Stability analysis and numerical simulations of a one dimensional open channel hydraulic system

Boumediène Chentouf and Nejib Smaoui

Applied Mathematics and Computation, 2018, vol. 321, issue C, 498-511

Abstract: This paper is dedicated to the qualitative analysis as well as numerical simulations of a one dimensional open channel hydraulics system which is commonly used in hydraulic engineering to model the unsteady flow dynamics in a river. First, an output feedback control is proposed. Next, the closed-loop system is proved to possess a unique solution in a functional space. Furthermore, the spectrum and resolvent sets of the system operator are characterized. Then, stability results are stated and proved according to a smallness assumption on the feedback gain. The proof invokes Lyapunov direct method. Last but not least, we adopt the Chebychev collocation method, that uses backward Euler method and the Gauss-Lobatto points, to provide numerical simulations in order to ascertain the correctness of the theoretical outcomes.

Keywords: Open channel hydraulic system; Output boundary feedback control; Stability; Chebychev collocation method (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:321:y:2018:i:c:p:498-511

DOI: 10.1016/j.amc.2017.10.058

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