatures each of which contains two sets of three-phase windings named x-winding and y-winding. For each planar armature, a magnetic field energy equation is established first. This equation describes the mechanism of the coupling between the permanent-magnet array, the x-winding and the y-winding in the core-type SPMPM. By using virtual work principle, x-direction thrust force, y -direction thrust force and vertical force acting on the planar armature are modeling analytically. For eliminating the coupling in these force models, the excitation flux linkages and phase currents are all transformed into d-q synchronous reference frame. From the decoupling force equations, some characteristics of the vertical component of force on the planar armature are obtained. The electromagnetic force model is helpful for the design of the contactless planar bearing and the servo control system of the SPMPM.

Analysis and comparison of two-dimensional permanent-magnet arrays for planar motor

This paper investigates three kinds of permanent-magnet arrays used in planar motors with polarity centers distributed in the lattices of a matrix. The magnetic field of every kind of magnet array is analyzed by analytical methods. First, we give a Laplace equation of magnetic scalar potential and a series of boundary conditions. Then, we derive the analytical expressions of magnet field strength and magnet flux density in the air gap of each kind of magnet array by the method of separation of variables. Finally, we compare the three types of magnet arrays on the basis of the analytical solutions.

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.

Modeling the Static Vertical Force of the Core-Type Permanent-Magnet Planar Motor

The vertical electromagnetic force affects the design of the air bearing or magnetic bearing of a synchronous permanent-magnet planar motor (SPMPM), whereas the static vertical electromagnetic force is one of the important components of the vertical electromagnetic force. This paper discusses the problem of modeling the static vertical force of the SPMPM analytically. First, we obtain an analytical model of the scalar potential and the equations for calculating the magnetic field energies (MFE) in the magnet array and in the air gap. Since the MFE in the yokes is small enough to be neglected, we obtain the overall MFE equation by summing both the air-gap MFE equation and the magnet array MFE equation. Second, using the virtual work principle, we establish an analytical model of the static vertical force. Using this analytical model, we discuss the characteristics of the static vertical force. To verify the usability of the vertical force model, we analyze a magnet array by the analytical method proposed in this paper and by the finite-element method (FEM). The results show that the vertical force model proposed in this paper is approximately equal to the result from the FEM. This indicates that the vertical force model can be used for estimating the value of the static vertical force in a core-type SPMPM. Furthermore, the analytical model produces continuous results in shorter calculation time.

LFT Structured Uncertainty Modeling and Robust Loop-Shaping Controller Optimization for an Ultraprecision Positioning Stage

In this paper, a practical modeling and robust controller optimization strategy is presented for an ultraprecision positioning stage with position-dependent dynamics to achieve ultraprecision positioning accuracy. A linear-fractional-transformation structured uncertainty modeling procedure is proposed to describe the varying dynamics of the stage. The modeling process involves the global curve fitting of frequency response functions and dimensionality reduction for the uncertainty structure so that the uncertainty set could be minimized. Then, a robust loop-shaping controller optimization method is presented to improve the control performances. The optimization objective includes the control bandwidth and the disturbance rejection ability, and μ analysis is employed as a nonconservative robust condition with respect to the structured uncertainty. A genetic algorithm is then utilized to determine the optimal parameters of the controller. Comparative experiments on a developed ultraprecision positioning stage are finally conducted, and the results validate that significant improvements on rising time, settling time, and positioning accuracy have been achieved.

Optimization of a phase stabilization controller for an ultra-precision positioning stage using a structured genetic algorithm

A practical controller optimization method is proposed to improve control performance in response speed and positioning accuracy of an ultra-precision positioning stage. The structural resonance characteristics as well as the time delay effect severely limit the control bandwidth, and the direct drive feature enabled by aerostatic bearing and voice coil motors makes the stage very sensitive to various disturbances. Therefore, a phase stabilization controller is employed owing to its superior performance in suppressing resonances compared with a traditional notch-based controller. By developing candidates of controller structure based on phase stabilization design criteria, the controller design involves the determination of both structure and parameters, which can achieve better performance than merely tuning parameters of a controller with predefined structure. Consequently, the design of structure and parameters of the controller are formulated into an optimization problem, and the objective function considers both control bandwidth and disturbance rejection to obtain balanced improvements of both response speed and positioning accuracy. Then a structured genetic algorithm is applied to optimize the structure and parameters of the controller simultaneously. Experiments are carried out for comparison of the proposed strategy with the traditional notch-based proportional–integral–derivative controller and the manually tuned phase stabilization controller. Comparative experimental results validate that the optimized controller achieves the smallest positioning error and shortest settling time, which demonstrates the effectiveness of the proposed method in practical application.

Augmentation of Propulsion Based on Coil Array Commutation for Magnetically Levitated Stage

This paper focuses on augmenting the propulsion via commutation of coil array for the long-stroke magnetically levitated stage with moving coils, whose mechatronics structure have been defined. The used commutation of coil array is based on the analytical force/torque-decomposing model of the stage and it is characterized by bounding the coil currents. Through this current-bounded commutation, the 1-norm of commutated coil current vector is increased so that the propulsion can be augmented, and simultaneously the infinite norm of commutated coil current vector is limited so that the amplitudes of commutated coil currents are not beyond the capacity of selected coil power amplifiers. By the investigation example of a long-stroke magnetically levitated stage with moving coils, it is theoretically verified that the propulsion (acceleration) can be augmented by 125% as well as the commutated coil currents can be kept within the capacity of selected coil power amplifiers, 3 A. The study results indicate that the propulsion of a magnetically levitated stage can be augmented via current-bounded commutation of coil array rather than via reconfiguring the mechatronics structure of stage or reselecting coil power amplifiers of larger capacity.

Optimal synchronous trajectory tracking control of wafer and reticle stages

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.