Continuous nonlinear model predictive control of a hybrid water system

Incorporating weather forecasts in the control of land surface water levels requires predictions of the net inflow to the water system. This net inflow is the combined flow of an incoming load (rain, evaporation, etc.) and outgoing pump rates. Because the pump costs are considerable, optimal pump schedules have minimal energy consumption. Model predictive control (MPC) is able to compute, revise and apply such optimized schedules by incorporating a model of the water system. The pumps typically cause discontinuities in the model, which leads to mathematical complications. Avoiding advanced solving techniques for these hybrid systems, this paper introduces an alternative that enables pure continuous MPC by smoothing the jumps. Although the resulting underlying model is continuous, it is also highly nonlinear. This requires use of the specialized class of nonlinear model predictive control (NMPC), which is able to cope with the arising nonlinearities. Control inputs computed by these methods can be translated to the original hybrid system by a final post-processing step. This paper presents the outlined scheme, and verifies it by applying an optimized NMPC implementation (the DotX nonlinear predictive controller, DNPC), equipped with the approximated continuous nonlinear model, to a real-life hybrid water system.