A Physically Regularized Control-Oriented State Model and Nonlinear Model Predictive Control Framework for an Ice Rink Refrigeration System

Energy-intensive refrigeration systems require predictive models that remain informative under counterfactual control trajectories, not only on archived operation. This paper develops a control-oriented multi-step state model and a nonlinear model predictive control framework for an indoor ice-rink refrigeration system. Historical state, control, and exogenous variables are encoded jointly with an admissible future control trajectory, and a normalized thermal-balance residual is added to the training objective. A lightweight conditioned transformer predicts ice temperature, return-glycol temperature, supply-glycol temperature, and compressor power over a 30 min horizon. The selected weakly regularized model with regularization coefficient λphys = 0.001 decreases the normalized thermal-balance root-mean-square error on the horizon tail by 30.29% relative to the base model while increasing the average ice-temperature root-mean-square error by only 1.90%. In a surrogate-based counterfactual four-day evaluation, the resulting nonlinear model predictive controller reduces predicted daily energy by 4.84%, terminal violation share by 17.32%, mean absolute terminal ice-temperature deviation by 18.74%, and the mean objective value by 30.82% relative to historical admissible setpoint tracking. The mean full control cycle time is 0.0311 s, confirming real-time feasibility for a 5 min supervisory update interval. All controller results are surrogate-based rather than field-deployed and therefore represent receding-horizon benchmark results under learned-model evaluation, not realized field savings.