Kaiming Yang

A Data-Driven Iterative Decoupling Feedforward Control Strategy With Application to an Ultraprecision Motion Stage

This paper develops a data-driven decoupling feedforward control scheme with iterative tuning to meet the challenge of the crosstalk problem in multiple-input multiple-output (MIMO) motion control systems. In contrast to model-based approaches, iterative tuning fully utilizes the available data to address the practical difficulty in obtaining an accurate dynamic model. The MIMO feedforward signal is iteratively updated by minimizing the developed crosstalk criterion. Specifically, to make the optimal problem convex, the MIMO feedforward controller is structuralized with a finite impulse response (FIR) filter and is parameterized by corresponding coefficients. A data-driven unbiased gradient approximation based on the Toeplitz matrix is then developed for updating the parameter vector. Furthermore, to deal with the Hessian inverse problem encountered in the numerical calculation of the update law, a stable inversion method combined with singular value decomposition is employed. The basic characteristics of the proposed scheme, including convergence accuracy and convergence rate, are illustrated through simulation. Finally, the proposed data-driven decoupling control scheme is applied to a developed ultraprecision motion stage, and the results show that the approach can significantly attenuate the servo error caused by the crosstalk problem. This simplicity and accuracy oriented control method without need of dynamic modeling is definitely suitable for industrial applications.

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.

A time-varying Q-filter design for iterative learning control with application to an ultra-precision dual-stage actuated wafer stage

Iterative learning control is known as an effective technique for improving the performance of systems that require repetitive work. In general, a linear time-invariant low-pass Q-filter is employed to provide robustness to modeling errors and model uncertainties, as well as to suppress the noise transmission in the learning process. A lower bandwidth of Q-filter results in less noise amplification but at the cost of decreasing the learning performance. The filter’s bandwidth thus forms a fixed trade-off between attenuation of repetitive errors and amplification of noise. Although linear time-varying Q-filter in finite impulse response type has been proposed, the performance is still unsatisfactory for the filter of this type has a low attenuation rate in high frequency and is unable to obtain a low bandwidth as well. Therefore, in this article, a linear time-varying Q-filter in infinite impulse response type is put forward, providing a better means to deal with the trade-off. To demonstrate that, experiments have been conducted on the developed dual-stage actuated wafer stage, which consists of a short-stroke stage for accurate positioning and a long-stroke stage for coarse positioning. The results illustrate that the proposed method results in a significant improvement in tracking performance, which includes lower converged error and decreased settling time.

Nonlinear iterative learning control applied to an aerostatic X–Y planar motion stage:

The planar motion stage with multiple degrees of freedom, positioning in large travel ranges, has been widely used in high-accuracy applications such as semiconductor fabrication equipment and advanced scientific instruments. To achieve precision motion control, iterative learning control has been regarded as an effective means. However, linear iterative learning control techniques attenuate recurring disturbances while amplifying the non-recurring, suffering a fixed trade-off between convergence rates and noise amplification. In the present paper, an amplitude-based nonlinear iterative learning control is proposed with learning gain continuously updated to improve the control performance of the planar motion stage. For error levels beyond a predefined threshold, additional learning gain will be effectively used to diminish the low-frequency tracking error. Below the threshold, the original low gain value is maintained to avoid high-frequency noise amplification. Performance assessment on the developed non-contact planar motion stage shows that the amplitude-based nonlinear iterative learning strategy can realize a remarkable performance which includes micrometer positioning over large travel ranges, and provides a more desirable means to deal with the convergence rate and noise amplification.

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.

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.

Neural Network Learning Adaptive Robust Control of an Industrial Linear Motor-Driven Stage With Disturbance Rejection Ability

In this paper, a neural network learning adaptive robust controller (NNLARC) is synthesized for an industrial linear motor stage to achieve good tracking performance and excellent disturbance rejection ability. The NNLARC scheme contains parametric adaption part, robust feedback part, and radial basis function (RBF) neural network (NN) part in a parallel structure. The adaptive part and the robust part are designed based on the system dynamics to meet the challenge of parametric variations and uncertain random disturbances. It must be noted that in actual industrial machining situations, precision motion equipment is always disturbed by unknown factors, which usually cannot be described by mathematical models but affect the tracking accuracy significantly. Therefore, the RBF NN part is employed to further approximate and compensate the complicated disturbances with high reconstructing accuracy and fast training rate. The stability of the proposed NNLARC strategy is analyzed and proved through the Lyapunov theorem. Comparative experiments under various external disturbances such as completely unknown disturbance added by polyfoam are conducted on an industrial linear motor stage. The experimental results consistently validate that the proposed NNLARC control strategy can excellently meet the challenge of complicated disturbance in practical applications. The proposed scheme also provides a guidance for control strategy synthesis with both good tracking performance and disturbance rejection.

A Data-Driven Variable-Gain Control Strategy for an Ultra-Precision Wafer Stage With Accelerated Iterative Parameter Tuning

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. To overcome the inherent limitations of fix-gain feedback control and improve the servo performance, a performance-oriented variable-gain control strategy with accelerated iterative parameter tuning is proposed for an ultra-precision wafer stage. The variable-gain controller comprises a fix-gain proportional-integral-derivative (PID) controller and add-on variable-gain elements, which are the focus of this paper. Specifically, the add-on variable-gain elements are significantly designed based on the main tracking error sources and error frequency of different reference trajectory phases. A weighted two-norm regarding the performance indexes of wafer stages, i.e., moving average (MA) and moving standard deviation (MSD) of the tracking error, is synthesized as the objective function, and the data-driven Levenberg-Marquardt-based iterative parameter tuning scheme is employed to find the optimal parameter values of the proposed variable-gain controller. Furthermore, to improve the convergence rate, a multiparameter accelerated iterative method is developed based on Aitkens method. Finally, the proposed variable-gain control strategy is implemented on an ultra-precision wafer stage developed in our laboratory. Comparative experimental results demonstrate that the strategy performs best and achieves excellent improvement on both MA and MSD. During the scanning phase, MA and MSD are less than 1.02 and 2.35 nm, respectively. The proposed variable-gain control strategy is also suitable for other industrial applications.

An Integrated Model-Data-Based Zero-Phase Error Tracking Feedforward Control Strategy With Application to an Ultraprecision Wafer Stage

In precision motion control, well-designed feedforward control can effectively compensate the reference-induced tracking error. To achieve excellent tracking performance such as nanometer accuracy regardless of reference variations, an integrated model-data-based zero-phase error tracking feedforward control (ZPETFC) strategy is synthesized for precision motion systems with complex and nonminimum phase (NMP) dynamics. The feedforward controller comprises a conventional ZPETFC controller and a gain compensation filter structured with symmetric finite impulse response (FIR) filter. Especially, the conventional ZPETFC is predesigned based on the plant model, and consequently, the feedforward controller is parameterized by the gain compensation filter coefficients, which results in excellent capacity for approximating the inverse behavior of the complex and NMP dynamics. In order to compensate the modeling error in the conventional ZPETFC design and improve the tracking performance, a data-based instrumental-variable method with impulse response experiment is developed to obtain the optimal parameter vector under the existence of noise and disturbances. Furthermore, the ridge estimate method using singular value decomposition is employed to guarantee a fast convergent iteration in the case of ill-conditioned Hessian matrix. The proposed ZPETFC strategy enables a convex optimization procedure with the inherent stability in the iterative tuning process, and is finally implemented on a developed ultraprecision wafer stage. Comparative experimental results demonstrate that the strategy is insensitive to reference variations in comparison with iterative learning control, and outperforms preexisting model-based ZPETFC and data-based FIR feedforward control.

Optimal feedforward control with a parametric structure applied to a wafer stage

To meet the ever-increasing requirements for accurate manufacturing equipment, feedforward control has been widely regarded as an effective method. A nominal feedforward controller equals to the inverse model, which conventional model-based approaches could not acquire accurately due to the inevitable model error, the stability of the inverse model and so on. Therefore, a data-based feedforward control based on a parametric structure is proposed. The structure takes acceleration and snap set-points as signal inputs and both paths equip finite impulse response filters. Each finite impulse response filter is parameterized by a series of coefficients, assuming that the difference between the actual output and nominal output is an affine function of these coefficients. The coefficients are obtained from a gradient and Hessian approximation–based algorithm and optimized by minimizing a quadratic objective function. Two methods are proposed to approximate the gradient: the direct approach and the Toeplitz matrix approach. Finally, the proposed algorithm is assessed on a developed wafer stage. The results show that the proposed parametric structure improves the scanning tracking performance and provides a more desirable way to deal with the model with several resonances in low frequency.