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.
Pareja et al. (Fri,) studied this question.