## 4 Results and Discussion
### Expert System Adaptive Control Evaluation
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Phases**} & \multicolumn{5}{c}{**Absolute Error of the Residuals [mm]**} \\ \cline{2-6}  & **1** & **2** & **3** & **4** & **5** \\ \hline Cycle 3 (initial response) & 0.861 & 3.384 & 2.594 & 0.920 & 1.761 \\ Cycle 3 (improved response) & 0.069 & 0.207 & 0.112 & 0.096 & 0.043 \\ Cycle 4 (initial response) & 0.911 & 2.157 & 1.820 & 0.888 & 3.207 \\ Cycle 4 (improved response) & 0.043 & 0.074 & 0.080 & 0.082 & 0.051 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Absolute error of response error \(\Delta X_{\text{C}}\) in the new validation scenarios. Figure 12: Improvement of adaptive control mechanisms in the existing observation area. system is improved by 92.0% with the PR-MPC mechanism. The response error \(\Delta X_{C}\) in the case of the hydraulic press cycle 4 reduces from 0.911 mm (initial response) to 0.043 mm (improved response), showcasing a 95.3% improvement in response error \(\Delta X_{C}\). In the (2) fast forward movement and initial control system, hydraulic press cycle 3 exhibits an absolute response error \(\Delta X_{C}\) = 3.384 mm. Moreover, hydraulic press cycle 4 exhibits an absolute response error \(\Delta X_{C}\) = 2.157 mm. Furthermore, the PR-MPC mechanism integrated into the expert system improves the absolute response error \(\Delta X_{C}\) in the case of hydraulic press cycle 3 to \(\Delta X_{C}\) = 0.207 mm and in the case of hydraulic press cycle 4 to \(\Delta X_{C}\) = 0.074 mm, showcasing a 93.9% and 96.6% improvement in \(\Delta X_{C}\). This indicates a clear improvement in the performance of the hydraulic press in phase (3), showcasing the effectiveness of the advanced control system in minimizing errors. In the (3) bending phase, the response error \(\Delta X_{C}\) decreases from 2.594 mm to 0.112 mm, showcasing a 95.7% improvement in response error \(\Delta X_{C}\) in the case of hydraulic press cycle 3. Moreover, in hydraulic press cycle 4, the response error \(\Delta X_{C}\) decreases from 1.820 mm to 0.080 mm, showcasing a 96.7% improvement in response error \(\Delta X_{C}\). In the (4) leveling phase, the initial error in hydraulic press cycle 1 is improved by 89.6% from an initial value 0.920 mm to a reduced absolute value 0.096 mm after the improved control is applied. For hydraulic press cycle 4, the response error \(\Delta X_{C}\) decreases from 0.888 mm to 0.082 mm, resulting in a 92.9% improvement in the response error \(\Delta X_{C}\). These improvements further confirm the ability of the advanced control system to reduce residual errors effectively across three operational phases. In the (5) fast backward movement of the hydraulic press cycle 3, the initial absolute response error \(\Delta X_{C}\) is 1.761 mm and is reduced to an improved absolute response error \(\Delta X_{C}\) of 0.043 mm. The hydraulic press cycle 4 absolute response error \(\Delta X_{C}\) is decreased from 3.207 mm to 0.051 mm, which is a 98.4% improvement. In conclusion, Table 6 clearly illustrates the positive impact of the improved response on reducing the absolute response error \(\Delta X_{C}\) for all validation scenarios. The most significant reductions are observed in the (1) holding, (2) fast forward movement, and (3) bending phases, underscoring the substantial effectiveness of the PR-MPC mechanism in enhancing the precision of the hydraulic press. These improvements demonstrate the control system's capability to adapt and significantly optimize performance in diverse operational environments.