Model selection and parameter optimization of model predictive control for building radiant systems

In this work, we present a comprehensive parametric investigation quantifying the influence of reduced-order models (ROMs) of varying fidelity on both dynamic and steady-state performance of a Model Predictive Control (MPC) loop for building thermal regulation. Through simulations using the full-order model and ROMs of orders 1–6, we systematically determined that ROMs of order 4 or higher achieve temperature overshoots within 0.2 °C, settling times under 15 min, and steady-state errors below 0.5 °C when paired with prediction horizons of 12–24 steps and control horizons ≥ 2, thus matching full-order MPC performance while reducing computation by up to 70 %. In contrast, the lowest-order ROM (ROM1) requires a prediction horizon ≤ 12 and a control horizon ≥ 3 to limit overshoot to 1.0 °C and static error to 1.2 °C. Furthermore, the original model and high-order ROMs maintain robust control (overshoot < 0.5 °C, settling time < 10 min) across manipulated-variable rate weights from 0.1 to 1.0 and manipulated-output weights from 0.5 to 2.0, whereas ROM1 exhibits strong sensitivity, operating acceptably only near MV-rate ≈ 0.2 and MO weight ≈ 1.0. These quantitative guidelines enable practitioners to balance computational cost and control accuracy by selecting an appropriately ordered ROM and tuning horizons and weightings within the identified numerical ranges.