{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:40:49Z","timestamp":1680266449028},"reference-count":39,"publisher":"Walter de Gruyter GmbH","issue":"9","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2021,9,27]]},"abstract":"<jats:title>Zusammenfassung<\/jats:title>\n               <jats:p>Der Beitrag behandelt die Folgeregelung von Flachwasserwellen in einer partiell gef\u00fcllten R\u00f6hre, in der der Fl\u00fcssigkeitspegel durch einen beweglichen Kolben variiert werden kann. Zur Beschreibung der Flachwasserwellen werden die Saint-Venant-Gleichungen in Euler-Koordinaten verwendet, ein quasilineares hyperbolisches Differentialgleichungssystem zweiter Ordnung. Der Beitrag fasst bereits in Vorarbeiten erzielte Ergebnisse zur Flachheit und zum darauf basierenden Steuerungsentwurf zusammen und erweitert diese Resultate um eine einfache auf den linearisierten Modellgleichungen beruhende flachheitsbasierten Folgeregelung. Die Leistungsf\u00e4higkeit der entworfene Folgeregelung wird anhand von Simulationen und experimentellen Studien nachgewiesen.<\/jats:p>","DOI":"10.1515\/auto-2021-0069","type":"journal-article","created":{"date-parts":[[2021,9,8]],"date-time":"2021-09-08T21:00:36Z","timestamp":1631134836000},"page":"795-805","source":"Crossref","is-referenced-by-count":0,"title":["Flachheitsbasierte Trajektorienfolgeregelung von Flachwasserwellen in einer R\u00f6hre mit bewegtem Kolben"],"prefix":"10.1515","volume":"69","author":[{"given":"Jens","family":"Wurm","sequence":"first","affiliation":[{"name":"UMIT - Universit\u00e4t f\u00fcr Gesundheitswissenschaften, Informatik und Technik GmbH , Institut f\u00fcr Automatisierungs- und Regelungstechnik , Eduard-Walln\u00f6fer-Zentrum 1 , , Hall in Tirol , \u00d6sterreich"}]},{"given":"Frank","family":"Woittennek","sequence":"additional","affiliation":[{"name":"UMIT - Universit\u00e4t f\u00fcr Gesundheitswissenschaften, Informatik und Technik GmbH , Institut f\u00fcr Automatisierungs- und Regelungstechnik , Eduard-Walln\u00f6fer-Zentrum 1 , , Hall in Tirol , \u00d6sterreich"}]}],"member":"374","published-online":{"date-parts":[[2021,9,9]]},"reference":[{"key":"2023033110360546346_j_auto-2021-0069_ref_001","doi-asserted-by":"crossref","unstructured":"J.\u2009M. Augenbaum, \u201cA Lagrangian method for the shallow water equations based on a Voronoi mesh \u2013 one dimensional results\u201d, J. Computational Physics, Jg.\u200953, Nr.\u20092, S.\u2009240\u2013265, 1984.","DOI":"10.1016\/0021-9991(84)90040-8"},{"key":"2023033110360546346_j_auto-2021-0069_ref_002","doi-asserted-by":"crossref","unstructured":"G. Bastin and J.-M. Coron, Stability and Boundary Stabilization of 1-D Hyperbolic Systems. Birkh\u00e4user Basel, 2016.","DOI":"10.1007\/978-3-319-32062-5"},{"key":"2023033110360546346_j_auto-2021-0069_ref_003","doi-asserted-by":"crossref","unstructured":"H. Chanson, Environmental Hydraulics for Open Channel Flows. Elsevier Science, 2004.","DOI":"10.1016\/B978-075066165-2.50034-5"},{"key":"2023033110360546346_j_auto-2021-0069_ref_004","doi-asserted-by":"crossref","unstructured":"M.\u2009H. Chaudhry, Open-Channel Flow. Springer-Verlag, 2008.","DOI":"10.1007\/978-0-387-68648-6"},{"key":"2023033110360546346_j_auto-2021-0069_ref_005","doi-asserted-by":"crossref","unstructured":"J.-M. Coron, B. d\u2019Andr\u00e9a-Novel and G. Bastin, \u201cA Lyapunov approach to control irrigation canals modeled by Saint-Venant equations\u201d, in Proceedings of the 1999 European Control Conference (ECC), 1999, S.\u20093178\u20133183.","DOI":"10.23919\/ECC.1999.7099816"},{"key":"2023033110360546346_j_auto-2021-0069_ref_006","doi-asserted-by":"crossref","unstructured":"R. Courant and P. Lax, \u201cOn nonlinear partial differential equations with two independent variables\u201d, Communications on Pure and Applied Mathematics, Jg.\u20092, Nr.\u20092-3, S.\u2009255\u2013273, 1949.","DOI":"10.1002\/cpa.3160020206"},{"key":"2023033110360546346_j_auto-2021-0069_ref_007","doi-asserted-by":"crossref","unstructured":"J. Deutscher, \u201cFinite-time output regulation for linear 2\u00d72 hyperbolic systems using backstepping\u201d, Automatica, Jg.\u200975, S.\u200954\u201362, 2017.","DOI":"10.1016\/j.automatica.2016.09.020"},{"key":"2023033110360546346_j_auto-2021-0069_ref_008","doi-asserted-by":"crossref","unstructured":"M. Fliess, J. L\u00e9vine, P. Martin and P. Rouchon, \u201cFlatness and defect of non-linear systems: introductory theory and examples\u201d, Int. J. Control, Jg.\u200961, Nr.\u20096, S.\u20091327\u20131361, 1995.","DOI":"10.1080\/00207179508921959"},{"key":"2023033110360546346_j_auto-2021-0069_ref_009","doi-asserted-by":"crossref","unstructured":"J.-F. Gerbeau and B. Perthame, \u201cDerivation of viscous Saint-Venant system for laminar shallow water; Numerical validation\u201d, Discrete & Continuous Dynamical Systems - B, Jg.\u20091, Nr.\u20091, S.\u200989\u2013102, 2001.","DOI":"10.3934\/dcdsb.2001.1.89"},{"key":"2023033110360546346_j_auto-2021-0069_ref_010","unstructured":"W. hans Graf and M.\u2009S. Altinakar, Fluvial Hydraulics: Flow and Transport Processes in Channels of Simple Geometry. Wiley, 1998."},{"key":"2023033110360546346_j_auto-2021-0069_ref_011","doi-asserted-by":"crossref","unstructured":"J. de Halleux, G. Bastin, B. d\u2019Andr\u00e9a-Novel and J.-M. Coron, \u201cA Lyapunov approach for the control of multi reach channels modelled by Saint-Venant equations\u201d, IFAC Proceedings Volumes, Jg.\u200934, Nr.\u20096, S.\u20091429\u20131434, 2001.","DOI":"10.1016\/S1474-6670(17)35389-2"},{"key":"2023033110360546346_j_auto-2021-0069_ref_012","doi-asserted-by":"crossref","unstructured":"J. de Halleux, C. Prieur, J.-M. Coron, B. d\u2019Andr\u00e9a-Novel and G. Bastin, \u201cBoundary feedback control in networks of open channels\u201d, Automatica, Jg.\u200939, S.\u20091365\u20131376, 2003.","DOI":"10.1016\/S0005-1098(03)00109-2"},{"key":"2023033110360546346_j_auto-2021-0069_ref_013","doi-asserted-by":"crossref","unstructured":"A. Janon, M. Nodet, C. Prieur and C. Prieur, \u201cGlobal sensitivity analysis for the boundary control of an open channel\u201d, Mathematics of Control, Signals, and Systems, Jg.\u200928, Nr.\u20091, 2015.","DOI":"10.1007\/s00498-015-0151-4"},{"key":"2023033110360546346_j_auto-2021-0069_ref_014","doi-asserted-by":"crossref","unstructured":"T. Kn\u00fcppel and F. Woittennek, \u201cControl design for quasi-linear hyperbolic systems with an application to the heavy rope\u201d, IEEE Trans. Automat. Control, Jg.\u200960(1), S.\u20091365\u20131376, 2015.","DOI":"10.1109\/TAC.2014.2336451"},{"key":"2023033110360546346_j_auto-2021-0069_ref_015","doi-asserted-by":"crossref","unstructured":"T. Kn\u00fcppel, F. Woittennek, I. Boussaada, H. Mounier and S.-I. Niculescu, \u201cFlatness-based control for a non-linear spatially distributed model of a drilling system\u201d, in Low-Complexity Controllers for Time Delay Systems, Ser. Adv. in Delays and Dynamics, A. Seuret, H. \u00d6zbay, C. Bonnet and H. Mounier, Hrsg., Bd.\u20092, Springer-Verlag, 2014, S.\u2009205\u2013218.","DOI":"10.1007\/978-3-319-05576-3_14"},{"key":"2023033110360546346_j_auto-2021-0069_ref_016","doi-asserted-by":"crossref","unstructured":"T. Kn\u00fcppel, F. Woittennek and J. Rudolph, \u201cFlatness based trajectory planning for the shallow water equations\u201d, PAMM Proceedings in Applied Mathematics and Mechanics, Jg.\u200910, Nr.\u20091, S.\u2009617\u2013618, 2010.","DOI":"10.1002\/pamm.201010301"},{"key":"2023033110360546346_j_auto-2021-0069_ref_017","doi-asserted-by":"crossref","unstructured":"J. Kopp and F. Woittennek, \u201cFlatness based trajectory planning and open-loop control of shallow-water waves in a tube\u201d, Automatica, 2020.","DOI":"10.1016\/j.automatica.2020.109251"},{"key":"2023033110360546346_j_auto-2021-0069_ref_018","doi-asserted-by":"crossref","unstructured":"J. Kopp and F. Woittennek, \u201cFlatness-based control design for the Saint-Venant equations with experimental results\u201d, IFAC-PapersOnLine, Jg.\u200952, Nr.\u200916, S.\u200960\u201365, 2019.","DOI":"10.1016\/j.ifacol.2019.11.756"},{"key":"2023033110360546346_j_auto-2021-0069_ref_019","doi-asserted-by":"crossref","unstructured":"P. Kotyczka, \u201cDiscrete-time flatness-based feedforward control for the 1D shallow water equations\u201d, IFAC-PapersOnLine, Jg.\u200952, Nr.\u200916, S.\u200942\u201347, 2019.","DOI":"10.1016\/j.ifacol.2019.11.753"},{"key":"2023033110360546346_j_auto-2021-0069_ref_020","doi-asserted-by":"crossref","unstructured":"H.\u2009G. Landau, \u201cHeat conduction in a melting solid\u201d, Quarterly of Applied Mathematics, Jg.\u20098, Nr.\u20091, S.\u200981\u201394, 1950.","DOI":"10.1090\/qam\/33441"},{"key":"2023033110360546346_j_auto-2021-0069_ref_021","doi-asserted-by":"crossref","unstructured":"A.\u2009F. Lynch and J. Rudolph, \u201cFlatness-based boundary control of a class of quasilinear parabolic distributed parameter systems\u201d, Int. J. Control, Jg.\u200975, Nr.\u200915, S.\u20091219\u20131230, 2002.","DOI":"10.1080\/00207170210163640"},{"key":"2023033110360546346_j_auto-2021-0069_ref_022","doi-asserted-by":"crossref","unstructured":"B.\u2009L.\u2009P. Martin and P. Rouchon, \u201cMotion planning for the heat equation\u201d, Int. J. Robust Nonlinear Control, Jg.\u200910, S.\u2009629\u2013643, 2000.","DOI":"10.1002\/1099-1239(20000715)10:8<629::AID-RNC502>3.0.CO;2-N"},{"key":"2023033110360546346_j_auto-2021-0069_ref_023","doi-asserted-by":"crossref","unstructured":"T. Meurer, Control of Higher-Dimensional PDEs: Flatness and Backstepping Designs. Springer-Verlag, 2012.","DOI":"10.1007\/978-3-642-30015-8"},{"key":"2023033110360546346_j_auto-2021-0069_ref_024","doi-asserted-by":"crossref","unstructured":"T. Meurer and A. Kugi, \u201cTrajectory planning for boundary controlled parabolic pdes with varying parameters on higher-dimensional spatial domains\u201d, IEEE Trans. Automat. Control, Jg.\u200954, Nr.\u20098, S.\u20091854\u20131868, 2009.","DOI":"10.1109\/TAC.2009.2024572"},{"key":"2023033110360546346_j_auto-2021-0069_ref_025","doi-asserted-by":"crossref","unstructured":"N. Petit and P. Rouchon, \u201cDynamics and solutions to some control problems for water-tank systems\u201d, IEEE Trans. Automat. Control, Jg.\u200947, Nr.\u20094, S.\u2009594\u2013609, 2002.","DOI":"10.1109\/9.995037"},{"key":"2023033110360546346_j_auto-2021-0069_ref_026","doi-asserted-by":"crossref","unstructured":"N. Petit and P. Rouchon, \u201cFlatness of heavy chain systems\u201d, SIAM J. Control Optim., Jg.\u200940, S.\u2009475\u2013495, 2001.","DOI":"10.1137\/S0363012900368636"},{"key":"2023033110360546346_j_auto-2021-0069_ref_027","doi-asserted-by":"crossref","unstructured":"C. Prieur and J. de Halleux, \u201cStabilization of a 1-D tank modeled by the shallow water equations\u201d, Journ\u00e9es \u00e9quations aux d\u00e9riv\u00e9es partielles, S.\u20091\u201313, 2002.","DOI":"10.5802\/jedp.611"},{"key":"2023033110360546346_j_auto-2021-0069_ref_028","doi-asserted-by":"crossref","unstructured":"R. Rothfu\u00df, J. Rudolph and M. Zeitz, \u201cFlachheit: Ein neuer Zugang zur Steuerung und Regelung nichtlinearer Systeme\u201d, at, Jg.\u200945, S.\u2009517\u2013525, 1997.","DOI":"10.1524\/auto.1997.45.11.517"},{"key":"2023033110360546346_j_auto-2021-0069_ref_029","unstructured":"J. Rudolph, J. Winkler and F. Woittennek, Flatness Based Control of Distributed Parameter Systems: Examples and Computer Exercises from Various Technological Domains. Aachen: Shaker Verlag, 2003."},{"key":"2023033110360546346_j_auto-2021-0069_ref_030","unstructured":"A.\u2009B. de Saint-Venant, \u201cTh\u00e9orie du mouvement non permanent des eaux, avec application aux crues des rivi\u00e8res et \u00e0 l\u2019introduction de mar\u00e9es dans leurs lits\u201d, Comptes Rendus des S\u00e9ances de l\u2019Acad\u00e9mie des Sciences, Jg.\u200973, 147\u2013154 and 237\u2013240, 1871."},{"key":"2023033110360546346_j_auto-2021-0069_ref_031","unstructured":"J. Sainte-Marie, \u201cModels and numerical schemes for free surface flows. Beyond the Saint-Venant system\u201d, Habilitation, Universit\u00e9 Pierre et Marie Curie - Paris VI, 2010."},{"key":"2023033110360546346_j_auto-2021-0069_ref_032","doi-asserted-by":"crossref","unstructured":"A. Smyshlyaev, E. Cerpa and M. Krstic, \u201cBoundary stabilization of a 1-D wave equation with in-domain antidamping\u201d, SIAM J. Control Optim., Jg.\u200948, Nr.\u20096, S.\u20094014\u20134031, 2010.","DOI":"10.1137\/080742646"},{"key":"2023033110360546346_j_auto-2021-0069_ref_033","doi-asserted-by":"crossref","unstructured":"R. Szymkiewicz, Numerical Modeling in Open Channel Hydraulics. Springer-Verlag, 2010.","DOI":"10.1007\/978-90-481-3674-2"},{"key":"2023033110360546346_j_auto-2021-0069_ref_034","doi-asserted-by":"crossref","unstructured":"F. Woittennek, Beitr\u00e4ge zum Steuerungsentwurf f\u00fcr lineare, \u00f6rtlich verteilte Systeme mit konzentrierten Stelleingriffen, Ser. Berichte aus der Steuerungs- und Regelungstechnik. Aachen: Shaker Verlag, 2007.","DOI":"10.1524\/auto.2007.55.9.497_2"},{"key":"2023033110360546346_j_auto-2021-0069_ref_035","doi-asserted-by":"crossref","unstructured":"F. Woittennek, \u201cBeobachterbasierte Zustandsr\u00fcckf\u00fchrungen f\u00fcr hyperbolische verteiltparametrische Systeme\u201d, at, Jg.\u200960, Nr.\u20098, S.\u2009462\u2013474, 2012.","DOI":"10.1524\/auto.2012.1022"},{"key":"2023033110360546346_j_auto-2021-0069_ref_036","doi-asserted-by":"crossref","unstructured":"F. Woittennek, \u201cFlatness based feedback design for hyperbolic distributed parameter systems with spatially varying coefficients\u201d, IFAC Proceedings Volumes, Jg.\u200946, S.\u200937\u201342, 26 2013, 1. IFAC Workshop on Control Systems Modelled by Partial Differential Equations.","DOI":"10.3182\/20130925-3-FR-4043.00058"},{"key":"2023033110360546346_j_auto-2021-0069_ref_037","doi-asserted-by":"crossref","unstructured":"F. Woittennek, \u201cOn flatness and controllability of simple hyperbolic distributed parameter systems\u201d, IFAC Proceedings Volumes, Jg.\u200944, Nr.\u20091, S.\u200914452\u201314457, 2011.","DOI":"10.3182\/20110828-6-IT-1002.02618"},{"key":"2023033110360546346_j_auto-2021-0069_ref_038","doi-asserted-by":"crossref","unstructured":"F. Woittennek and J. Rudolph, \u201cController canonical forms and flatness based state feedback for 1D hyperbolic systems\u201d, IFAC Proceedings Volumes, Jg.\u200945, Nr.\u20092, S.\u2009792\u2013797, 2012.","DOI":"10.3182\/20120215-3-AT-3016.00140"},{"key":"2023033110360546346_j_auto-2021-0069_ref_039","doi-asserted-by":"crossref","unstructured":"J. Wurm, L. Mayer and F. Woittennek, \u201cFeedback control of water waves in a tube with moving boundary\u201d, European Journal of Control, 2021.","DOI":"10.1016\/j.ejcon.2021.06.016"}],"container-title":["at - Automatisierungstechnik"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2021-0069\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2021-0069\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T12:15:07Z","timestamp":1680264907000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/auto-2021-0069\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,1]]},"references-count":39,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2021,9,9]]},"published-print":{"date-parts":[[2021,9,1]]}},"alternative-id":["10.1515\/auto-2021-0069"],"URL":"https:\/\/doi.org\/10.1515\/auto-2021-0069","relation":{},"ISSN":["2196-677X","0178-2312"],"issn-type":[{"value":"2196-677X","type":"electronic"},{"value":"0178-2312","type":"print"}],"subject":[],"published":{"date-parts":[[2021,9,1]]}}}