Research Article
Exact Predictive Ventilation Control with Causal Occupancy Forecasts and Concentration Guarantees
Abstract
Predictive ventilation depends on both the mathematical plant and the information available when an airflow command is selected. We study these dependencies in a fully specified, single-zone apartment benchmark. For a well-mixed carbon dioxide balance with nonnegative generation and piecewise constant airflow, we derive an exact propagation map and prove that predicted concentration is jointly convex in the planned airflow sequence after the state variables are eliminated. The resulting finite-horizon problem retains the cubic fan law without successive linearization. A monotone one-step filter then enforces a selected concentration bound under declared occupancy and plant-parameter envelopes. We evaluate seven controllers on twelve independent, paired week-long simulations, using eight separate training weeks for occupancy-model estimation and reactive-controller tuning. Filtered Model Predictive Control (MPC) consumes 26.386 kWh/week of modeled fan-plus-heating energy, compared with 27.726 for the tuned rule and 28.965 for the original 1000/850 ppm rule. Its paired difference from the tuned rule is −1.340 kWh/week, with a pointwise 95% interval of [−1.465, −1.214]. A causal conditional-mean forecast with a five-minute occupancy-report delay yields only 0.045 occupants of one-step Mean Absolute Error (MAE), yet its unfiltered controller spends 44.175 minutes per occupied person-hour above 1000 ppm, predominantly through small exceedances. The filter removes these exceedances in the matched model at an added 0.037 kWh/week. Four paired mismatch tests show why the guarantee must use valid parameter envelopes. The results establish a reproducible separation between forecast quality, energy performance, and conditional concentration invariance; they do not constitute residential field validation or a general indoor-air-quality guarantee.
Keywords
Demand-controlled ventilation Exact discretization Convex optimization Causal occupancy forecasting Model predictive control Concentration invarianceReferences (31)
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