## 4 Simulation and Discussion  
Numerical simulation and experimental tests are carried out on PEMFC power supply for the proposed controllers and observers under the given test conditions listed in Table 2.  
H-100 PEMFC with 100 W rate power is selected to feed DC/DC buck converter to configure the power supply, and \(L_{0}\) = 470 uH and \(C_{0}\) = 1000 uF are the nominal values of the converter. The test conditions are mainly used for checking the transient response and the tracking performance as well as the robustness against uncertainties and disturbances. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Test Conditions**} & \multicolumn{2}{c}{**Parameters with Time**} \\ \cline{2-3}  & **Setpoints** & **Load Resistor** \\ \hline Condition 1: current transient response & \(i_{L,ref}\) = 4 A & \(R\) = 3 \(\Omega\) \\ Condition 2: step response for different current & \(i_{L,ref}\) = 2 A @ [4,6] s; \(i_{L,ref}\) = 4 A at & \(R\) = 3 \(\Omega\) \\  & other time & \(R\) = 3 \(\Omega\) \\ Condition 3: step response for different voltage & \(v_{o,ref}\) = 8 V @ [4,6] s; \(v_{o,ref}\) = 12 V at & \(R\) = 3 \(\Omega\) \\ Condition 4: disturbance injection in current control & \(i_{L,ref}\) = 4 A & \(R\) = 0.5 \(\Omega\) @ [0.88, 2.2] s; \(R\) = 2 \(\Omega\) at \\  & other time & other time \\ Condition 5: disturbance injection in voltage control & \(v_{o,ref}\) = 12 V & \(R\) = 3 \(\Omega\) @ [1.6, 2.8] s; \(R\) = 5 \(\Omega\) at \\  & other time & other time \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of the test conditions. The results of different control techniques in Condition 1 are shown in Figure 3. The simulation analysis results show that the response time of the output current controlled by backstepping SMC (BSMC) is the fastest, but the overshoot of the output current is obvious. The response time of the output current controlled by SMC is 0.014 s, which is similar to the control result of adaptive backstepping SMC (ABSMC). Compared with RBF control performance, it is 0.011 s slower. In addition, from the response stage, the current controlled by the SMC has an obvious oscillation phenomenon. Regardless of whether it is considered from the protection of the life of the fuel cell or the utilization of electric energy on the output side, this phenomenon will have an adverse effect. In contrast, the output current response stage of ABSMC and RBF control is relatively smooth. At the same time, the RBF adaptive controller has the advantages of faster response speed, no overshoot, no overshoot phenomenon in the output voltage, and the fuel cell current/voltage overshoot range is within an acceptable range. Moreover, by exploring the sliding manifolds and the associate trajectories in the phase plane displayed in Figure 4a,b, the typical reaching behaviors of the designed controllers were manifested, and the RBFNN presented a high convergence precision. In Condition 2, the tracking setpoints were abruptly changed at the constant load condition. The load was rapidly changing from 4 A to 2 A at 4 s and 2 A to 4 A at 6 s. The current controlled by the SMC and ABSMC has an obvious oscillation phenomenon. The controller with RBFNN indicates the best performance (see Figure 5), where the settling time in current tracking control is 0.002 s and 0.005 s in output voltage tracking control. In Condition 3 and 4, the tracking setpoints were abruptly changed at the constant load condition, the controller with RBFNN indicates the best performance (see Figures 6 and 7), where the settling time in current tracking control is 0.002 s and 0.006 s in output voltage tracking  
Figure 4: Current control transient response: (a) sliding manifold S; (b) S vs. dS/dt. Figure 3: Simulation results in Condition 1: (a) by different control methods; (b) PEMFC current and voltage response when regulated by RBFNN. control, without overshoot and undershoot.