# Sliding Mode Integral Separation PID Control for Hydrogen Fuel Cell Systems
## 4 Analysis of PEMFC Experimental Results
### Polarization Curve Analysis of Electric Stacks  
The established simulation model and control strategy are verified based on the completed 3 kW PEMFC. The variables that have the greatest influence on the output characteristics of PEMFC are gas volume, temperature, and pressure. The experimental data within a spectrum of operational conditions were collected to draw the fuel cell polarization curves and were compared with the simulation results. The parameters of the 3 kW water\(-\)cooled proton\(-\)exchange membrane power electric stack are detailed in Table 1.  
The 3 kW proton\(-\)exchange membrane electric stack parameters listed in Table 1 provide detailed hardware specifications and operating ranges for experiments and simulations. These parameters, including the power rating of the electric stack, current and voltage ranges, number of cells, ambient and operating temperatures, humidity, dimensions, weight, etc., are all critical factors that must be considered when designing and evaluating fuel cell systems. Through precise control and optimization of these parameters, the performance and reliability of the system can be improved, laying a solid foundation for the commercialization and application of hydrogen fuel cell technology. During the simulation and experiment, the working conditions are used as follows: the oxygen excess ratio is 2, the ambient temperature is kept at 27 \({}^{\circ}\)C, the working temperature of the stack is kept at 70 \({}^{\circ}\)C, the cathode-anode differential pressure of the stack is kept at 20 kPa (anode pressure is 0.17 MPa, cathode pressure is 0.15 MPa), the anode\(-\)side pressure is changed along with the size of the cathode\(-\)side pressure, and the loading current is in the range of 0\(-\)48 A. The stack's polarization profiles are represented in Figure 4.  
As can be obtained from Figure 4 in the low\(-\)current region, the experimental data points are not uniformly distributed on both sides of the simulated values due to the uneven temperature distribution of the electric stack during system starting, which leads to the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameters** & **Values** \\ \hline Rated power & 3 kW \\ Current range & 0\(-\)48 A \\ Voltage range & 42\(-\)84 VDC \\ Number of cells & 83 pieces \\ Optimal oxygen flow rate & 141.99 L/min \\ Optimal hydrogen flow & 45.05 L/min \\ Optimal coolant flow & 4.84 L/min \\ Environmental temperature & \(-\)20\(-\)55 \({}^{\circ}\)C \\ Environmental humidity & 20\(-\)100\% \\ Sizes & 324 \(\times\) 115 \(\times\) 83 mm \\ Weights & 12 kg \\ \hline \hline \end{tabular}
\end{table} 
Table 1: 3 kW electric stack parameters. uneven wetting of the membrane electrode; therefore, the internal resistance of the electric stack is larger at the place where the membrane wetting is low. In the intermediate\(-\)current region, the experimental data points are uniformly distributed on the simulation curves with small errors. In the region characterized by high\(-\)current density, the water generated by the normal operation of the system reaction cannot be discharged in time. The experimental data points are all lower than the simulation value. The overall experimental data points are slightly lower than the simulation results, the overall trend of the experimental data points is consistent with the polarization curves, and the model is in accordance with the operation of functioning fuel cell. By changing the stack temperature to 60 \({}^{\circ}\)C and 75 \({}^{\circ}\)C, the impact of the stack's temperature on output performance is investigated. The anode pressure of the stack is adjusted 20 kPa higher than the cathode pressure during the simulation and experiment. Figure 5 illustrates the effect of the stack's temperature on the output characteristics. Figure 5 illustrates how the battery's output voltage rises with the electric stack's temperature and how the experimental and simulated values converge more closely.