## 4 Results and Discussion
### Control Model Effectiveness  
Figure 9a compares the simulation and experimental results of coolant inlet and outlet temperature difference feedforward control. In the loading experiment, during the period 0-300 s, the stack operates in the low-current range with low heat generation, and the coolant inlet and outlet temperature difference is within 2 \({}^{\circ}\)C. During the period 300-500 s, the operating current gradually increases, the heat generation inside the stack increases, and the temperature difference reaches 5 \({}^{\circ}\)C. After 500 s, the temperature difference reaches 8 \({}^{\circ}\)C when the stack is loaded to a higher current, and the temperature difference is 5.8 \({}^{\circ}\)C on average. After applying the feedforward correction, although the temperature fluctuation makes the temperature difference slightly higher than 5 \({}^{\circ}\)C at some moments, the coolant inlet and outlet temperature difference is always kept within 5 \({}^{\circ}\)C, with an average temperature difference of 4.3 \({}^{\circ}\)C. Therefore, the model effectively fulfills the operational requirement.  
Figure 8: Artificial neural network validation results: (**a**) training data regression; (**b**) validation data regression; (**c**) mean square error; (**d**) test data regression; (**e**) all data regression; (**f**) error histogram with 20 bins.  
Figure 9: (**a**) Effect of coolant inlet and outlet temperature difference feedforward control; (**b**) effect of coolant inlet temperature control when load current changes; (**c**) effect of coolant inlet temperature control when preset temperature changes.  
In Figure 9b,c, the dynamic performance of the control model is simulated. In Figure 9b, the initial temperature of the stack is set to 60 \({}^{\circ}\)C, the target temperature is 65 \({}^{\circ}\)C, and the current is 300 A. At this time, the stack is in the heating stage, and the overshoot reaches 5.72% compared to that under traditional PID control. Applying the control model, no overshoot is found, and the temperature stabilizes at the set temperature much faster. After reaching the target temperature, the stack is in the heat dissipation stage, and a current loading in the 500 th second and a load shedding in the 1000 th second are set to test the dynamic performance. The temperature overshoot under the traditional PID control reaches 5.00%, the regulation time is 115 s, and many fluctuations in the temperature response curve indicate poor dynamic performance. The temperature can be stabilized at the set temperature quickly under the control model; the regulation time is only 30 s, and the overshoot is 2.60%. Accordingly, when the temperature rises and the load changes, the performance of the control model is significantly improved compared with the traditional PID control. It can be concluded that the control model has outstanding anti-disturbance and control capabilities for the load current changes in the experiment.  
The control model also has a reliable control effect on the perturbation from the set temperature changes. Dynamic simulation experiments are designed for the model, with the initial stack temperature of 60 \({}^{\circ}\)C, the target temperature of 65 \({}^{\circ}\)C, and the current of 300 A. After the operation is stabilized, the target temperature is increased to 68 \({}^{\circ}\)C in the 500 th second and decreased back to 65 \({}^{\circ}\)C in 1000 th second. The control effect is shown in Figure 9c. Respectively, 8% and 16.60% overshoots of the traditional PID control occur during the temperature increase and decrease. The response curve with the control model changes smoothly during two dynamic changes without overshoot, and the regulation time is shorter.