<![CDATA[Abstract — This paper presents a comparative study of PID controller tuning strategies for a battery thermal management system (BTMS) using Peltier thermoelectric elements. A 4S1P 18650 lithium-ion pack cooled by TEC1-12706 modules is modelled as a second-order plant with transport delay and a quadratic actuator nonlinearity. The controller gains are optimized by Particle Swarm Optimization (PSO), Ant Colony Optimization for continuous domains (ACO-R), and Grey Wolf Optimizer (GWO) using an ITAE objective penalized by overshoot, settling time, and TEC energy. Ziegler-Nichols (ZN) tuning derived from the half-rule serves as the benchmark. Twenty independent runs per algorithm were executed in Python-based numerical simulations, covering a step response from 45 to 30 °C, a 2C load disturbance, an ambient rise, and a plus-minus 20 % parameter variation test. All three algorithms reduce ITAE by 50,4 %, settling time by 67,0 %, overshoot from 15,82 % to 0,02 %, and TEC energy by 8,9 % relative to ZN. The key finding is that the three algorithms converge to practically identical solutions, differing by only 0,0007 % in objective value, so none is superior in solution quality. The meaningful difference lies in search behaviour: PSO is the most consistent (standard deviation 0,272), ACO-R converges fastest (iteration 11,6) but is the least consistent (3,948), and GWO is the slowest (20,9) with intermediate consistency. Adopting optimization-based tuning matters far more than choosing among these algorithms. Keywords — battery thermal management; grey wolf optimizer; particle swarm optimization; PID tuning; thermoelectric Peltier cooler]]>
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