Model predictive control for water level control in the case of spills

Model predictive control (MPC) is one of the most popular control techniques that has been widely used in many fields of water resources management, such as canal control for drainage, irrigation, and navigation. MPC uses an internal mathematical model to describe system dynamics over a given prediction horizon and then minimizes a hard-constrained optimization problem based on actual objectives. Due to the use of hard constraints, the optimization problem may occasionally be infeasible. A compromise is sometimes made to look for a feasible solution by softening the hard constraints, which means that the limit on water levels or flows is allowed to be violated to a certain extent. For example, water in a canal may go above the top of a dike during a high-discharge event, resulting in a spill. This amount of spilling water leaves the water system and does not flow back, which therefore should be deducted in the mathematical model of the water system. To deal with this spill, past studies often utilized a hybrid model and an integer optimization. However, the system in the hybrid model is usually nonlinear and nonsmooth, especially when it transits from one discrete state to another. In this paper, an alternative way is proposed to link the spill with the softened constraint, still maintaining the linearity of the water system. Results show that the proposed way to tackle the spilling water is easy to implement and the water level is more accurately regulated around the setpoint in a canal control problem.