Data-Based Motion Control of Wafer Scanners

Heertjes, Marcel

doi:10.1016/j.ifacol.2016.07.918

Cited by 17 publications

(11 citation statements)

References 41 publications

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“…As shown in Figure 2, the expression of the global optimum will be given in (10) and (11) in Section 4.1 based on the feedforward parameterisation in (3) and (4). In Sections 4.2-4.4, the variables required in (10) and (11), including Sr, S p r and the instrumental variable, are derived to make the global optimum calculable.…”

Section: Estimation Of the Optimal Parameter Based On Instrumental Va...mentioning

confidence: 99%

“…The motivations of selecting V (𝜃) in ( 6) as the objective criterion are twofold. First, the resulting optimisation problem is convex and the global optimum 𝜃 opt can be directly obtained from (10) and (11), which is different from the nonconvex optimisation problem suffered when the norm of the reference-induced error is optimised directly. Second, the introduction of the instrumental variable in ( 6) is crucial for the optimisation of parameter estimation accuracy in Sections 4 and 5.…”

Section: Determine the Optimal Parameter Via Instrumental Variablementioning

confidence: 99%

“…The achievable performance is restricted by the inevitable model uncertainties and modelling error, especially for precision motion systems which are generally with complex dynamics [9]. Compared to traditional methods, data-driven methods are carried out using the measured data directly, and no accurate parametric model is required [10,11]. Consequently, the restrictions resulted from the usage of parametric model are greatly mitigated.…”

Section: Introductionmentioning

confidence: 99%

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Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Huang

Yang

Zhu

et al. 2021

IET Control Theory & Appl

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Feedforward control has been widely used to improve the tracking performance of precision motion systems. This paper develops a new data-driven feedforward tuning approach associated with rational basis functions. The aim is to obtain the global optimum with optimal estimation accuracy. First, the instrumental variable is employed to ensure the unbiased estimation of the global optimum. Then, the optimal instrumental variable which leads to the highest estimation accuracy is derived, and a new refined instrumental variable method is exploited to estimate the optimal instrumental variable. Moreover, the estimation accuracy of the optimal parameter is further improved through the proposed parameter updating law. Simulations are conducted to test the parameter estimation accuracy of the proposed approach, and it is demonstrated that the global optimum is unbiasedly estimated with optimal parameter estimation accuracy in terms of variance with the proposed approach. Experiments are performed and the results validate the excellent performance of the proposed approach for varying tasks. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Section: Estimation Of the Optimal Parameter Based On Instrumental Va...mentioning

confidence: 99%

Section: Determine the Optimal Parameter Via Instrumental Variablementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Huang

Yang

Zhu

et al. 2021

IET Control Theory & Appl

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“…In general, stability is not guaranteed with this method. Some works which devised robust stability conditions for the IFT method are asserted in [5, 6], and recent applications of robust IFT controller design methods have been addressed in [7, 8]. Virtual reference feedback tuning (VRFT) [9] is another offline one‐shot method which minimises the (filtered)

{scriptH}_{2}

norm of the difference between a desired reference model and the achieved closed‐loop system.…”

Section: Introductionmentioning

confidence: 99%

Data‐driven approach to iterative learning control via convex optimisation

Nicoletti

Martino

Aguglia

2020

IET Control Theory & Applications

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“…Compared to model-based methods, no parametric model is required and only measured data is used in data-driven methods. 12,13 Iterative learning control (ILC) 14,15 is a widely used data-driven method. In ILC, data measured from the last trail is exploited to generate the feedforward signal for the next trail.…”

Section: Introductionmentioning

confidence: 99%

Data-driven rational feedforward tuning: With application to an ultraprecision wafer stage

Huang

Yang

Zhu

et al. 2019

Proceedings of the Institution of Mechanical Engineers, Part I:

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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.

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Data-Based Motion Control of Wafer Scanners

Cited by 17 publications

References 41 publications

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Data‐driven parameter tuning for rational feedforward controller: Achieving optimal estimation via instrumental variable

Data‐driven approach to iterative learning control via convex optimisation

Data-driven rational feedforward tuning: With application to an ultraprecision wafer stage

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