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Analytical approximation of open-channel flow for controller design. (English) Zbl 1147.76558

Summary: The integrator delay (ID) model is a popular and simple way to model a canal for control purposes. In this paper, particular attention is given to accurately model the delay and the integrator gain in any flow configuration. Based on a previous work by the authors allowing to have a very accurate frequency domain representation of Saint-Venant equations, the paper proposes a new approximate model: the integrator delay zero (IDZ) model has an integrator and a delay in low frequencies, and models the high frequencies by a constant gain and a delay. Analytical formulas are derived to compute the model parameters for a canal pool possibly in backwater conditions. The IDZ model is compared with an accurate model on two example canals for different flow conditions. The comparisons done in the frequency domain and in the time domain show the accuracy of the model.

MSC:

76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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References:

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