# Soft Fuzzy Reinforcement Neural Network Proportional-Derivative Controller
## 4 Results and Discussion
### Testing Performance Evaluation
#### 4.2.2 Case 2: CSTR System Training Performance Evaluation
From the analysis of the data in Table 5, it can be observed that the SFPD algorithm showed significant improvements in both the absence and presence of Gaussian noise interference. In the absence of noise, the SFPD algorithm showed substantial improvements in ISE across different sampling intervals when compared to the SAC algorithm, with percentage gains of 17.14%, 66.44%, 85.88%, 37.84%, and 65.14%. However, when compared to the traditional PD algorithm, the improvements were less pronounced, with percentage changes of \(-\)5.40%, 0%, \(-\)0.05%, \(-\)7.73%, and \(-\)0.84%, indicating some negative improvements in specific cases. When noise was introduced, the SFPD algorithm's performance in ISE remained strong relative to the SAC algorithm, achieving improvements of 41.88%, 68.93%, 93.46%, 73.15%, and 82.68%. Comparatively, the improvements over the traditional PD algorithm were more moderate, with percentage gains of 7.94%, 41.00%, 1.24%, 12.35%, and 21.06%. Similarly, the SFPD algorithm exhibited significant improvements in IAE. Without noise, the percentage improvements over the SAC algorithm were 64.06%, 83.48%, 92.58%, 84.77%, and 88.63%. Compared to the traditional PD algorithm, the gains were more modest, with percentage changes of 12.88%, 15.56%, 0.46%, 2.50%, and 2.40%. Under noisy conditions, the SFPD algorithm continued to outperform the SAC algorithm, with percentage improvements in IAE of 65.69%, 72.73%, 93.05%, 77.99%, and 87.94%. The enhancements over the traditional PD algorithm in this scenario were 32.04%, 48.44%, 33.12%, 42.45%, and 53.46%. Overall, the SFPD algorithm excelled in both ISE and IAE metrics, particularly in challenging conditions with noise interference. While the advantages of the SFPD algorithm over the traditional PD algorithm were less pronounced in some instances, it required no \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**SI**} & \multirow{2}{*}{**WGN**} & \multicolumn{2}{c}{**SFPD**} & \multicolumn{2}{c}{**SAC**} & \multicolumn{2}{c}{**Traditional PD**} \\ \cline{3-8}  & & **ISE** & **IAE** & **ISE** & **IAE** & **ISE** & **IAE** \\ \hline
0–100 s & No & 1757 & **115** & 2121 & 320 & **1667** & 132 \\  & Yes & **1746** & **140** & 3003 & 408 & 1896 & 206 \\ \hline
100–200 s & No & **252** & **38** & 751 & 230 & 252 & 45 \\  & Yes & **272** & **66** & 875 & 242 & 461 & 128 \\ \hline
200–500 s & No & 4351 & **218** & 30,832 & 2939 & **4349** & 219 \\  & Yes & **4539** & **309** & 69,403 & 4449 & 4596 & 462 \\ \hline
500–800 s & No & 1031 & **78** & 1659 & 512 & **957** & 80 \\  & Yes & **1043** & **189** & 3885 & 859 & 1190 & 329 \\ \hline
800–1200 s & No & 2644 & **122** & 7584 & 1074 & **2622** & 125 \\  & Yes & **2777** & **242** & 16,036 & 2008 & 3518 & 520 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Quantitative metrics of testing results on CSTR (Note: SI = sampling interval, WGN = with Gaussian noise). human intervention and demonstrated greater robustness. The SFPD algorithm consistently outperformed the SAC algorithm, making it a strong candidate for applications where robustness and stability are crucial.