Fujimoto, Hiroshi

Ohnishi, Wataru

Oomen, Tom

van Zundert, Jurgen

English

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 Balancing On-Sample and Intersample Behavior in Sampled-Data System InversionCitation for published version (APA):Ohnishi, W., van Zundert, J., Fujimoto, H., & Oomen, T. (2020). Balancing On-Sample and Intersample Behaviorin Sampled-Data System Inversion. In R. Carloni, B. Jayawardhana, & E. Lefeber (Eds.), 39th Benelux Meetingon Systems and Control: Book of Abstracts (pp. 107). University of Groningen.Document status and date:Published: 01/01/2020Document 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: 17. Nov. 2023Balancing on-sample and intersample behaviorin sampled-data system inversionWataru Ohnishi1,2, Jurgen van Zundert3, Hiroshi Fujimoto1, Tom Oomen21The University of Tokyo, Graduate School of Engineering, Japan. Email: ohnishi@koseki.t.u-tokyo.ac.jp2Eindhoven University of Technology, Department of Mechanical Engineering, The Netherlands3Demcon Advanced Mechatronics, Best, The Netherlands1 IntroductionSystem inversion is essential in feedforward and learningcontrol. Ideally, perfect tracking can be achieved by ex-act system inversion. Due to a digital controller imple-mentation, the system inversion has to be performed in thediscrete-time domain.2 DescriptionZeros discretized by zero-order-hold can be classified as twotypes: 1) intrinsic zeros corresponding to the system dynam-ics; or 2) discretization zeros due to signal sampling [1].If the plant relative order is even, one of the discretizationzero(s) is located close to z =  1 [2]. The system inversionfor zero at z '  1 brings high-oscillating control input [3]and results in poor inter-sample performance [4].3 ApproachTo balance the on-sample and inter-sample tracking er-ror, a novel sampled-data system inversion shown in Fig-ure 1 is proposed. The single-rate inversion achieves exacttracking on sample at the cost of poor inter-sample perfor-mance, whereas multi-rate inversion achieves better inter-sample performance compromising on-sample tracking er-ror (at control period Tu). In the developed approach, thesystem is decomposed into two parts and the inversion isapplied separately.4 ResultsThe developed approach is applied to a positioning sys-tem shown in Figure 2 with non-equidistant sampling. Asshown in Figure 3, the proposed inversion yields the bet-ter performance compared with the existing approach. Itis concluded that the proposed approach exploits additionaldegrees of freedom for discrete-time system inversion anddemonstrates better performance.References[1] T. Hagiwara, T. Yuasa, and M. Araki, “Stability of the limiting ze-ros of sampled-data systems with zero-and first-order holds,” InternationalJournal of Control, vol. 58, no. 6, pp. 1325–1346, 1993.[2] K. Åström, P. Hagander, and J. Sternby, “Zeros of sampled sys-tems,” Automatica, vol. 20, no. 1, pp. 31–38, 1984.H2 H1intersampleu[k]Hu1[k] y2[k]H1on-sampleH2inversionx̂1[k]Fy[k]r[k] inversionFigure 1: Block diagram of the proposed approach. The discrete-time system H is decomposed into H1 and H2. Multi-rate inversion is applied to H1 for the purpose of inter-sample behavior. Single-rate inversion is applied to H2for the purpose of on-sample behavior.yuFigure 2: Motion system used in simulations and for experimen-tal validation.0 1 2 3 4 5 6 7 810 710 5n1ke(t)k2Figure 3: Continuous-time versus on-sample error in simula-tions. The approach balances the intersample behaviorand the on-sample behavior for continuous-time perfor-mance.[3] K. L. Moore, S. P. Bhattacharyya, and M. Dahleh, “Capabilitiesand limitations of multirate control schemes,” Automatica, vol. 29, no. 4,pp. 941–951, 1993.[4] J. van Zundert, W. Ohnishi, H. Fujimoto, and T. Oomen, “Improv-ing Intersample Behavior in Discrete-Time System Inversion: With Appli-cation to LTI and LPTV Systems,” IEEE/ASME Transactions on Mecha-tronics, vol. 25, no. 1, pp. 55–65, 2020.39th Benelux Meeting on Systems and Control Book of Abstracts107

Balancing On-Sample and Intersample Behavior in Sampled-Data System Inversion

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Balancing On-Sample and Intersample Behavior in Sampled-Data System Inversion

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