Asymptotic analysis of a control–oriented open channel flow model

This paper presents the development and mathematical analysis of an open-channel flow model. A tanks-in-series model relying on systems engineering perspectives is constructed. Through a series of assumptions, the obtained nonlinear model is approximated by a linear dynamics, and its asymptotic modal behavior is analysed in infinite dimensions using rigorous mathematical machinery. The analysis exploits the repeating tridiagonal structure of the system matrix using Chebyshev polynomials and elaborates the dependence of the modal dynamics on the so-called flow coefficient, which accounts for the description of the flow of the model. The analysis presented in this paper reveals that using constant flow coefficient for flow description in cascade arrangement of liquid storages results in physically meaningless asymptotic modal behavior. The asymptotic modal behavior is well defined if the flow coefficient is an affine function or higher-order polynomial of the number of elements in the cascade structure.