Blanken, L.L.G.

Boeren, F.A.J.

Bruijnen, D.J.H.

Oomen, T.A.E.

English

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 Iterative feedforward control with application to a wafer stageCitation for published version (APA):Blanken, L. L. G., Boeren, F. A. J., Bruijnen, D. J. H., & Oomen, T. A. E. (2015). Iterative feedforward controlwith application to a wafer stage. In 34th Benelux Meeting on Systems and Control, March 24-26, 2015,Lommel, Belgium (pp. 112)Document status and date:Published: 01/01/2015Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 05. Oct. 2023Iterative Feedforward Control with Application to a Wafer StageLennart Blanken1, Frank Boeren1, Dennis Bruijnen2, Tom Oomen11Eindhoven University of Technology, Dept. of Mechanical Engineering, Control Systems Technology, The Netherlands2Philips Innovation Services, Mechatronics Technologies, Eindhoven, The Netherlandsl.l.g.blanken@student.tue.nlIntroductionFeedforward control enables high performance in industrialmotion systems. The key performance enhancement is ingeneral obtained by using feedforward with respect to thereference trajectory. In existing methods, typically a trade-off exists between the attainable performance and the re-quired robustness to changes in the reference. Through newdevelopments in feedforward control it is aimed to attainhigh performance for a class of reference signals.Iterative feedforward control with a rational basisIterative feedforward control can attain high performancefor a class of reference signals [1]. To achieve this, mea-sured data from previous tasks is exploited in conjunctionwith a suitable parametrization for the feedforward con-troller C f f (θ). The need for an approximate model of thesystem, as is common in ILC [2], is eliminated by formu-lating the approach as an instrumental variable-based esti-mation problem as in [3]. The corresponding control con-figuration is depicted in Fig. 1. The parameters θ j+1 in the( j+1)th task result from an optimization problem based onmeasured data from the jth task.r ej yjvj−Cj+1ff (θj+1)Cfb P0C∆ffCjff (θj)Figure 1: Control configuration for iterative feedforward control.Existing approaches focus on a polynomial parametrizationof C f f , see e.g. [1], [4]. However, in [2] it is shown thatfor a rational system P0, a rational parametrization is re-quired for C f f to attain high performance for a class of ref-erence signals. The present research aims to introduce sucha parametrization in iterative feedforward control using sys-tem identification techniques.A system identification approach to iterativefeedforward controlThe present research consists of three main aspects. First,a framework is presented for iterative feedforward controlwith a rational parametrization. This approach is based oninstrumental variables, as in [3], [5]. Second, the limits ofaccuracy are investigated and an iterative algorithm is pro-posed that obtains parameter estimates θ j+1 with optimalaccuracy in terms of variance. Third, an experimental vali-dation of the proposed methodology is presented.Experimental resultsThe proposed approach is implemented on a wafer stage.The experimental results in Fig. 2 and 3 illustrate that supe-rior servo performance is achieved with the proposed ratio-nal parametrization for C f f .0 1 2 3 4 510−610−5Task j [−]||ej ||2 [m]Figure 2: Wafer stage (left) and experimental results (right): su-perior performance is achieved with a rational parametrization (#)compared to a polynomial parametrization (×).0.05 0.1 0.15 0.2−505x 10−6Time [s]e1 [m]0.05 0.1 0.15 0.2−505x 10−6Time [s]Figure 3: Time domain plot of measured error signal e1 inthe first task. Left: polynomial parametrization, right: rationalparametrization.Ongoing researchCurrent work is aimed at generalizing the proposed ap-proach to multivariable systems, extensions to position-dependent behavior, and trajectory design.References[1] S. van der Meulen and R. Tousain and O. Bosgra, Fixed StructureFeedforward Controller Design exploiting Iterative Trials: Application to aWafer Stage and a Desktop Printer, Journal of Dynamic Systems, Measure-ment, and Control, 130(5):0510061-05100616, 2008.[2] J. Bolder and T. Oomen, Rational basis functions in iterative learn-ing control - With experimental verification on a motion system, IEEETransactions on Control Systems Technology, 23(22):722-729, 2015.[3] T. Söderström and P. Stoica, Instrumental Variable Methods forSystem Identification, ser. LNCIS, vol. 57, Springer-Verlag, Germany,Berlin, 1983.[4] F. Boeren, and T. Oomen and M. Steinbuch, Iterative motion feed-forward tuning: A data-driven approach based on instrumental variableidentification, Control Engineering Practice, vol. 37, 11-19, 2015.[5] M. Gilson, H. Garnier, P. Young and P. Van den Hof, Optimal in-strumental variable method for closed-loop identification. IET Control The-ory & Applications, 5(10):1147-1154, 2011.This research is supported by Philips Innovation Services.Book of Abstracts 34th Benelux Meeting on Systems and Control112

Iterative feedforward control with application to a wafer stage

 Iterative feedforward control with application to a wafer stageCitation for published version (APA):Blanken, L. L. G., Boeren, F. A. J., Bruijnen, D. J. H., & Oomen, T. A. E. (2015). Iterative feedforward controlwith application to a wafer stage. In 34th Benelux Meeting on Systems and Control, March 24-26, 2015,Lommel, Belgium (pp. 112)Document status and date:Published: 01/01/2015Document Version:Publisher’s PDF, also known as Version of Record (includes final page, issue and volume numbers)Please check the document version of this publication:• A submitted manuscript is the version of the article upon submission and before peer-review. There can beimportant differences between the submitted version and the official published version of record. Peopleinterested in the research are advised to contact the author for the final version of the publication, or visit theDOI to the publisher's website.• The final author version and the galley proof are versions of the publication after peer review.• The final published version features the final layout of the paper including the volume, issue and pagenumbers.Link to publicationGeneral rightsCopyright and moral rights for the publications made accessible in the public portal are retained by the authors and/or other copyright ownersand it is a condition of accessing publications that users recognise and abide by the legal requirements associated with these rights.            • Users may download and print one copy of any publication from the public portal for the purpose of private study or research.            • You may not further distribute the material or use it for any profit-making activity or commercial gain            • You may freely distribute the URL identifying the publication in the public portal.If the publication is distributed under the terms of Article 25fa of the Dutch Copyright Act, indicated by the “Taverne” license above, pleasefollow below link for the End User Agreement:www.tue.nl/taverneTake down policyIf you believe that this document breaches copyright please contact us at:openaccess@tue.nlproviding details and we will investigate your claim.Download date: 04. Oct. 2023Iterative Feedforward Control with Application to a Wafer StageLennart Blanken1, Frank Boeren1, Dennis Bruijnen2, Tom Oomen11Eindhoven University of Technology, Dept. of Mechanical Engineering, Control Systems Technology, The Netherlands2Philips Innovation Services, Mechatronics Technologies, Eindhoven, The Netherlandsl.l.g.blanken@student.tue.nlIntroductionFeedforward control enables high performance in industrialmotion systems. The key performance enhancement is ingeneral obtained by using feedforward with respect to thereference trajectory. In existing methods, typically a trade-off exists between the attainable performance and the re-quired robustness to changes in the reference. Through newdevelopments in feedforward control it is aimed to attainhigh performance for a class of reference signals.Iterative feedforward control with a rational basisIterative feedforward control can attain high performancefor a class of reference signals [1]. To achieve this, mea-sured data from previous tasks is exploited in conjunctionwith a suitable parametrization for the feedforward con-troller C f f (θ). The need for an approximate model of thesystem, as is common in ILC [2], is eliminated by formu-lating the approach as an instrumental variable-based esti-mation problem as in [3]. The corresponding control con-figuration is depicted in Fig. 1. The parameters θ j+1 in the( j+1)th task result from an optimization problem based onmeasured data from the jth task.r ej yjvj−Cj+1ff (θj+1)Cfb P0C∆ffCjff (θj)Figure 1: Control configuration for iterative feedforward control.Existing approaches focus on a polynomial parametrizationof C f f , see e.g. [1], [4]. However, in [2] it is shown thatfor a rational system P0, a rational parametrization is re-quired for C f f to attain high performance for a class of ref-erence signals. The present research aims to introduce sucha parametrization in iterative feedforward control using sys-tem identification techniques.A system identification approach to iterativefeedforward controlThe present research consists of three main aspects. First,a framework is presented for iterative feedforward controlwith a rational parametrization. This approach is based oninstrumental variables, as in [3], [5]. Second, the limits ofaccuracy are investigated and an iterative algorithm is pro-posed that obtains parameter estimates θ j+1 with optimalaccuracy in terms of variance. Third, an experimental vali-dation of the proposed methodology is presented.Experimental resultsThe proposed approach is implemented on a wafer stage.The experimental results in Fig. 2 and 3 illustrate that supe-rior servo performance is achieved with the proposed ratio-nal parametrization for C f f .0 1 2 3 4 510−610−5Task j [−]||ej ||2 [m]Figure 2: Wafer stage (left) and experimental results (right): su-perior performance is achieved with a rational parametrization (#)compared to a polynomial parametrization (×).0.05 0.1 0.15 0.2−505x 10−6Time [s]e1 [m]0.05 0.1 0.15 0.2−505x 10−6Time [s]Figure 3: Time domain plot of measured error signal e1 inthe first task. Left: polynomial parametrization, right: rationalparametrization.Ongoing researchCurrent work is aimed at generalizing the proposed ap-proach to multivariable systems, extensions to position-dependent behavior, and trajectory design.References[1] S. van der Meulen and R. Tousain and O. Bosgra, Fixed StructureFeedforward Controller Design exploiting Iterative Trials: Application to aWafer Stage and a Desktop Printer, Journal of Dynamic Systems, Measure-ment, and Control, 130(5):0510061-05100616, 2008.[2] J. Bolder and T. Oomen, Rational basis functions in iterative learn-ing control - With experimental verification on a motion system, IEEETransactions on Control Systems Technology, 23(22):722-729, 2015.[3] T. Söderström and P. Stoica, Instrumental Variable Methods forSystem Identification, ser. LNCIS, vol. 57, Springer-Verlag, Germany,Berlin, 1983.[4] F. Boeren, and T. Oomen and M. Steinbuch, Iterative motion feed-forward tuning: A data-driven approach based on instrumental variableidentification, Control Engineering Practice, vol. 37, 11-19, 2015.[5] M. Gilson, H. Garnier, P. Young and P. Van den Hof, Optimal in-strumental variable method for closed-loop identification. IET Control The-ory & Applications, 5(10):1147-1154, 2011.This research is supported by Philips Innovation Services.Book of Abstracts 34th Benelux Meeting on Systems and Control112

Iterative feedforward control with application to a wafer stage

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