A new formulation of physical thermal models for variable plug flow through a pipe is proposed. The derived model is based on a commonly used onedimensional distributed parameter model, which explicitly takes into account the heat capacity of the jacket of the pipe. The main result of the present contribution is the constitution of the equivalence of this model with a serial connection of a pure delay or transport system and another partial-differential equation (PDE), subsequently called delay-partial-differential equation (DPDE)-model. The means for obtaining the proposed model comprise operational calculus in the Laplace domain as well as classical theory of characteristics. The finitedimensional approximation of the DPDE-model leads to a delay-differential equation (DDE)-system, which can be seen as a generalization of commonly used DDE-models consisting of a first-order low-pass filter subject to an input delay. The proposed model is compared to several alternative models in simulations and experimental studies.
Zusammenfassung
Der Beitrag behandelt die Folgeregelung von Flachwasserwellen in einer partiell gefüllten Röhre, in der der Flüssigkeitspegel 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 Leistungsfähigkeit der entworfene Folgeregelung wird anhand von Simulationen und experimentellen Studien nachgewiesen.
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