On-Off versus PI Control of Room Temperature: A Lumped-Parameter Simulation of Accuracy, Switching and Energy

Room-temperature control is the textbook example of a thermal cyber-physical system. This paper uses a lumped-parameter simulation (thermal capacity 3 MJ/K, heat-loss coefficient 100 W/K, outdoor temperature 2 ± 5 °C over 24 h, sensor noise 0.05 K) to compare on-off control with three hysteresis widths and two PI controllers. On-off control kept the mean absolute error at 0.031 K with ±0.1 K hysteresis but needed 387 switchings per day, while ±1.0 K hysteresis reduced switching to 19 per day at a mean error of 0.48 K. The PI controllers, which assume a continuously modulated heater, reached mean errors of 0.068 K and 0.026 K without switching. The daily energy differed by less than 1 % between all cases (49.2–49.4 kWh). The study is a simulation of one idealised room. This is a simulation study; all results are outputs of the deposited Python code with assumed parameters. Source code is attached.