## 5 Results
### Experimental Results  
Real-time experiments were performed on the ARM STM32F4 xx system with a digital signal processing unit and internal clock of 167 MHz. The angle and velocity of the system are measured with a rotary encoder with 3200 positions per revolution. The sampling time of the controller is the same as in the simulation experiment. For the aim of the comparison and validation of the proposed algorithm, the input disturbance \(d_{sim}\) is generated at the output of the BSTA controller. The span of the disturbance \(d_{sim}\) is selected in such a manner that the requirements of STA stability are fulfilled. For experimental testing, the disturbance is selected as \(d_{sim}=1.2\), which is 10% of the allowed input voltage. The real-time experiment structure with generated disturbance \(d_{sim}\) is depicted in Figure 6.  
Figure 7 presents the real-time experiment of the positioning system with the STA controller. Figure 6: Real-time experiment structure with disturbance. Figure 7: System response with the STA algorithm. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(RMS_{\varphi}\) & \(RMS_{\sigma}\) & \(RMS_{n}\) \\ \hline STA & 95.87 & 3.411 & 0.902 \\ BSTA & 95.71 & 3.45 & 0.41 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The root mean square (RMS) values of the variables \(\varphi\), \(\sigma\), \(u\). Figure 8 shows the results of the closed-loop system with the BSTA algorithm. Figure 9 presents the value of the \(\widetilde{K}_{\text{BF}}(\sigma)\) function and a closer view of the sliding variable with the BF adaptation boundary. Figure 10 presents the comparison between STA and BSTA, with real-time experiments' data. Figure 8: System response with the BSTA algorithm. Figure 9: Barrier function value and adaptation boundary of the BSTA coefficients. The RMS values Equation (29) of the variables calculated from the real-time experiment are given in Table 4.  
The tracking capability of the BSTA compared to the STA remained unchanged, which can be confirmed by the \(RMS_{\varphi}\) value in Table 4. It can be noticed that the controller output value is notably reduced, and the \(RMS_{u}\) value of BSTA is remarkably smaller. After the tracking capability test, the disturbance suppression ability needs to be inspected. For the real-time experiment, the input disturbance is added to the system. For the given disturbance experiment, the input disturbance amount is 34% of the whole controller output span, and the stepwise function was used. Figure 11 shows the STA's capability of disturbance suppression. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & \(RMS_{\varphi}\) & \(RMS_{\sigma}\) & \(RMS_{u}\) \\ \hline STA & 221.27 & 344.1 & 4.56 \\ BSTA & 221.21 & 341.2 & 3.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The RMS values of the real-time experiment of the variables \(\varphi\), \(\sigma\), \(u\). Figure 10: Barrier function value and adaptation boundary of the BSTA coefficients. Figure 12 presents the reaction of the BSTA with disturbance. Figure 13 shows the values of the \(\widetilde{K}_{\text{BF}}(\sigma)\) function and closer view of the adaptation boundaries. Figure 11: Disturbance rejection of the STA controller. Figure 12: Disturbance rejection of the BSTA controller. Figure 14 presents the comparison between the STA and BSTA algorithms with disturbance. Figure 15 shows a closer view of the section where disturbance was present. Figure 14: Comparison of the STA and BSTA with disturbance. Figure 13: Barrier function value and adaptation boundary of the BSTA coefficients with disturbance. Figure 15: Closer view of the disturbance rejection capability of the STA and BSTA algorithms. RMS values for the disturbance rejection capability are presented in Table 5.  
From the simulation results in Figure 5; Figure 6, it can be concluded that the BSTA algorithm outperforms the standard STA. There is a significant difference in chattering phenomena alleviation.