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Iterative learning control (ILC) enables high performance for motion systems executing repetitive tasks. The robustness filter of ILC enhances the robustness w.r.t. model uncertainties and disturbances, but results in that the repetitive error cannot be eliminated. In this article, a dual-loop ILC (DILC) approach is proposed for precision motion systems to explicitly address the design tradeoff of standard ILC between robustness and tracking performance. In the proposed DILC approach, the standard ILC is paralleled with an additional feedforward signal. When ILC converges, the additional feedforward signal is updated by the converged total feedforward signal, and then, the ILC begins a new iteration. As a result, the nonzero asymptotic error caused by the robustness filter is eliminated by adding an iterative action over the feedforward signal onto ILC. Comparative simulation and experimental results confirm that, compared to ILC, the proposed DILC can significantly enhance the tracking performance without the sacrifice of robustness w.r.t. model uncertainties and disturbances. Application to an ultraprecision wafer stage illustrates that the proposed DILC decreases the peak values of moving average and moving standard deviation of the tracking error by 52.7% and 43.9%, respectively. [ABSTRACT FROM AUTHOR]

Rational basis functions are introduced into iterative learning control to enhance the flexibility towards nonrepeating tasks. At present, the application of rational basis functions either suffers from nonconvex optimization problem or requires the predefinition of poles, which restricts the achievable performance. In this article, a new data-driven rational feedforward tuning approach is developed, in which convex optimization is realized without predefining the poles. Specifically, the optimal parameter which eliminates the reference-induced error is directly solved using the least square method. No parametric model is involved in the parameter tuning process and the optimal parameter is estimated using the measured data. In the noisy condition, it is proved that the estimated optimal parameter is unbiased and the estimation accuracy in terms of variance is analysed. The performance of the proposed approach is tested on an ultraprecision wafer stage. The experimental results confirm that high performance is achieved using the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents linear-fractional-trans-formation (LFT)-structured uncertainty state-space modeling for robust control of the multiple-input multiple-output (MIMO) ultra-precision wafer stage with flexible structures to meet the challenges of vibration-dependent model uncertainties. Specifically, based on the modal MIMO state-space model, a parametric uncertainty model related with flexible modes is presented, and the uncertainty parameters are structured to a diagonal matrix with the LFT method. Meanwhile, a multiplicative uncertainty model is employed to express the uncertainty in high frequency with respect to ignored high-order modes. Thus, the final uncertainty model is structured with uncertainty parameters and high-frequency uncertainty. Based on the proposed uncertainty model, a comprehensive robust control scheme is proposed. Specifically, the weighting function matrixes are designed by the loop-shaping approach, and a $\mu$ analysis is employed to achieve a nonconservative solution with respect to the structured uncertainty. A standard stability criterion of a $\bf{M} \boldsymbol{\Delta}$ structure system is then utilized to determine the system stability by the largest structure singular value. Comparative experiments on a developed ultra-precision wafer stage are finally conducted, and the results validate that the proposed method achieves significant improvements on control performance, robustness, and robust stability in all exposure fields. [ABSTRACT FROM AUTHOR]

In precision motion systems, well-designed feedforward control can effectively compensate for the reference-induced error. Compared to iterative learning control (ILC), data-based fixed-structure feedforward control (DFFC) possesses robustness against reference variations, but results in mediocre performance in exactly repeating tasks. In this paper, a novel data-based switching feedforward control (DSFC) approach is synthesized to well balance the tradeoff between the extrapolation capabilities and servo performance. Specifically, a theoretical framework is developed for the proposed DSFC approach, where the feedforward control is switched between ILC and DFFC according to whether the successive references are repeated or not. When operating in the DFFC mode, a new iterative parameter tuning algorithm is proposed to enable the performance enhancement compared to the pre-existing DFFC and overcome the limitation of the allowable reference variations. Furthermore, an unbiased estimate method for the convolution matrix of the (process) sensitivity function is developed based on the impulse response experiment. No parametric model is required throughout the proposed DSFC procedure, and the optimal parameters of the DFFC mode can be unbiasedly estimated. Experimental results on an ultraprecision wafer stage confirm that the proposed DSFC combines advantages of ILC and DFFC, and achieves high performance for both repeating and varying tasks. [ABSTRACT FROM AUTHOR]

With high velocity/acceleration and nanometer level motion accuracy requirements, the flexible dynamic behavior of ultraprecision wafer stage motion systems will significantly induce structural deformation, deteriorate control performance, and consequently, influence the final lithography accuracy. Inspired by this challenge, a new pole assignment control is proposed in this paper for multiinput–multiout (MIMO) systems with flexible structures. Specifically, through a closed-loop subspace identification and a modal approach, the modal state-space model is expressed as a diagonal subspace form that presents each rigid and flexible mode in these individual subspaces. Based on this model, a full-state feedback control architecture with a MIMO pole assignment control algorithm is developed to realize the modes’ control aims. The proposed control strategy is applied to a developed ultraprecision wafer stage. Comparative experiments were conducted on a single-input–single-output control, a MIMO control method with linear quadratic regulator control, and the proposed MIMO pole assignment algorithm. The results validate that the proposed scheme could achieve better disturbance rejection performance, transient performance, and excellent tracking accuracy in practical ultraprecision applications. [ABSTRACT FROM AUTHOR]

Wafer stage is an important mechatronic unit of industrial lithography tool for manufacturing integrated circuits. This paper presents a novel state/model-free variable-gain discrete sliding mode control (DSMC) to suppress the unmolded position-dependent dynamics and disturbances in the nanopositioning wafer stage. The proposed DSMC is essentially composed of feedforward control term, linear feedback control term, and nonlinear switching control term, which can be designed separately. The gain of the switching control term is meaningfully designed to be variable to balance the tradeoff between the robustness and the chattering. Data-driven parameter optimization approach is employed to achieve the optimal controller parameters of the typically nonlinear controller, where off-line parameter updating is iteratively carried out based on the input/output data to minimize a predefined objective function. This scheme facilitates a rapid implementation without either a parameter model or a state observer, and excellent tracking performance with the optimal controller parameters. Moreover, the closed-loop stability is analyzed, and the proposed DSMC is finally implemented on an ultraprecision wafer stage developed in our lab. Comparative experimental results demonstrate that it not only achieves nanoscale tracking accuracy but also possesses promising robustness to position-dependent dynamics and disturbances. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM PUBLISHER]

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 Aitken’s 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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]

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. [ABSTRACT FROM PUBLISHER]