## 4 Experiment Verification  
The efficacy, dependability, and practical feasibility of the innovative control strategy for the APF system are validated through experimental implementation. The following provides an overview of the hardware experiment, including comparative results. The practical feasibility of the IT2 FNN-SFR STSMC is validated using a real-time experimental apparatus for single-phase APF, which is based on the DSPACE DS1104. The parameter of the hardware experiment is given in Table 1, where the sampling period is \(T_{s}=50\) us. The real-time experimental apparatus is depicted in Figure 4. It can be seen that the implement is composed of an APF circuit module, an AC power supply module, a DC power supply module, a DSPACE control module, and an oscilloscope. As depicted, the APF main circuit, shown in Figure 5, encompasses components such as the IGBT driver, IGBTs, DC capacitor, nonlinear load, additional nonlinear load, and a signal acquisition circuit. The DC power is used to power the IGBT drive. Experimental waveforms and spectrum analyses of the power supply current are captured using the Agilent DSO-X3034A oscilloscope (Keysight Technologies, Santa Rosa, CA, USA). The necessary current and voltage signals are gathered by sensors, and these measured signals are subsequently transmitted to the controller via the A/D converter. The IGBT receives the Pulse Width Modulation (PWM) signal computed by the controller to produce the compensation current. \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameters** & **Values** \\ \hline Supply voltage & 24 V/50 Hz \\ \hline APF main circuit & \(L_{c}=18\) mH, \(R_{c}=0.1\)\(\Omega\), \\  & \(C_{0}=2200\) uF, \(U_{dc}^{*}=50\) V \\ \hline Nonlinear load at steady state & \(R_{1}=5\)\(\Omega\), \(R_{2}=15\)\(\Omega\), \(C_{1}=1000\) uF \\ \hline Additional nonlinear load in parallel & \(R_{1}=15\)\(\Omega\), \(R_{2}=15\)\(\Omega\), \(C_{2}=1000\) uF \\ \hline Sampling time & \(T_{s}=50\) us \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters in experiment. As shown in Figure 6, the signal waveform curves obtained from the oscilloscope under different methods during stable operation are depicted. The four curves from top to bottom represent the AC power voltage, load current, harmonic compensation current, and AC current, respectively. When the APF is not operational (as shown in Figure 6a), the compensation current is 0 A, indicating severe distortion in the current waveform. Under the influence of different control algorithms (the designed IT2 FNN-SFR STSMC, adaptive sliding mode control (ASMC), and traditional super-twisting sliding mode control (STSMC)), compensation of the supply current can be achieved, transforming the distorted waveform into an approximately sinusoidal shape. To further intuitively compare the compensation performance differences among the various methods, a frequency spectrum analysis of the power current is conducted, and the total harmonic distortion (THD) of the supply current under each control method is calculated (results are shown in Figure 7). The results indicate that the harmonic components in the power current are significantly suppressed under the control algorithms. Specifically, the THD corresponding to the control algorithm designed in this paper is improved by 1.24% and 0.55% compared to ASMC and STSMC, respectively, which is below the international standard of 5%. Figure 6: Curves of power supply voltage, load current, compensation current, and power supply current measured at steady state under different methods: (**a**) no compensation algorithm is applied; (**b**) IT2 FNN-SFR STSMC algorithm; (**c**) ASMC algorithm; (**d**) traditional STSMC algorithm. Figure 7: Comparison of THD at steady state under different methods: (**a**) no compensation algorithm is applied; (**b**) IT2 FNN-SFR STSMC algorithm; (**c**) ASMC algorithm; (**d**) traditional STSMC algorithm. In practice, as the electrical equipment changes, so will the load.