Development of A Multiparametric Model Predictive Control System for Temperature Regulation of a Window - Type Air Conditioner
D. O. Aborisade *
Department of Electronic and Electrical Engineering, Faculty of Engineering and Technology, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
O. A. Adegbola
Department of Electronic and Electrical Engineering, Faculty of Engineering and Technology, Ladoke Akintola University of Technology, Ogbomoso, Nigeria.
S. O. Oladeji
Electrical and Electronic Department, Federal Polytechnic Ede, Nigeria.
T. P. Ajayi
Department of Electrical and Electronics Engineering, School of Engineering and Engineering Technology, Federal University of Technology, Minna, Nigeria.
A.S. Adekanmi
Electrical and Electronic Department, Federal Polytechnic Ede, Nigeria.
H.B. Omodeni
Electrical and Electronic Department, Federal Polytechnic Ede, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Multiparametric model predictive control, window-type air conditioning, thermal dynamics, lumped-parameter model, energy efficiency, explicit control law.