Optimization of modeling and temperature control of air-cooled PEMFC based on TLBO-DE

The temperature control of the air-cooled proton exchange membrane fuel cell (PEMFC) is important for effective and safe operation. To develop a practical and precise controller, this study combines the Radial Basis Function (RBF) neural network with Back Propagation neural network adaptive Proportion Integration Differentiation (BP-PID), and then a metaheuristic algorithm is used to optimize the parameters of RBF-BP-PID for further improvement in temperature control. First, an air-cooled PEMFC system model is established. To match the simulation data with the experimental data, Teaching Learning Based Optimization–Differential Evolution (TLBO-DE) is proposed to identify the unknown parameters, and the maximum relative error is <3.5 %. Second, RBF neural network is introduced to identify the stack temperature and provide the accurate $\frac{\partial y\left(k\right)}{\partial u\left(k\right)}$ for BP-PID, which solves the problem of using sign function sgn($\frac{\partial y\left(k\right)}{\partial u\left(k\right)}$) to approximate the $\frac{\partial y\left(k\right)}{\partial u\left(k\right)}$ in BP-PID. Regarding the temperature control of air-cooled PEMFC, several controllers are compared, including PID, Fuzzy-PID, BP-PID and RBF-BP-PID. The proposed RBF-BP-PID achieves the best control effect, which reduces the integrated time and absolute error (ITAE) by 3.4 % and 15.8 % based on BP-PID in the startup and steady phases, respectively. Since the $\frac{\partial y\left(k\right)}{\partial u\left(k\right)}$ provided by RBF changes softly and continuously during the control process, the parameters self-tuning ability of RBF-BP-PID is better than BP-PID. Third, to improve the control effect of RBF-BP-PID further, TLBO-DE is adopted to optimize the parameters of RBF neural network and BP neural network.