Comparative analysis of model predictive control performance using different building RC-models and state estimation techniques

• Multiple MPCs are developed for a two-zone use-case from BOPTEST • Different orders of RC-models are combined with several state estimators in MPC • The Least-Derivative-Squares (LDS) method is proposed, which tracks derivatives during system identification • Good MPC performance is guaranteed with an LDS-model and a dedicated state estimator • Multiple MPC formulations reduce thermal discomfort below the threshold of 100 Kh/year/zone Model Predictive Control (MPC) applied to buildings often relies on gray-box controller models, such as RC network models, for which different orders can be considered. It is widely accepted that the prediction accuracy of RC-models increases with a higher order if properly identified. However, gray-box MPC performance can depend on the quality of the considered state estimator as well. Recent comparative analyses consider either different controller models or different state estimators. This work assesses multiple gray-box MPCs, ranging from a 1 st to a 3 rd order RC-model, each combined with a Time-Varying Kalman Filter and a Moving Horizon Estimator and compares with using no state observer. System identification results show that tracking derivatives facilitates the challenging parameter estimation process. Therefore, a novel approach for system identification of RC-models is proposed by explicitly tracking model derivatives during training. Well-performing MPCs reduce thermal discomfort by 84.5% to 94.3% at the cost of an increased energy use of 51.4% to 100%. However, this is compared to a rule-based controller which yields unacceptable thermal discomfort due to lack of heating, leading to a low energy use. These results elucidate the necessity of both a good derivative-tracking controller model and a dedicated state estimator to guarantee good MPC performance.