Adaptive PID Control Based on Laplace Distribution for Multi-Environment Temperature Regulation in Smart Refrigeration Systems

This study presents an Adaptive PID controller designed to enhance temperature stability and energy performance in household refrigerator systems subject to non-stationary disturbances. Classical PID control is limited by fixed gains and the assumption of linear time-invariant dynamics, which is frequently violated by door opening, load variation, and compressor cycling. To address this issue, the proposed approach introduces a Laplace-distribution-based adaptive gain function L(t) that adjusts controller sensitivity according to the statistical rarity of the composite temperature error. The method preserves the conventional PID control structure while introducing a lightweight gain-scaling mechanism suitable for embedded implementation. Experimental validation using a commercial two-compartment refrigerator demonstrated substantial improvements in performance compared with a classical PID controller. The Adaptive PID achieved reduced temperature deviations in both compartments, significantly smoother compressor and fan actuation, and a 4.6% reduction in total energy consumption under an identical disturbance schedule. These results confirm that the proposed controller provides a practical, embedded-friendly solution that improves thermal regulation, actuator longevity, and energy efficiency under the tested disturbance schedule representative of typical household usage.