MPC approaches for modulating air-to-water heat pumps in radiant-floor buildings

A modulating heat pump and water tank result in a nonlinear model due to the load dependency of the heat pump performance, and variable water flows. Nonlinear model predictive control is an effective way to deal with many physical constraints and nonlinear formulations. Alternatively, linear time-varying MPC can be used, based on successive linearizations around a reference trajectory. The goal of the paper is to analyze the advantages and disadvantages of those MPC techniques for temperature control in radiant-floor buildings. The results show that nonlinear on-line optimization is real-time feasible for the application considered here, as the slow dynamics allows for a fairly long sampling time. Alternatively, the linear time-varying MPC approach shows a significantly better performance compared to the Standard MPC scheme if a feasible reference trajectory is provided. Nonlinear MPC can save up to 6% energy and improve the comfort by 4% with respect to Standard MPC for the given application, while its difference with LTV-MPC is negligible. Moreover, a robustness analysis has been conducted, showing the impact of the heat pump efficiency on the control performance.