Blanken, L.L.G.

Koekebakker, S.H.

Oomen, T.A.E.

English

Pure OAI Repository

 Data-driven inverse-model feedforward control using non-causal rational basis functionsCitation for published version (APA):Blanken, L. L. G., Koekebakker, S. H., & Oomen, T. A. E. (2018). Data-driven inverse-model feedforward controlusing non-causal rational basis functions. In 37th Benelux Meeting on Systems and Control, March 27-29, 2018,Soesterberg, The Netherlands (pp. 142-142)Document status and date:Published: 01/01/2018Document 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. 2023Data-Driven Inverse-Model Feedforward Controlusing Non-Causal Rational Basis FunctionsLennart Blanken1, Sjirk Koekebakker2, Tom Oomen1Eindhoven University of Technology, Dept. of Mechanical Engineering, Control Systems Technology, The NetherlandsOcé Technologies B.V., Venlo, The Netherlands. Email: l.l.g.blanken@tue.nlBackgroundFeedforward can compensate for known disturbances beforethese affect the system, enabling high performance. This istypically achieved by inverting a model of the system. Inview of the achievable control performance, the quality ofthe parametric inverse model is crucial. Especially for li-ghtly damped mechatronic systems such as flatbed printers,see Figure 2, such accurate parametric models can be diffi-cult and expensive to obtain due to, e.g., complex dynamics,and numerical issues. This motivates to directly estimatethe inverse model based on measured input/output data, ob-tained in the same setting as the model is going to be usedin, i.e., a feedforward control configuration.Data-Driven Feedforward: Non-Causal ControlIn data-driven feedforward control, measured data is used toiteratively determine a fixed-structure controller F (θ), suchthat the tracking error e = 11+PC (1−PF (θ))r is minimizedwhen F (θ) is applied, see Fig. 1. Optimal tracking perfor-mance, i.e., Ee = 0, ∀r, is achieved if F (z, θ) = P−1(z).The key difficulty is to choose a compact parametrization forF (θ), capable to accurately model the inverse system P−1.r e y−C PfF (θ)uvFigure 1: Control configuration for data-driven feedforward: theparameters θ are iteratively optimized based on measured data.Crucially, if P has non-minimum phase (NMP) zeros, thenP−1 has poles outside the typical stability region. Interestin-gly, this can effectively be dealt with in feedforward, wherenon-causality can be exploited to compensate ‘unstable’ po-les. The aim of this research is to enable non-causal controlusing a suitable parametrization for F (θ).The main contribution of the presented research is the deve-lopment of a compact parametrization for inverse systems,that is suited for inverse-model feedforward control. Cru-cially, the developed parametrization builds on the use of ge-neral non-causal rational orthonormal basis functions (RO-BFs) in L2 [1], to compensate poles outside the usual stabi-lity region. As special cases, causal ROBFs in H2 [2] andfinite impulse response (FIR) models are recovered.Experimental Results: Industrial Flatbed PrinterThe developed approach is applied to the Arizona flatbedprinter, shown in Fig. 2, which has 3 NMP zeros with inputFL [N ] and output xR [m]. The results in Fig. 3 show that:• non-causality, through basis functions in L2, is crucial tocompensate poles outside the typical stability region;• rational functions enable high performance using com-pact models, in contrast to polynomial (FIR) functions.carriagegantry printing surfaceFLFRFyxLxRyFigure 2: Océ Arizona flatbed printer @TU/e CST Motion Lab.−10010f 10[A]0.5 1 1.5 2 2.5−0.500.5Time [s]e 10[mm]Figure 3: Experimental results: non-causal ROBFs ( ) ena-ble infinitely long pre-actuation and post-actuation. Compared to(non-causal) FIR basis functions ( ), which enable only a smalland finite amount of preview, the error e10 is significantly reduced.References[1] L. Blanken, G. Isil, S. Koekebakker, and T. Oomen, “Data-drivenfeedforward learning using non-causal rational basis functions: Applicationto an industrial flatbed printer,” In American Control Conference, 2018.[2] P. Heuberger, P. Van den Hof, and B. Wahlberg. “Modelling andidentification with rational orthogonal basis functions,” Springer-Verlag,London, UK, 2005.Book of Abstracts 37th Benelux Meeting on Systems and Control142

Data-driven inverse-model feedforward control using non-causal rational basis functions

https://pure.tue.nl/ws/files/93839119/BlankenKoeOom2018_blux.pdf

Data-driven inverse-model feedforward control using non-causal rational basis functions

Abstract

Similar works

Full text

Available Versions

Pure OAI Repository