Thermal management of lithium-ion batteries in a vented cavity with hybrid nanofluid using Proportional, Proportional–Integral, and Proportional–Integral–Derivative controllers

In this study, thermal management of a cylindrical lithium-ion battery pack with Al2O3−Cu−H2O hybrid nanofluid cooling is studied using Proportional (P), Proportional–Integral (PI), and Proportional–Integral–Derivative (PID) controllers to maintain the temperature at the center of the central battery. The complex geometry of the system, the use of a liquid hybrid nanofluid, probe point placement in the solid domain, and control of conjugate heat transfer with volumetric heat sources make the study an unprecedented work. Despite having one control probe point, all three controllers succeeded in keeping the temperature of all batteries within the optimum range of operation with minimal fluctuation. Moreover, a cost function-based evaluation and tuning method is proposed, analyzing the tuning design space and the minimum gain values of nine different cost functions. Results indicate that the Integral Time Absolute Error (ITAE) is the best cost function for mining optimal system responses in terms of both error accumulation and energy usage amongst the investigated. Conversely, Integral Squared Error (ISE) and Integral Square of Control Output (ISCO) might lead to unsettled responses as their minimization results in parsimonious usage of energy. Although further incorporating a derivative term improved suboptimal PI controllers, the optimal PI controller (Kp0.075ms−1K−1, Ki0.001ms−2K−1) exhibited a worse response. Moreover, the smaller gradient of error with respect to time in the prolonged timescale of conjugate heat transfer necessitates higher derivative gains in PID controllers to have a considerable influence. Additionally, spatial variations in steady-state Nusselt numbers emphasize the importance of battery arrangement in achieving uniform thermal regulation.