Input disturbance predictive control of shallow water flows

The purpose of this paper is to describe the predictive control of flood flows over the surface of reservoirs in a mountainous area, with a complicated terrain shape. It is expected that damage to villages around the reservoir can be reduced if the water elevation of water discharge is controlled using an artificially constructed aqueduct. The control method uses the first-order adjoint equation and the numerical technique used is the finite element method. In order to control water elevation, prediction of input discharge is necessary, and optimal discharges can accordingly be determined. Predictive control of water flows is carried out in this study. The adjoint equation method is applied to obtain the optimal control. A performance function is used as the index of the optimal control, which is defined by the sum of the square of the computed water elevation at the target points. As a minimization technique, the weighted gradient method is applied. The gradient of the extended performance function with respect to the control of water discharge is obtained by solving the first-order adjoint equation. The predictive control method employed in this paper is a technique to make prediction of the input disturbance and compute the optimal control value at a certain time duration. The shallow water equation based on the water discharge and elevation is used as the governing equation. As the spatial discretization, the finite element method based on the linear function interpolation is employed. As the temporal discretization, the two-step explicit scheme is applied. After verification based on the predictive control of the water elevation in simple rectangular channel and sinusoidal water elevation model, the present method is applied to flood control of the Ikari reservoir located in the Tochigi prefecture in Japan.