Hybrid PSO-Tuned Fractional-Order Control with Rule-Based Adaptive Supervision for Embedded Thermoelectric Temperature Regulation

Thermal regulation using Peltier cells presents challenges due to high inertia, memory effects, and energy constraints in embedded systems. This paper introduces the FOPID with Adaptive Supervisor (FOPID-AS) scheme, combining a PSO-optimized fractional-order controller (FOPID) with a deterministic rule-based gain-scheduling supervisor. Experimental validation compares four strategies: PID, Fuzzy-PID, static FOPID, and the proposed FOPID-AS. During the transient phase (t<105 s), FOPID-AS reaches the ±0.5 °C tolerance band in 31.20 s, with an ITAE of 6612.97 and transient energy consumption of 0.18 Wh, outperforming PID, Fuzzy-PID, and FOPID in speed and tracking quality. In steady state (t≥105s), FOPID-AS exhibits steady-state error ess = 0.08 °C, σss = 0.10 °C, and peak-to-peak ripple of 0.67 °C, with steady-state energy consumption of 0.30 Wh, showing lower dispersion than PID and comparable values to the other fractional controllers, while maintaining low computational load suitable for real-time applications.