Categorization of trapezoidal open channels based on flow conditions for the choice of simple models

Abstract

Many applications in water management rely on keeping the water levels of an open water channel within given bounds, e.g. irrigation canals, drainage systems, and hydropower systems. These are all open water channels where the water level is influenced by several known and unknown factors like precipitation, operation of structures, etc. Water levels can be efficiently controlled by model predictive control (MPC). In MPC the optimization algorithms give advice at every time step based on the current state of the system as well as on the expected future state. These algorithms need a model to predict the response of the system to the control inputs. In most cases, the need to guarantee convexity of the optimization problem leads to the requirement that these models should be linear. To date, several such linear models are available in literature, which are suited for control purposes. However, the choice between these models is not straightforward. In this work, we extend a categorization of open channels, based on which the choice of a simple model can be advised.

How to Choose Suitable Physics‐Based Models Without Tuning and System Identification for Model‐Predictive Control of Open Water Channels?

“…(1998) for uniform flow conditions in rectangular channels and is extended by Horváth et al. (2018) for trapezoidal channels and for other flow conditions. According to Baume et al.…”

“…The extension of this categorization for trapezoidal channels proposed in Horváth et al. (2018) is: $$$\eta =3\zeta =\frac{3\sqrt{2g}QL}{4{C}^{2}RB{H}^{3/2}}$$$ and $$$\chi =\frac{3L}{10}\frac{{C}_{p}}{{D}_{p}},$$$ where B is the bottom width, ζ is the wave damping coefficient (van Overloop et al., 2014), C is the Chezy friction coefficient and R is the hydraulic radius which can be obtained as $$$R=A/P$$$ where P is the wet perimeter. Coefficients C p and D p are described below.…”

“…A categorization of open-water channels based on flow conditions is developed by Baume et al (1998) for uniform flow conditions in rectangular channels and is extended by Horváth et al (2018) for trapezoidal channels and for other flow conditions. According to Baume et al (1998) fluctuations in discharge and water depth are mainly determined by two physical phenomena: wave propagation (perturbation) and mass transport (long waves).…”

“…Two other candidate models are the Linearized Saint Venant and integrator resonance (IR) model. Second, Horváth et al (2018) presented a categorization of open water channels based on geometry, flow and water level. In this work, we use these channel categories to test six different linear models in order to determine the best performing model for each channel category.…”