Dongdong Yu

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.

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.

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.

A cascaded iterative learning motion control scheme for an ultra-precision dual-stage actuated wafer stage

This paper proposes a cascaded iterative learning control (ILC) scheme for the developed wafer stage to achieve ultra-precision motion control performance. In practical motion systems, standard iterative learning control is frequently utilized to realize high tracking performance. However, Q-filter of the standard ILC inevitably causes residual tracking error as a result of a limited cut-off frequency and its non-ideal magnitude characteristic below the cut-off frequency. Therefore, a cascaded ILC scheme is developed to further eliminate the residual tracking error. Specifically, once the tracking error converges to its limit under standard ILC, the learned feedforward signal is frozen and injected to the control loop as constant feedforward. Based on the forzen feedforward, new learning process begins. The same operations are repeated several times until no more improvement can be obtained. Comparative experiments are conducted on our developed wafer stage which consists of a short-stroke stage for fine positioning and a long-stroke stage for coarse positioning. The results show that the proposed cascaded ILC scheme can significantly improve the tracking performance - the moving average (MA) of tracking error is decreased from 14nm to 3nm and the settling time is reduced from 17ms to 4ms. The proposed precision motion control scheme is also suitable for application in practical semiconductor manufacturing equipments and robotic systems.

Frequency Dependent Nonlinear Iterative Learning Control With Application to a Wafer Stage

This paper deals with the control design of a wafer stage setup, catering for the increasing demand for ultra-precision positioning and high throughput devices in line with further miniaturization of the LCD, semiconductor and electronic parts. The developed wafer stage employs a dual stroke principle: a short stroke for fine positioning and a long stroke for coarse positioning. The short stroke is a stage of six-degree-of-freedom with integrated magnetic bearing to counteract the gravity, while the long stroke is a planar motion stage consisting of a integrated three-axis drive motor, which can move along the surface of the Halbach permanent magnet array without generating friction due to being elevated with air bearings. To achieve precision tracking control with zero settling time under high acceleration/velocity motion, iterative learning control has been regarded as an effective means. Linear iterative learning control techniques attenuate the recurring disturbances and amplify the nonrecurring, suffering from a fixed trade-off between convergence rate and noise amplification. In this paper, a frequency dependent amplitude-based nonlinear iterative learning control is proposed. Within a frequency range of interest, the learning gain is continuously updated to improve the control performance of the planar motion stage. Based on the frequency contents of error signal, 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 wafer stage setup shows that the proposed nonlinear iterative learning strategy can realize a remarkable performance which includes nanometer positioning and tracking over large travel ranges, and provides a more desirable means to deal with the convergence rate and noise amplification.Copyright

Design, Control of an Aerostatic X-Y Planar Motion Stage for Precision Positioning

Recently the manufacturing industry has seen increasing demand for micro-components in biomedical, opto-mechatronics, and automotive applications. In particular, a positioning table system combining high accuracy with high speed over large travel ranges. However, the traditional stage constructed by stacking one-axis stages to achieve multiple degrees of freedom motion, are no longer a viable solution to meet the tighter tolerances required by the customers. In order to meet these demands simultaneously, the paper proposes an aerostatic X-Y planar motion stage featuring high resolution (80nm), long stroke, non-contact moving, lightweight and compact structure. It employs a slider consisting of four three-phase coils, which can move along the surface of a standard hal bach permanent magnetic array in a non-contact condition due to being elevated with air bearing. Furthermore, control system is designed including feedback and feed forward controllers. To further improve the tracking performance and eliminating recurrent disturbances, iterative learning control is employed. Performance evaluation results show that the developed planar motion stage can realize a remarkable performance which includes fast settling time and micrometer positioning with high speed over large ranges.

Physical Interpretation on Anti-resonance of Systems with Mechanical Flexibilities and Its Notch Filter

Physical interpretation on anti-resonance in two systems with mechanical flexibilities is presented. It is shown that the anti-resonance is caused by two modes with opposite coefficients determined by the location of actuator and sensor. Notch-type filters are discussed with their physical meaning to compensate the resonance and anti-resonance. It is validated by simulation that for system with non-colocation in the measuring point and working point, compensating resonance would improve the control quality while compensating anti-resonance would not.