From Linear to Nonlinear Model Predictive Control of a Building

In the building climate control area, the linear model predictive control (LMPC)—nowadays considered a mature technique—benefits from the fact that the resulting optimization task is convex (thus easily and quickly solvable). On the other hand, while nonlinear model predictive control (NMPC) using a more detailed nonlinear model of a building takes advantage of its more accurate predictions and the fact that it attacks the optimization task more directly, it requires more involved ways of solving the non-convex optimization problem. In this paper, the gap between LMPC and NMPC is bridged by introducing several variants of linear time-varying model predictive controller (LTVMPC). Making use of linear time-varying model of the controlled building, LTVMPC obtains predictions which are closer to reality than those of linear time invariant model while still keeping the optimization task convex and less computationally demanding than in the case of NMPC. The concept of LTVMPC is verified on a set of numerical experiments performed using a high fidelity model created in a building simulation environment and compared to the previously mentioned alternatives (LMPC and NMPC) looking at both the control performance and the computational requirements.