Development of A Multiparametric Model Predictive Control System for Temperature Regulation of a Window - Type Air Conditioner

Abstract

Aims/Objectives: This study aimed to develop a multiparametric Model Predictive Control (mp-MPC) framework for the thermal regulation of a single-zone space conditioned by a window-type air-conditioning (AC) unit. The framework shifts the optimisation burden offline so that an explicit piecewise-affine control law can be synthesised for deployment on low-cost embedded hardware, and its performance is benchmarked against conventional online MPC and reactive baseline controllers under varying ambient temperature scenarios. Methodology: A lumped-parameter thermal dynamics model derived from the first law of thermodynamics was formulated. A discrete-time state-space mp-MPC model was then designed to regulate supply-air and room temperatures, with ambient temperature incorporated as a measured disturbance. The controller was implemented in MATLAB/Simulink (R2023a) and compared with an online MPC, a Ziegler-Nichols-tuned PID controller, an ON-OFF thermostat, and an open-loop case under three ambient-temperature conditions: constant high temperature (45°C), normal daytime temperature (35°C), and an extreme heatwave ramp (30-50°C). Performance was measured using Mean Square Error (MSE), Integral Square Error (ISE), and Integral Absolute Error (IAE). Results: Conventional online MPC produced the lowest MSE values (0.250-0.302), representing an 81-97% improvement over mp-MPC. The explicit mp-MPC performed competitively near the nominal design point, with a steady-state error of 0.0018°C at 35°C, but exhibited boundary-switching offsets of up to 3.75°C under non-stationary disturbances. The ON-OFF thermostat showed the weakest regulation, with MSE values up to 118 times higher than those of MPC. Conclusion: Although mp-MPC remains a computationally attractive option for severely resource-constrained microcontrollers, conventional online MPC is preferable for window-type AC temperature regulation when embedded hardware can support online quadratic programming. The results provide a replicable simulation benchmark for future investigations into the hardware-in-the-loop deployment of explicit predictive control on residential cooling equipment.