Comparative Robustness Analysis of Frequency-Constrained Metaheuristic PID Tuning for Zero-Overshoot Polymerase Chain Reaction Thermal Control

The success of DNA amplification in Polymerase Chain Reaction (PCR) devices inherently depends on the rapid and absolute zero-overshoot temperature control of thermoelectric cooler (TEC) systems. In the literature, metaheuristic algorithms employed for proportional–integral–derivative (PID) tuning typically operate within unconstrained search spaces, relying exclusively on time-domain error metrics like ITAE. This conventional approach causes ‘gradient blindness’ and neglects frequency-domain robustness, resulting in excessive temperature overshoots that violate biological safety limits and lead to enzyme denaturation. To solve this problem, we propose a hybrid frequency-time domain optimization framework. Utilizing a first order plus dead-time (FOPDT) model for TEC dynamics, the PID search space is analytically restricted via Ziegler–Nichol’s stability boundaries. Furthermore, Phase Margin (PM ≥ 45°) and absolute zero-overshoot conditions are integrated into the objective function as a strict penalty mechanism. Evaluations conducted with five distinct metaheuristic algorithms (PSO, GWO, WOA, ABC, and ACO) prove that while traditional unconstrained methods yield overshoots up to 19.04%, the proposed architecture successfully confines all optimization agents to a globally stable region, enabling specific algorithms like ABC, PSO, and WOA to achieve exactly 0.00% overshoot. Validated across a realistic multi-step PCR cycle (95–55–75 °C), the developed robust controller settles into the denaturation phase with a 0.00 °C peak error, guaranteeing biological sample safety and delivering a reliable control framework for rapid-cycle PCR platforms.